{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Smoothing\n", "\n", "<img src=\"media/cover.png\" style=\"width: 40%; display: block; margin: auto;\">" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Introduction\n", "\n", "In the previous lectures, we learned that:\n", "- A time series consists of measurements characterized by temporal dependencies.\n", "- The measurements are (usually) collected at equally-spaced intervals.\n", "- A time series can be decomposed into trend, seasonality, and residuals.\n", "- Many time series models require the data to be stationary in order to make forecasts. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- In this lecture, we will build upon that knowledge and explore another important concept called **smoothing**.\n", "- In particular, we will cover:\n", " 1. An introduction to smoothing and why it is necessary.\n", " 2. Common smoothing techniques.\n", " 3. How to smooth time series data with Python and generate forecasts." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import sys\n", "\n", "# Install dependencies if the notebook is running in Colab\n", "if 'google.colab' in sys.modules:\n", " !pip install -U -qq tsa-course" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "skip" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "# Imports\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import requests\n", "from io import BytesIO\n", "from tsa_course.lecture2 import run_sequence_plot\n", "np.random.seed(0) # reproducibility" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "- A data collection process is often affected by noise. \n", "- If too strong, the noise can conceal useful patterns in the data. \n", "- Smoothing is a well-known and often-used technique to recover those patterns by *filtering out noise*.\n", "- It can also be used to *make forecasts* by projecting the recovered patterns into the future." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We will explore two important techniques to do smoothing:\n", " 1. Simple smoothing.\n", " 2. Exponential smoothing." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- We start by generating some stationary data.\n", "- We discussed the importance of visually inspecting the time series with a run-sequence plot. \n", "- So, we will also define the `run_sequence_plot` function to visualize our data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "# Generate stationary data\n", "time = np.arange(100)\n", "stationary = np.random.normal(loc=0, scale=1.0, size=len(time))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_sequence_plot(time, stationary, title=\"Stationary time series\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "source": [ "\n", "---" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Simple smoothing techniques" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- There are many techniques for smoothing data. \n", "- The most simple ones are:\n", " 1. Simple average\n", " 2. Moving average\n", " 3. Weighted moving average" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Simple average\n", "\n", "- Simple average is the most basic technique. \n", "- Consider the stationary data above.\n", "- The most conservative way to represent it is through its **mean**.\n", "- The mean can be used to predict the future values of the time series.\n", "- This type of representation is called *simple average*." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "# find mean of series\n", "stationary_time_series_avg = np.mean(stationary)\n", "\n", "# create array composed of mean value and equal to length of time array\n", "sts_avg = np.full(shape=len(time), fill_value=stationary_time_series_avg, dtype='float')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = run_sequence_plot(time, stationary, title=\"Stationary Data\")\n", "ax.plot(time, sts_avg, 'tab:red', label=\"mean\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Mean squared error (MSE)\n", "\n", "- The approximation with the mean seems reasonable in this case.\n", "- In general we want to measure how far off our estimate is from reality. \n", "- A common way of doing it is by calculating the *Mean Squared Error* (MSE) \n", "\n", "$$MSE = \\frac{1}{T}\\sum_{t=1}^{T} (X(t) - \\hat{X}(t))^2$$\n", "\n", "- where $X(t)$ and $\\hat{X}(t)$ are the true and estimated values at time $t$, respectively. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Example**\n", "\n", "- Let's consider the following example.\n", "- Say we have a time series of observed values $X = [0, 1, 3, 2]$.\n", "- The predictions given by our model are $\\hat{X} = [1, 1, 2, 4]$. \n", "- We calculate the MSE as: \n", "\n", "$$\\frac{(0-1)^{2} + (1-1)^{2} + (3-2)^{2} + (2-4)^{2}}{4} = 1.5$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "- Say we had another model that give us the estimate $\\hat{X} = [0, 0, 1, 0]$.\n", "- The MSE in this case is: \n", "\n", "$$\\frac{0^{2} + 1^{2} + 2^{2} + 2^{2}}{4} = 2.25$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- The MSE allows to compare different estimates to see which is best. \n", "- In this case, the first model gives us a better estimate than the second one. \n", "- This idea of measuring how a model performs is important in machine learning and we will use it often in this course.\n", "- Let's create a function to calculate MSE that we will use as we go forward." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "def mse(observations, estimates):\n", " \"\"\"\n", " INPUT:\n", " observations - numpy array of values indicating observed values\n", " estimates - numpy array of values indicating an estimate of values\n", " OUTPUT:\n", " Mean Square Error value\n", " \"\"\"\n", " # check arg types\n", " assert type(observations) == type(np.array([])), \"'observations' must be a numpy array\"\n", " assert type(estimates) == type(np.array([])), \"'estimates' must be a numpy array\"\n", " # check length of arrays equal\n", " assert len(observations) == len(estimates), \"Arrays must be of equal length\"\n", " \n", " # calculations\n", " difference = observations - estimates\n", " sq_diff = difference ** 2\n", " mse = np.mean(sq_diff)\n", " \n", " return mse" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let's test the ``mse`` function." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.5\n" ] } ], "source": [ "zeros = mse(np.array([0, 1, 3, 2]), np.array([1, 1, 2, 4]))\n", "print(zeros)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.25\n" ] } ], "source": [ "ones = mse(np.array([0, 1, 3, 2]), np.array([0, 0, 1, 0]))\n", "print(ones)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Next, we add a *trend* to our stationary time series." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trend = (time * 2.0) + stationary\n", "run_sequence_plot(time, trend, title=\"Time series with trend\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Suppose we use again the simple average to represent the time series." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# find mean of series\n", "trend_time_series_avg = np.mean(trend)\n", "\n", "# create array of mean value equal to length of time array\n", "avg_trend = np.full(shape=len(time), fill_value=trend_time_series_avg, dtype='float')\n", "\n", "run_sequence_plot(time, trend, title=\"Time series with trend\")\n", "plt.plot(time, avg_trend, 'tab:red', label=\"mean\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Clearly, the simple average does not work well in this case.\n", "- We must find other ways to capture the underlying pattern in the data. \n", "- We start with something called a *moving average*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Moving Average (MA)\n", "\n", "- Moving average has a greater sensitivity than the simple average to local changes in the data.\n", "- The easiest way to understand moving average is by example. \n", "- Say we have the following values:\n", "\n", "<img src=\"media/values.png\" style=\"width: 30%; display: block; margin: auto;\">" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- The first step is to select a window size. \n", "- We'll arbitrarily choose a size of 3. \n", "- Then, we start computing the average for the first three values and store the result. \n", "- We then slide the window by one and calculate the average of the next three values. \n", "- We repeat this process until we reach the final observed value. \n", "\n", "<img src=\"media/EqWMA.gif\" style=\"width: 40%; display: block; margin: auto;\">" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Now, let's define a function to perform smoothing with the MA.\n", "- Then, we compare the MSE obtained from applying simple and moving average on the data with trend. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [], "source": [ "def moving_average(observations, window=3, forecast=False):\n", " cumulative_sum = np.cumsum(observations, dtype=float)\n", " cumulative_sum[window:] = cumulative_sum[window:] - cumulative_sum[:-window]\n", " ma = cumulative_sum[window - 1:] / window\n", " if forecast:\n", " observations = np.append(observations, np.nan)\n", " ma_forecast = np.insert(ma, 0, np.nan*np.ones(window))\n", " return observations, ma_forecast\n", " else:\n", " return ma" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE:\n", "--------\n", "simple average: 3324.01\n", "moving_average: 4.57\n" ] } ], "source": [ "MA_trend = moving_average(trend, window=3)\n", "\n", "print(f\"MSE:\\n--------\\nsimple average: {mse(trend, avg_trend):.2f}\\nmoving_average: {mse(trend[2:], MA_trend):.2f}\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Clearly, the MA manages to pick up much better the trend data.\n", "- We can also plot the result against the actual time series." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_sequence_plot(time, trend, title=\"Time series with trend\")\n", "plt.plot(time[1:-1], MA_trend, 'tab:red', label=\"MA\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Note that the output of the MA is shorter than the original data.\n", "- The reason is that the moving window is not centered on the first and last elements of the time series.\n", "- Given a window of size $P$, the MA will be $P-1$ steps shorter than the original time series." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "12\n" ] } ], "source": [ "x = np.arange(20)\n", "print(len(moving_average(x, window=9)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Now, we try the MA on a periodic time series, which could represent a seasonality." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "run_control": { "marked": false }, "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [], "source": [ "seasonality = 10 + np.sin(time) * 10 + stationary\n", "MA_seasonality = moving_average(seasonality, window=3)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_sequence_plot(time, seasonality, title=\"Seasonality\")\n", "plt.plot(time[1:-1], MA_seasonality, 'tab:red', label=\"MA\")\n", "plt.legend(loc='upper left');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "- It's not perfect but clearly picks up the periodic pattern.\n", "- Lastly, let's see how MA handles trend, seasonality, and a bit of noise." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "trend_seasonality = trend + seasonality + stationary\n", "MA_trend_seasonality = moving_average(trend_seasonality, window=3)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_sequence_plot(time, trend_seasonality, title=\"Trend, seasonality, and noise\")\n", "plt.plot(time[1:-1], MA_trend_seasonality, 'tab:red', label=\"MA\")\n", "plt.legend(loc='upper left');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- This method is picking up key patterns in these toy datasets. \n", "- However, it has several limitations." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "1. MA assigns equal importance to all values in the window, regardless of their chronological order. \n", " - For this reason it fails in capturing the often more relevant recent trends." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "2. MA requires the selection of a specific window size, which can be arbitrary and may not suit all types of data. \n", " - a small window may lead to noise\n", " - a too large window could oversmooth the data, missing important short-term fluctuations." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "3. MA does not adjust for changes in trend or seasonality. \n", " - This can lead to inaccurate predictions, especially when these components are nonlinear and time-dependent." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "### Weighted moving average (WMA)\n", "\n", "- WMA weights recent observations more than more distant ones. \n", "- This makes intuitive sense. \n", " - Think of the stock market: it has been observed that today's price is a good predictor of tomorrow's price. \n", "- By applying unequal weights to past observations, we can control how much each affects the future forecast. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- There are many ways to set the weights.\n", "- For example, we could define them with the following system of equations: \n", "\n", "$$\n", "\\begin{cases}\n", "& w_1 + w_2 + w_3 = 1\\\\ \n", "& w_2 = (w_1)^2 \\\\ \n", "& w_3 = (w_1)^3\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- This gives the following weights:\n", " \n", "$$\n", "\\begin{aligned}\n", "& w_1 \\approx 0.543 & \\text{weights associated to $t-1$}\\\\ \n", "& w_2 \\approx 0.294 & \\text{weights associated to $t-2$} \\\\ \n", "& w_3 \\approx 0.16 & \\text{weights associated to $t-3$}\n", "\\end{aligned}\n", "$$\n", "\n", "<img src=\"media/ExpWMA.gif\" style=\"width: 40%; display: block; margin: auto;\">" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "**📝Note**\n", "\n", "- There are numerous methods to find the optimal weighting scheme based on the data and the task at hand. \n", "- A full discussion is beyond the scope of the lecture. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "### Forecasting with MA\n", "\n", "- Instead of pulling out the inherent pattern within a series, the smoothing functions can be used to create *forecasts*. \n", "- The forecast for the next time step is computed as follows:\n", "\n", "$$\\hat{X}(t+1) = \\frac{X(t) + X(t-1) + \\dots + X(t-P+1)}{P}$$ \n", "\n", "- where $P$ is the window size of the MA." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Let's consider the following time series $X= [1, 2, 4, 8, 16, 32, 64]$. \n", "- In particular, we apply the smoothing process and use the resulting value as forecast for the next time step.\n", "- With the MA technique and a window size $P=3$ we get the following forecast." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [], "source": [ "x = np.array([1, 2, 4, 8, 16, 32, 64])\n", "ma_x, ma_forecast = moving_average(x, window=3, forecast=True)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(len(ma_x))\n", "run_sequence_plot(t[:-4], ma_x[:-4], title=\"Nonlinear data\")\n", "plt.plot(t[-5:], ma_x[-5:], 'k', label=\"True values\", linestyle='--')\n", "plt.plot(t, ma_forecast, 'tab:red', label=\"MA forecast\", linestyle='--')\n", "plt.legend(loc='upper left');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The result shows that MA is lagging behind the actual signal.\n", "- In this case, it is not able to keep up with changes in the trend.\n", "- The lag of MA is also reflected in the forecasts it produces." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Let's focus on the [forecasting formula](#forecasting-with-ma) we just defined. \n", "- While easy to understand, one of its properties may not be obvious.\n", "- What's the lag associated with this technique? \n", "- In other words, after how many time steps do we see a local change in the underlying signal?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The answer is: $\\frac{(P+1)}{2}$. \n", "- For example, say you're averaging the past 5 values to make the next prediction.\n", "- Then the forecast value that most closely reflects the current value will appear after $\\frac{5+1}{2} = 3$ time steps.\n", "- Clearly, the lag increases as you increase the window size for averaging. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- One might reduce the window size to obtain a more responsive model. \n", "- However, a window size that's too small will chase noise in the data as opposed to extracting the pattern. \n", "- There is a tradeoff between *responsiveness* and *robustness to noise*. \n", "- The best answer lies somewhere in between and requires careful tuning to determine which setup is best for a given dataset and problem at hand. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Let's make a practical example to show this tradeoff.\n", "- We will generate some toy data and apply a MA with different window sizes. \n", "- To make things more clear, we generate again data with trend and seasonality, but we add more noise." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "noisy_noise = np.random.normal(loc=0, scale=8.0, size=len(time))\n", "noisy_trend = time * 2.75\n", "noisy_seasonality = 10 + np.sin(time * 0.25) * 20\n", "noisy_data = noisy_trend + noisy_seasonality + noisy_noise\n", "\n", "run_sequence_plot(time, noisy_data, title=\"Noisy data\");" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# Compute MA with different window sizes\n", "lag_2 = moving_average(noisy_data, window=3)\n", "lag_3 = moving_average(noisy_data, window=5)\n", "lag_5 = moving_average(noisy_data, window=9)\n", "lag_10 = moving_average(noisy_data, window=19)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1100x600 with 4 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, axes = plt.subplots(2,2, figsize=(11,6))\n", "axes[0,0] = run_sequence_plot(time, noisy_data, title=\"MA with lag 2\", ax=axes[0,0])\n", "axes[0,0].plot(time[1:-1], lag_2, color='tab:blue', linewidth=2.5)\n", "axes[0,1] = run_sequence_plot(time, noisy_data, title=\"MA with lag 3\", ax=axes[0,1])\n", "axes[0,1].plot(time[2:-2], lag_3, color='tab:orange', linewidth=2.5)\n", "axes[1,0] = run_sequence_plot(time, noisy_data, title=\"MA with lag 5\", ax=axes[1,0])\n", "axes[1,0].plot(time[4:-4], lag_5, color='tab:green', linewidth=2.5)\n", "axes[1,1] = run_sequence_plot(time, noisy_data, title=\"MA with lag 10\", ax=axes[1,1])\n", "axes[1,1].plot(time[9:-9], lag_10, color='tab:red', linewidth=2.5)\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Clearly, the larger the window size the smoother the data.\n", "- This allows to get rid of the noise but, eventually, also the underlying signal is smoothed out. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Forecasting with WMA\n", "\n", "- Next, we use the WMA to generate forecasts.\n", "- The previous [forecasting formula](#forecasting-with-ma) is modified to weight differently the past observations in the window:\n", "\n", "$$\\hat{X}(t+1) = \\frac{w_1 \\cdot X(t) + w_2 \\cdot X(t-1) + \\dots + w_P \\cdot X(t-P+1)}{P}$$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def weighted_moving_average(observations, weights, forecast=False):\n", " \n", " if len(weights) != len(observations[0:len(weights)]):\n", " raise ValueError(\"Length of weights must match the window size\")\n", " \n", " # Normalize weights\n", " weights = np.array(weights) / np.sum(weights)\n", " \n", " # Initialize the result array\n", " result = np.empty(len(observations)-len(weights)//2)\n", " result[:] = np.nan\n", " \n", " # Calculate weighted moving average\n", " for i in range(len(weights)//2, len(result)):\n", " window = observations[i-(len(weights)//2):i+len(weights)//2+1]\n", " result[i] = np.dot(window, weights)\n", " \n", " # Handle forecast option\n", " if forecast:\n", " result = np.insert(result, 0, np.nan*np.ones(len(weights)//2+1))\n", " observations = np.append(observations, np.nan*np.ones(len(weights)//2))\n", " return observations, result\n", " else:\n", " return result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- We repeat the experiment on the same time series $X= [1, 2, 4, 8, 16, 32, 64]$. \n", "- We will use the set of weights that we defined before, `[0.160, 0.294, 0.543]`." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "weights = np.array([0.160, 0.294, 0.543])\n", "wma_x, wma_forecast = weighted_moving_average(x, weights, forecast=True)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.arange(len(wma_x))\n", "run_sequence_plot(t[:-4], ma_x[:-4], title=\"Nonlinear data\")\n", "plt.plot(t[-5:], ma_x[-5:], 'k', label=\"True values\", linestyle='--')\n", "plt.plot(t, ma_forecast, 'tab:red', label=\"MA forecast\", linestyle='--')\n", "plt.plot(t, wma_forecast, 'tab:blue', label=\"WMA forecast\", linestyle='--')\n", "plt.legend(loc='upper left');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- WMA solves some issues of MA.\n", " - It is more sensitive to local changes.\n", " - Is more flexible, as it can adjust the importance of different time steps.\n", " - It does not require a fixed window size as it applies an exponentially decreasing weight to all past observations.\n", "- However it still struggle in keeping pace with nonlinear and fast-changing trends... There's a significant lag.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exponential Smoothing\n", "\n", "There are three key exponential smoothing techniques:\n", "\n", "|Type | Capture trend | Capture seasonality|\n", "|:----:|:---------------:|:--------------------:|\n", "|Single Exponential Smoothing | ❌ | ❌ |\n", "|Double Exponential Smoothing | ✅ | ❌ |\n", "|Triple Exponential Smoothing | ✅ | ✅ |" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Single exponential smoothing\n", "\n", "- 💡 Useful if your data lacks trend and seasonality and you want to approximately extract patterns. \n", "- It is analogous to the WMA we saw previously.\n", "- The basic formulation is:\n", "\n", "$$S(t) = \\alpha X(t) + (1-\\alpha)S(t-1)$$ \n", "\n", "- where:\n", " - $S(t)$ is the smoothed value at time *t*,\n", " - $\\alpha$ is a smoothing constant,\n", " - $X(t)$ is the value of the series at time *t*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Expanding the formula we get:\n", "\n", "$$\n", "\\begin{aligned} \n", "S(0) &= \\alpha X(0) \\\\ S(1) &= \\alpha X(1) + (1 - \\alpha)S(0) = \\alpha X(1) + \\alpha(1 - \\alpha)X(0) \\\\\n", "S(2) & = \\alpha X(2) + (1 - \\alpha)S(1) = \\alpha X(2) + (1 - \\alpha)[\\alpha X(1) + \\alpha(1 - \\alpha)X(0)]\\\\\n", "& = \\alpha X(2) + \\alpha(1 - \\alpha)X(1) + \\alpha(1 - \\alpha)^2 X(0) \n", "\\end{aligned}\n", "$$\n", "\n", "The formula for a generic time step $\\tau$ is:\n", "\n", "$$ S(\\tau) = \\sum_{t=0}^{\\tau} \\alpha(1 - \\alpha)^{\\tau-t}X(t) $$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "#### Initialization\n", "\n", "- There are many initialization strategies. \n", "- A simple one is to set $S(0) = X(0)$. \n", "- Another strategy is to find the mean of the first couple of observations, e.g., $S(0) = \\frac{X(0) + X(1) + X(2)}{3}$. \n", "- Once you've initialized it, you can use the update rule above to calculate all values. \n", "- In practice, we don't perform this process by hand, but we use the functions in ``statsmodels``. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "#### Setting $\\alpha$\n", "- Choosing the optimal value for $\\alpha$ is also done by ``statsmodels``. \n", "- A solver uses a metric like MSE to find the optimal $\\alpha$. \n", "- Even if we do not choose the value manually, is good to have a basic idea of what's happening under the hood." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "### Double exponential smoothing\n", "\n", "- 💡 It has all the benefits of Single Exponential plus the ability to pickup on trend. \n", "\n", "$$\n", "\\begin{aligned} \n", "S(t) = \\alpha X(t) + (1-\\alpha) \\big(S(t-1) + b(t-1)\\big) & \\hspace{2cm} \\text{Smoothed values of the series} \\\\\n", "b(t) = \\beta\\big(S(t) - S(t-1)\\big) + (1 - \\beta)b(t-1) & \\hspace{2cm} \\text{Estimated trend} \\\\ \n", "\\hat{X}(t+1) = S(t) + b(t) & \\hspace{2cm} \\text{Forecasts} \n", "\\end{aligned}\n", "$$\n", "\n", "- The parameter $\\beta \\in [0,1]$ controls the decay of the influence of change in the trend." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Initialization**\n", "\n", "- $S(0) = X(0)$.\n", "- $b(0) = X(1) - X(0)$.\n", "- Other initializations are also possible.\n", "\n", "**Forecasts beyond 1-step ahead**\n", "- $\\hat{X}(t+\\tau) = S(t) + \\tau b(t)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "### Triple exponential smoothing\n", "\n", "- 💡 It has all the benefits of Double Exponential with the ability to also model the seasonality.\n", "- It does this by adding a third component that smooths out seasonality of length $L$.\n", "- There are two variants in the model:\n", " - additive seasonality,\n", " - multiplicative seasonality." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Additive seasonality model**\n", "\n", "- This method is preferred when the seasonal variations are roughly constant through the series.\n", "\n", "$$\n", "\\begin{aligned} \n", "S(t) = \\alpha \\big(X(t) - c(t-L)\\big) + (1-\\alpha) \\big(S(t-1) + b(t-1)\\big) & \\hspace{2cm} \\text{Smoothed values} \\\\\n", "b(t) = \\beta\\big(S(t) - S(t-1)\\big) + (1 - \\beta)b(t-1) & \\hspace{2cm} \\text{Estimated trend} \\\\ \n", "c(t) = \\gamma \\big(X(t) - S(t-1) - b(t-1)\\big) + (1-\\gamma)c(t-L) & \\hspace{2cm} \\text{Seasonal correction} \\\\ \n", "\\hat{X}(t+\\tau) = S(t) + \\tau b(t) + c(t-L + 1 + (\\tau - 1)\\text{mod}(L)) & \\hspace{2cm} \\text{Forecasts} \n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Multiplicative seasonality model**\n", "\n", "- This method is preferred when the seasonal variations are changing proportional to the level of the series.\n", "\n", "$$\n", "\\begin{aligned} \n", "S(t) = \\alpha \\frac{X(t)}{c(t-L)} + (1-\\alpha) \\big(S(t-1) + b(t-1)\\big) & \\hspace{2cm} \\text{Smoothed values} \\\\\n", "b(t) = \\beta \\big(S(t) - S(t-1)\\big) + (1 - \\beta)b(t-1) & \\hspace{2cm} \\text{Estimated trend} \\\\ \n", "c(t) = \\gamma \\left( \\frac{X(t)}{S(t)} \\right) + (1-\\gamma)c(t-L) & \\hspace{2cm} \\text{Seasonal correction} \\\\ \n", "\\hat{X}(t+\\tau) = \\big( S(t) + \\tau b(t) \\big)c(t-L + 1 + (\\tau - 1)\\text{mod}(L)) & \\hspace{2cm} \\text{Forecasts} \n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "**Initialization**\n", "\n", "- $b(0) = \\frac{1}{L} \\left( \\frac{X(L+1) - X(1)}{L} + \\frac{X(L+2) - X(2)}{L} + \\dots + \\frac{X(L+L) - X(L)}{L} \\right)$\n", "- $c(t) = \\frac{1}{N} \\sum_{j=1}^N \\frac{X(L(j-1)+t)}{A_j}$ for $t=1,2,\\dots,L$, where $N$ is the total number of seasonal cycles in the data and $A_j = \\frac{\\sum_{t=1}^L X(2(j-1)+t)}{L}$\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exponential smoothing in Python" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Let's now see how to perform smoothing in Python. \n", "- As we've done in the past, we'll leverage ``statsmodels`` to do the heavy lifting for us. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "- We'll use the same time series with trend and seasionality to compare simple average, single, double, and triple exponential smoothing. \n", "- We will holdout the last 5 samples from the dataset (i.e., they become the *test set*).\n", "- We will compare the predictions made by the models with these values." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "# Train/test split\n", "train = trend_seasonality[:-5]\n", "test = trend_seasonality[-5:]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Simple Average\n", "\n", "- This is a very crude model to say the least.\n", "- It can at least be used as a baseline. \n", "- Any model we try moving forward should do much better than this one. " ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictions: [109.21734351 109.21734351 109.21734351 109.21734351 109.21734351]\n", "MSE: 9549.121874364564\n" ] } ], "source": [ "# find mean of series\n", "trend_seasonal_avg = np.mean(trend_seasonality)\n", "\n", "# create array of mean value equal to length of time array\n", "simple_avg_preds = np.full(shape=len(test), fill_value=trend_seasonal_avg, dtype='float')\n", "\n", "# mse\n", "simple_mse = mse(test, simple_avg_preds)\n", "\n", "# results\n", "print(\"Predictions: \", simple_avg_preds)\n", "print(\"MSE: \", simple_mse)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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c8ePHQ1dXF927d/9mm5SUFMTFxWVYNOdmHgJA4cKFUaVKFQDA9evX8eeff2LJkiU/PO7LJB/16tWTbTt16lS6dhs3bsSmTZuwf//+DK9yGRkZwcjICABw8OBBPHjwAN7e3gqdy7ccP34cnTt3RsOGDbF///7vFtNERBlhIUVEhM8FQIkSJdChQwdUqFABUqkUN2/exJIlS1C4cGGMGTMmx2OwtLREx44dMXv2bBQrVgxBQUEICQmBt7c39PT0vnnc8uXL0bBhQzRq1AjDhw9H6dKlER8fj0ePHuHQoUM4efLkN4+1t7eHlpYWevfujUmTJiExMRGrV6/+5uKnDg4OKFGiBEaMGIHo6Gi52/qAz9O4z5kzB9OmTcOTJ0/QunVrGBkZ4dWrV7hy5QoKFSr0w5kEK1SogDJlymDy5MkQQsDY2BiHDh1CSEhIurZz5sxBu3bt0KpVK4wZMwZpaWlYtGgRChcuLDeFdYMGDTBkyBAMHDgQV69eRePGjVGoUCFERUXh/PnzqFKlCoYPH/7duLLDwcEBDg4O320TGxuL0qVLo3v37mjZsiWsrKyQkJCA06dPY/ny5ahYsSIcHR3ljnn16pXcbXRfGBgYoFKlSgCAZ8+eoUyZMnBycsL69eu/G8Pp06cRGhqKqlWrQgiBK1euwNvbG61bt4abm5us3blz5zB37lx06dIFNjY2SExMxB9//IG1a9eiefPm6NChg6ztf5cK+O84wOfvy5ermACwZ88eREZGomLFikhMTJSd+7Bhw9CpUye5PsqWLQtA/krl69evZbdd3r59GwDwxx9/wNTUFKampmjSpAkA4Pz58+jcuTMsLCwwderUdFdgK1WqlOGCyUREclT6hBYRUR6xc+dO0adPH1GuXDlRuHBhoampKUqWLCn69+8v7t69K9f2W5NNLFq0SK7dqVOnBACxa9cuue1fJpAIDQ2VbStVqpRo166d2L17t6hcubLQ0tISpUuXFj4+PnLHfmtB3vDwcOHi4iKKFy8uNDU1hampqbCzsxNeXl4/PPdDhw6JatWqCR0dHVG8eHExceJE8ccffwgA4tSpU+naT506VQAQVlZW31yseP/+/aJZs2bCwMBAaGtri1KlSolu3bqJEydOyNo4OTmJQoUKZXj83bt3hb29vdDX1xdGRkaie/fu4vnz5wKAmDVrllzbffv2iSpVqggtLS1RsmRJsWDBAjF69GhhZGSUrt8NGzaIunXrikKFCgldXV1RpkwZMWDAAHH16tUffp2yAplYLPfryRCSkpLE4sWLRZs2bUTJkiWFtra20NHRERUrVhSTJk1KN4EEvjNrX4MGDWTtvuSMk5PTD+O+cOGCqFu3ruz7ZmtrKxYvXiySk5Pl2j18+FC0bdtWFC9eXBZnlSpVxNy5czO1mO23JpvYt2+fqF69uuz7U7t2bbF+/foMJ4AoVaqUKFWqlNy2L//mMnr999/sl/G/9coo74mIviYR4geLVBARUY4rXbo0bG1t092SRlmXkpKC6tWro3jx4jh+/LiqwyEiogKKt/YREVG+5urqCnt7exQrVgzR0dHw9/fHvXv3sHz5clWHRkREBRgLKSIiytfi4+MxYcIEvH79GpqamqhZsyaCg4PRsmVLVYdGREQFGG/tIyIiIiIiyiIuyEtERERERJRFLKSIiIiIiIiyiIUUERERERFRFnGyCQBSqRSRkZHQ19eHRCJRdThERERERKQiQgjEx8fD0tISamrfvu7EQgpAZGQkrKysVB0GERERERHlEREREShRosQ397OQAqCvrw/g8xfLwMBApbFIpVK8fv0apqam362Aif6LeUOKYu6QIpg3pAjmDSkqt3MnLi4OVlZWshrhW1hIAbLb+QwMDPJEIZWYmAgDAwN+yFCmMW9IUcwdUgTzhhTBvCFFqSp3fvTID7OYiIiIiIgoi1hIERERERERZRELKSIiIiIioixiIUVERERERJRFLKSIiIiIiIiyiIUUERERERFRFrGQIiIiIiIiyiIWUkRERERERFnEBXmJiIiIiEhhaVKBf17F42bEe0THJsKlgTUM9TRVHVaOYyFFREREREQKmbL3Ng7cfImPyWmybVGxn7CwWzUVRpU7eGsfERERERF9lxAC5x6+xvjf/0aaVMi2SyTAx+Q0FNJSR+1SRgCAfTdeIvL9J1WFmmt4RYqIiIiIiDIkhMCpBzFY8ecj3Ix4DwBoVsEU7ataAgAGNbSGU/3SKGtWGOpqEvRaewl/PfkXa88+weyOlVUYec5jIUVERERERHKkUoHjd1/B99RDhL2MAwBoa6ihT92SqF3KWNbOxrSw3HEjm5XF87e3UN5CP1fjVQUWUkREREREJPPvh2T0XvsXHryKBwDoaamjf71SGNTIBqb62t89tmFZE5yZ1Aya6gX/CSIWUkREREREJGOkpwldLXXoa2vAya40XBpaw7iQVqaOlUgk0FSX5HCEeQMLKSIiIiIikpFIJFjcvRpMC2srPI15apoUB/+ORGqaQI86VkqOMG9gIUVERERERHLKmhX+caPvOHonGuN+/xvGhbTQoZoldLXUlRRZ3lHwb14kIiIiIqJc1bqyBayMdfHvh2TsCH2u6nByBAspIiIiIiJSKg11NQxrUgYAsPbsEySnSlUckfKxkCIiIiIiIqXrWrMEzPS1ERWbiH03Xqg6HKVjIUVEREREREqno6mOIY1tAACrTz9GmlSoOCLlUmkhNX/+fNSpUwf6+vowMzND586d8eDBA7k2QgjMnj0blpaW0NXVRdOmTXHnzh25NklJSRg1ahRMTExQqFAhdOzYES9eFLyql4iIiIgoP+n9a0kU0dPE07cfEXw7StXhKJVKC6kzZ85g5MiR+OuvvxASEoLU1FQ4ODjgw4cPsjYLFy6Ej48PfH19ERoaCgsLC9jb2yM+Pl7Wxt3dHfv27cOOHTtw/vx5JCQkoH379khLS1PFaREREREREYBC2hoYaGeNutbGKGaoo+pwlEoihMgz19hev34NMzMznDlzBo0bN4YQApaWlnB3d4eHhweAz1efzM3N4e3tjaFDhyI2NhampqbYsmULevbsCQCIjIyElZUVgoOD0apVqx+OGxcXB0NDQ8TGxsLAwCBHz/FHpFIpYmJiYGZmBjU13nlJmcO8IUUxd0gRzBtSBPPm55UmFVBX+98ivWEvY1HWrDB0NDM3JXpu505ma4M8tY5UbGwsAMDY2BgAEB4ejujoaDg4OMjaaGtro0mTJrh48SKGDh2Ka9euISUlRa6NpaUlbG1tcfHixQwLqaSkJCQlJcnex8XFAfj8TZJKVTujiFQqhRBC5XFQ/sK8IUUxd0gRzBtSxM+eN9HR0Vi6dClq1KiBDh06oFChQqoOKddIAEj///moj8mp6LzqAtTUJKhWwhB1ShujTmkj1CxZBPo6GS/+m9u5k9lx8kwhJYTAuHHj0LBhQ9ja2gL4nHAAYG5uLtfW3Nwcz549k7XR0tKCkZFRujZfjv/a/Pnz4enpmW7769evkZiYmO1zyQ6pVIrY2FgIIfjXGso05g0pirlDimDekCJ+9rxxd3fHrl27AAA6OjpwcHBAx44d0bx5c+jq6qo4utzz+M0nGOio49+PqQh9+g6hT98BAH4x1cXmvpUyPCa3c+e/jxB9T54ppNzc3HDr1i2cP38+3T6JRCL3XgiRbtvXvtdmypQpGDdunOx9XFwcrKysYGpqmidu7ZNIJDA1Nf0pP2RIMcwbUhRzhxTBvCFF/Mx58+HDB/zxxx8AgOLFi+Ply5c4ePAgDh48iMKFC6Njx47o0aMHGjZsmO7iQEFjZgaEViyJ8LcfEfr0X4SGv0Po039Rr4wZzMzMMjwmt3NHRydzz3LliUJq1KhROHjwIM6ePYsSJUrItltYWAD4fNWpWLFisu0xMTGyq1QWFhZITk7Gu3fv5BIvJiYGdnZ2GY6nra0NbW3tdNvV1NTyxD9siUSSZ2Kh/IN5Q4pi7pAimDekiJ81bw4fPoyEhARYW1vj0aNHuHHjBnbs2IHff/8dz58/x7Zt27Bt2zYAQLFixVCpUiVUrlxZ7lWkSBGlxhQfHw81NTWV3WJY1kwfZc300fvXUgCAlDTpd/MiN3Mns2OoNIuFEHBzc8PevXtx8uRJWFtby+23traGhYUFQkJCZNuSk5Nx5swZWZFUq1YtaGpqyrWJiopCWFjYNwspIiIiIqLcEhQUBADo168f1NTUUKtWLSxatAjh4eG4ePEixowZI/s9OCoqCn/++SdWrFiBoUOHyq5STZ48WWnxpKWloU+fPmjUqBEiIiKU1m92aKrnv+JapVekRo4ciW3btuHAgQPQ19eXPdNkaGgIXV1dSCQSuLu7Y968eShXrhzKlSuHefPmQU9PD3369JG1dXV1xfjx41G0aFEYGxtjwoQJqFKlClq2bKnK0yMiIiKin1xMTAyOHTsGAOjbt6/cPjU1NdSvXx/169fHsmXLEB8fj7t37+LOnTtyrxcvXsDb2xtt27ZF48aNsx3TlClTcPjwYejo6CAqKgpWVlbZ7vNnpNJCavXq1QCApk2bym0PDAyEs7MzAGDSpEn49OkTRowYgXfv3qFu3bo4fvw49PX1Ze2XLl0KDQ0N9OjRA58+fUKLFi2wceNGqKtnbkpFIiIiIqKcsHPnTqSlpaFOnTooX778d9vq6+ujbt26qFu3rtz2oUOHYu3atRg5ciSuX78OTc2MZ7fLjI0bN2LRokUAPv/O/euvvyrc188uT60jpSpcR4ryO+YNKYq5Q4pg3pAifta8qVu3Lq5cuYLly5dj9OjRCvXx9u1blC9fHm/fvoWPjw/Gjh2rUD/nz59H8+bNkZKSghkzZmDOnDkK9ZPb8uo6Uj9PFhMRERER5aJ//vkHV65cgbq6Onr27KlwP0WLFsWCBQsAALNmzUJkZGSW+3j69Cm6dOmClJQUdO3aFbNnz1Y4HvqMhRQRERERUQ7YunUrAMDBwSHduqhZ5eLignr16iE+Ph4TJkzI0rHx8fHo0KED3rx5g5o1a2LTpk0/1VXBnMKvIBERERGRkgkh5Gbryy41NTWsWrUKampq2L59O06ePJmp477M0BcWFoZixYrhwIEDKpvyvKBhIUVEREREpGR//fUXnjx5gkKFCqFTp05K6bNmzZoYPnw4AMDNzQ3Jyck/PGby5MmyGfr2798vt2YrZQ8LKSIiIiIqcFJTU+Hh4YEFCxZAKpXm+vhfrkY5Ojoq9QqQl5cXTE1Nce/ePSxbtuy7bQMCArB48WIAwIYNGzhDn5KxkCIiIiKiAsfb2xsLFy7ElClTMGjQIKSlpeXa2MnJydi5cycA5dzW919FihSRTV/u6emZbkHdlJQU7NixA/Xq1cPgwYMBADNmzEDv3r2VGgexkCIiIiKiAubGjRtys9IFBgZi4MCBuVZMHTt2DG/fvoWFhQWaN2+u9P4HDBiAhg0b4uPHjxg3bhyAz1OkL1iwANbW1ujduzcuX74MLS0tjBs3jjP05RAWUkRERERUYCQlJWHAgAFITU2Fo6Mjdu7cCXV1dWzZskW2Pad9ua2vd+/e0NDQUHr/EokEq1atgrq6Onbv3o1u3brBysoKU6ZMwcuXL2Fubi67WrVkyRLO0JdDlP+dJSIiIiJSkZkzZyIsLAxmZmbw9/eHqakp1NXV0atXL2zbtg2pqakICgqCpqZmjowfGxuLgwcPAlD+bX3/VbVqVYwaNQrLli3Dnj17AADVq1fH2LFj0bNnT2hra+fY2PQZCykiIiIiKhDOnz8ve35o7dq1MDU1BQB07doVu3fvRvfu3fH7778jNTUV27dvh5aWltJj2Lt3LxITE1GxYkXUqFFD6f3/l6enJx49egQdHR2MGjUKjRo1gkQiydEx6X94nY+IiIiI8r2EhAQ4OTlBCAFnZ+d0U4536tQJe/fuhZaWFvbu3YsePXogKSlJ6XH8d+2onC5qDAwMcOjQIezatQuNGzdmEZXLWEgRERERUb43ceJEPHnyBCVLlvzmtODt27fHgQMHoK2tjQMHDqBbt25KfWbqxYsXOHXqFACgb9++SuuX8iYWUkRERESUrx09ehT+/v4APs/QZ2ho+M22rVu3xqFDh6Cjo4PDhw9j+vTpSotjy5YtEEKgcePGKFWqlNL6pbyJhRQRERER5Vv//vsvXF1dAQCjR4/O1HTj9vb22LRpE4DP603t3bs323GEhYXht99+AwA4Oztnuz/K+1hIEREREVG+lJqaihEjRiAyMhK//PIL5s+fn+lje/ToIVuDycnJCffv31c4joSEBHTv3h2fPn2Cg4MDnJycFO6L8g8WUkRERESUr7x58wYLFiyAjY2N3DpRenp6WerH29sbTZo0QUJCAhwdHREfH5/lWIQQGDZsGO7fvw9LS0sEBQVx3aafBL/LRERERJQv3LhxAy4uLihRogSmTJmCiIgIFC1aFGvXrsWvv/6a5f40NDSwc+dOWFpa4t69e3BxcYEQIkt9BAQEYOvWrVBXV8eOHTtkU65TwcdCioiIiIjytL1796Jhw4aoWbMmAgMDkZSUJPv/Fy9ewMXFReG+zc3NsXv3bmhqamL37t3w8fHJ9LE3b97EqFGjAADz5s1Do0aNFI6D8h8WUkRERESUZwUGBqJr1664cOECNDQ00KtXL1y4cAFXr16Fs7MzdHR0sj1G/fr1ZVOme3h44PTp0z88Ji4uDt27d0dSUhLatWuHCRMmZDsOyl9YSBERERFRnvTu3TtMmjQJADBkyBA8e/YM27dvh52dndIXnx0+fDj69++PtLQ09OjRAy9evPhmWyEEBg0ahEePHqFkyZLYtGkTn4v6CfE7TkRERER50qxZs/DmzRtUqlQJvr6+sLS0zLGxJBIJ/P39Ua1aNbx+/Rrt2rXD4sWLcfz4cURFRck9O7Vq1Srs2rULmpqa+P3331G0aNEci4vyLg1VB0BERERE9LVbt25h1apVAIAVK1ZAU1Mzx8fU09PD3r17UatWLdy6dQsTJ06U7StatCiqVq2KChUqICAgAACwcOFC1K1bN8fjoryJhRQRERER5SlCCIwaNQpSqRRdu3ZFixYtcm1sGxsbhIaGYvv27bh9+zZu3bqFhw8f4u3btzh16hROnToFAOjSpQvGjBmTa3FR3sNCioiIiIjylJ07d+Ls2bPQ1dXFkiVLcn38smXLYsaMGbL3nz59wt27d2WFVXJyMubOnav057Qof2EhRURERER5RkJCgmwGvMmTJ6NUqVIqjgjQ1dVFrVq1UKtWLVWHQnkIJ5sgIiIiIhmpVIoxY8agadOmWLZsGV6+fJmr48+bNw8vX75E6dKl5Z5RIsprWEgRERERkYynpydWrFiBM2fOYOzYsbCyskLTpk3h7++P169f5+jYjx49kt3Kt3TpUujq6uboeETZwUKKiIiIiAB8fjZpzpw5AIARI0agQYMGEELgzJkzGD58OIoVK4bWrVtj+/btctOBK4u7uzuSk5Ph4OCATp06Kb1/ImViIUVEREREuHr1KpydnQEA48ePx6pVq3D+/Hk8e/YMixYtQu3atZGWloZjx46hT58+mD59ulLHP3LkCI4cOQJNTU2sWLGCEzlQnsdCioiIiOgnFxkZiU6dOiExMRFt27aFt7e3bF/JkiUxYcIEhIaG4uHDh/Dw8ADw+VkmHx8fpYyfmJgom0rc3d0d5cuXV0q/RDmJhRQRERHRT+zTp0/o3LkzIiMjUalSJWzfvh3q6uoZti1btiwWLFiA+fPnA/h85WrTpk3ZjsHX1xePHz9GsWLF5KYdJ8rLWEgRERER/aSEEHB1dUVoaCiMjY1x8OBBGBgY/PA4Dw8PjB8/HgDg6uqKgwcPKhxDQkKC7AqYl5cX9PX1Fe6LKDexkCIiIiL6Sc2fPx/bt2+HhoYGdu/ejTJlymTqOIlEgkWLFsHZ2RlpaWno0aMHzpw5o1AMq1atwps3b1CmTBkMGDBAoT6IVIGFFBEREdFPaN++fZg2bRqAz7fWNWvWLEvHSyQSrFu3Dh07dkRSUhI6duyIGzduZKmP+Ph4LFq0CAAwY8YMaGhoZOl4IlViIUVERET0k4mOjpZd/XFzc8PQoUMV6kdDQwM7duxAkyZNEBcXh1atWuGff/7J9PG+vr54+/YtypUrh759+yoUA5GqsJAiIiIi+sl4enoiISEBderUwdKlS7PVl66uLg4cOIAaNWrg9evXcHBwQGRk5A+Pi4uLk12NmjlzJq9GUb7DQoqIiIjoJ/LgwQOsW7cOALB48WKlFDCGhoY4evQoypUrh2fPnqFTp074+PHjd49ZsWIF3r17h/Lly6N3797ZjoEot7GQIiIiIsphKSkpOH78OJYsWYLLly9DCKGyWKZMmYK0tDR06NABjRs3Vlq/ZmZmOHr0KIoWLYqrV6/CxcXlm+cZGxuLJUuWAPh8Nepb060T5WW8hkpERESUA5KTk3Hy5Ens2rUL+/fvx7///ivbV6JECTg6OqJbt26ws7PLtULi4sWL2LdvH9TU1LBgwQKl929jY4M9e/agZcuW2LlzJypVqoSZM2ema7d8+XK8f/8eFStWRM+ePZUeB1Fu4BUpIiIiIiVJS0vDkSNHMHDgQJibm6NNmzbYsGED/v33X5iamqJNmzYoXLgwXrx4gRUrVqBx48YoXrw4hg8fjpMnT+bolSohBCZNmgQAGDhwICpVqpQj4zRp0gT+/v4AgFmzZmHXrl1y+9+/fw8fHx/Zfl6NovyKhRQRERGRkgwePBjt27fHxo0b8f79e5ibm8uKpMjISAQHB+P169c4cOAABgwYgCJFiuDVq1fw9/dHixYtZAVGTjhw4AAuXLgAXV1deHp65tg4wOdFeseOHQsAcHJywrVr12T7li9fjtjYWFSuXBndu3fP0TiIchILKSIiIiIluH//PjZu3AgAGDlyJM6cOYOXL1/Cz88PzZo1k03qoKOjg44dO2LTpk149eoVjh49il69egEAFi1ahOTkZKXHlpqaiilTpgAAxo4di+LFiyt9jK8tWrQIbdu2xadPn9CxY0dERkbi/fv3WLZsGYDPV6PU1PirKOVfzF4iIiIiJViyZAmEEOjYsSN8fX3RuHHjH962pqWlhVatWmHz5s0oVqwYXr16hX379ik9tg0bNuD+/fsoWrSo7Pa+nKauro7t27ejUqVKiIyMRJcuXbB8+XLExcWhSpUq6Nq1a67EQZRTWEgRERERZVNUVBQ2b94MAPDw8Mjy8ZqamhgyZAgAwM/PT6mxffjwAbNmzQIAzJgxA4aGhkrt/3sMDAxw6NAh2Ux+/312ilejKL9jBhMRERFl0/Lly5GcnIwGDRrAzs5OoT4GDx4MdXV1nD17FmFhYUqLzcfHB9HR0bCxscHw4cOV1m9m2djYYO/evdDU1AQAVKtWDV26dMn1OIiUjYUUERERUTbExsZi9erVABS7GvVF8eLF0blzZwCQ9ZddMTExWLhwIQBg7ty50NLSUkq/WdW4cWMEBgaiTJkyWLZsGa9GUYHALCYiIiLKhrVr1yIuLg4VK1ZEu3btstXXiBEjAACbN29GfHx8tmObM2cOEhISUKtWLfTo0SPb/WVH7969cf78eaUuAkykSiykiIiIiBSUlJQkm4Vu4sSJ2b7S0qxZM5QvXx4JCQkICgrKVl8BAQGyZ5IWLVrEq0BESqbSf1Fnz55Fhw4dYGlpCYlEgv3798vtd3Z2hkQikXvVq1dPrk1SUhJGjRoFExMTFCpUCB07dsSLFy9y8SyIiIjoZ7V161ZERkbC0tISffv2zXZ/EolEdlXKz89PoQV6k5KSMGTIEAwePBhpaWkYMGAAmjVrlu3YiEieSgupDx8+oFq1avD19f1mm9atWyMqKkr2Cg4Oltvv7u6Offv2YceOHTh//jwSEhLQvn17pKWl5XT4RERE9BOTSqVYtGgRgM9rMynr+aMBAwZAT08PYWFhOH/+fJaOjYiIQOPGjbFu3TpIJBLMnTsXgYGBSomLiORpqHLwNm3aoE2bNt9to62tDQsLiwz3xcbGYv369diyZQtatmwJAAgKCoKVlRVOnDiBVq1aKT1mIiIiIgA4fPgw7t+/D0NDQ9nU5cpQpEgR9O3bF+vWrYOfnx8aNWqUqeNOnTqFnj174vXr1zAyMsL27dv5uxBRDsrzN8uePn0aZmZm+OWXXzB48GDExMTI9l27dg0pKSlwcHCQbbO0tIStrS0uXryoinCJiIjoJ+Ht7Q0AGD58OAwMDJTa95fb+/bs2YPo6OjvthVCwMfHB/b29nj9+jWqV6+Oa9eusYgiymEqvSL1I23atEH37t1RqlQphIeHY8aMGWjevDmuXbsGbW1tREdHQ0tLC0ZGRnLHmZubf/dDJykpCUlJSbL3cXFxAD5fopdKpTlzMpkklUohhFB5HJS/MG9IUcwdUgTzBrhw4QIuXrwILS0tuLm5Kf1rUbVqVdSvXx+XLl1CQEAApk6dmmG7d+/eYcSIEfj9998BAP369cPq1auhp6eX574/zBtSVG7nTmbHydOFVM+ePWX/b2tri9q1a6NUqVI4cuQIHB0dv3mcEAISieSb++fPnw9PT89021+/fo3ExMTsBZ1NUqkUsbGxEEJwdh3KNOYNKYq5Q4pg3gBeXl4AgO7du0NdXV3ujhll6dOnDy5duoTVq1fD2dkZGhr/+7VNCIEjR45g2rRpiImJgYaGBjw9PTFw4EAkJCQgISFB6fFkF/OGFJXbuZPZpQfydCH1tWLFiqFUqVJ4+PAhAMDCwgLJycl49+6d3FWpmJiY764qPmXKFIwbN072Pi4uDlZWVjA1NVX6pfmskkqlkEgkMDU15YcMZRrzhhTF3CFF5HbevHnzBnPmzIG2tjZKlCiBEiVKwMrKClZWVjA3N8/13L179y6OHz8OiUSCadOmwczMLEfGcXFxgaenJyIjIxEaGopOnToBAF6+fIlRo0bhwIEDAIDy5ctj/fr1qF+/fo7EoSz8vCFF5Xbu6OjoZKpdviqk3r59i4iICBQrVgwAUKtWLWhqaiIkJES2yFxUVBTCwsJkq3hnRFtbG9ra2um2q6mp5Yl/2BKJJM/EQvkH84YUxdwhReRm3sydOxerVq3KcJ+GhgasrKzg5eWFPn365HgsAODj4wMA6Ny5MypWrJhj4+jp6cHFxQULFy6Ev78/OnXqhHXr1mHSpEmIi4uDhoYGJk+ejGnTpmX6Fz9V4+cNKSo3cyezY6i0kEpISMCjR49k78PDw3Hz5k0YGxvD2NgYs2fPRteuXVGsWDE8ffoUU6dOhYmJCbp06QIAMDQ0hKurK8aPH4+iRYvC2NgYEyZMQJUqVWSz+BEREVH+lZiYiC1btgD4fKtbSkoKIiIi8OLFC0RGRiI1NRXh4eFwcXFB/fr1YW1tnaPxREREyBbKnTRpUo6OBQBDhw7FokWLcPz4cdjZ2eHy5csAgF9//RUBAQGoUqVKjsdARBlT6Z8Drl69iho1aqBGjRoAgHHjxqFGjRqYOXMm1NXVcfv2bXTq1Am//PILnJyc8Msvv+DSpUvQ19eX9bF06VJ07twZPXr0QIMGDaCnp4dDhw5BXV1dVadFRERESrJv3z68e/cOVlZW2Lx5M37//XdcunQJERERSEpKQkREBJo1a4akpCRMmDAhx+NZunQpUlJS0LRpU9SrVy/Hx7OxsZEtFXP58mXo6elh2bJluHjxIosoIhWTCEWWzC5g4uLiYGhoiNjY2DzxjFRMTAzMzMx42ZsyjXlDimLukCJyM2+aN2+OU6dOYdasWZg9e3aGbcLCwlC9enWkpaXhxIkTaNGiRY7E8vbtW5QqVQofPnzA0aNHc2168UuXLqF169Zo2LAhVq1ahdKlS+fKuMrGzxtSVG7nTmZrA2YxERER5UmPHj3CqVOnIJFI4OLi8s12tra2snWXxowZg5SUlByJx9fXFx8+fECNGjXk1rDMafXr18f79+9x5MiRfFtEERVELKSIiIgoT1q/fj0AoFWrVihZsuR323p6eqJo0aK4c+cOVq9erfRYEhISsGLFCgDA5MmTv7vMSk7I7fGI6MdYSBEREVGek5KSgo0bNwIABg8e/MP2RkZGmDdvHgBg5syZeP36tVLjCQgIwL///osyZcqga9euSu2biPInFlJERESU5wQHByM6OhpmZmZo3759po5xdXVFjRo1EBsbi+nTpystluTkZCxZsgTA55n6OKEVEQEspIiIiCgPWrduHQDA2dkZWlpamTpGXV1ddvvdunXrcP36daXEsnXrVrx48QLFihWDk5OTUvokovyPhRQRERHlKS9evMAff/wB4PNVpqxo2LAh+vTpAyEERo8ejexOTiyVSuHt7Q0AGDt2LLS1tbPVHxEVHCykiIiIKE8JDAyEVCpF48aN8csvv2T5+IULF6JQoUK4cOECtm/fnq1YDhw4gAcPHqBIkSIYOnRotvoiooKFhRQRERHlGVKpVDZbX2YmmchI8eLFMXXqVADAxIkTkZCQoFA/QgjMnz8fADBy5EiVrzVJRHmLhqoDICIiIvrizz//xLNnz1CkSJFszY43btw4rF+/Hk+ePIG9vT1KlCgB4H/TiH/5b8WKFTFo0CDZ/v86deoUQkNDoaOjg9GjRyscCxEVTCykiIiIKM/4MslEv379oKurq3A/Ojo6WLp0KTp16oS//vrru229vLzg6OgINzc3NGrUSFZkfbka5erqCjMzM4VjIaKCiYUUERER5QmvX7/G/v37AQCDBg3Kdn8dO3bE4cOH8ezZMwCQTTzx5b8pKSnYv38/zp49i127dmHXrl2oVq0a3NzcUL58eZw4cQLq6uqYMGFCtmMhooKHhRQREdFP6sGDB4iOjkbp0qVRvHhxaGio9teCzZs3IyUlBbVr10a1atWU0me7du2+u3/s2LG4desWfH19ERQUhL///lvu2azevXujdOnSSomFiAoWTjZBRET0k5FKpfD09ESFChXQtGlTlC5dGjo6OrC2tkazZs0wcOBAeHp6IjQ0NNdiEkIgICAAgOKTTCiqatWqWLt2LV68eIHFixfD2toaAKCmpoZJkyblaixElH9IRHYXWCgA4uLiYGhoiNjYWJXPyCOVShETEwMzMzOoqbHOpcxh3pCimDs/n9jYWPTv3x+HDh0CAJQuXRqRkZFITk5O11ZNTQ3nzp2DnZ2d3PacyJsLFy6gYcOG0NPTQ1RUlEp/HqelpeHEiRPQ1dVF48aNVRZHQcPPG1JUbudOZmsD3tpHRET0k7h37x46d+6Mf/75B9ra2lizZg2cnJwglUoRHR2N8PBwPH36FE+fPsXRo0dx/vx59O3bFzdv3oShoWGOxZWWlobJkycDAHr27KnyP2qqq6ujVatWKo2BiPI+FlJEREQ/gX379mHAgAFISEiAlZUV9u7di9q1awP4fOXJ0tISlpaWaNCgAQDAzc0N1atXx9OnTzFy5EgEBQXlWGzz5s3D+fPnoa+vj+nTp+fYOEREysTrqkRERAVYWloaZsyYAUdHRyQkJKBp06a4du2arIj6FkNDQ2zduhXq6urYunUrtm7dmiPxXbp0CZ6engCAVatWwcbGJkfGISJSNhZSREREBVRSUhI6deoELy8vAJ9nqAsJCYGpqWmmjrezs8OMGTMAAMOHD0d4eLhS44uNjUWfPn2QlpaGPn36oF+/fkrtn4goJ7GQIiIiKqD8/f1x5MgR6OrqIigoCD4+Plme4nzatGlo0KAB4uPj0bdvX6SmpiotvpEjR+Lp06coXbo0/Pz8ZAvhEhHlByykiIiICqDExEQsXLgQALBs2TL07dtXoX40NDQQFBQEAwMDXLp0Cb/99ptS4gsKCpLdOrht27YcncyCiCgnsJAiIiIqgDZu3IjIyEiUKFECTk5O2eqrdOnS8Pf3BwB4eXnh/Pnz2ervyZMnGDFiBABg5syZqF+/frb6IyJShSwXUhEREXjx4oXs/ZUrV+Du7o61a9cqNTAiIiJSTEpKChYsWAAA8PDwgLa2drb77N27NwYMGACpVIoBAwYgNjZW4dj69OmD+Ph4NGzYEFOnTs12bEREqpDlQqpPnz44deoUACA6Ohr29va4cuUKpk6dijlz5ig9QCIiIsqaoKAgPHv2DObm5nB1dVVav76+vrCxscGzZ88wadIkhZ6XmjNnDi5fvgxDQ0MEBQVl+ZktIqK8IsuFVFhYGH799VcAwO+//w5bW1tcvHgR27Ztw8aNG5UdHxEREWVBamoq5s2bBwCYOHEidHV1lda3vr4+tm3bBnV1dRw8eBB169bF5cuXM3WsEAJ79uyRxbZmzRqUKlVKabEREeW2LBdSKSkpslsETpw4gY4dOwIAKlSogKioKOVGR0RERFny+++/49GjRyhatCiGDh2q9P7r1q2LzZs3o0iRIrh58ybq16+P4cOH4927dxm2F0Lg0KFDqFevHrp16wapVApnZ2f07NlT6bEREeWmLBdSlStXhr+/P86dO4eQkBC0bt0aABAZGYmiRYsqPUAiIqL85NatW/jzzz8hhMj1saVSKebOnQsAGDduHAoXLpwj4/Tq1Qvnzp3DgAEDIISAv78/KlSogKCgINl5S6VS7NmzBzVr1kTHjh1x5coV6OrqYuzYsVi1alWOxEVElJuyXEh5e3tjzZo1aNq0KXr37o1q1aoBAA4ePCi75Y+IiOhnkpiYiKCgINjZ2aFatWpo2bIlZs6cmevF1L59+3D37l0YGhpi5MiROTqWiYkJAgMDcfr0aVSsWBExMTHo378/WrRogbVr16JKlSro1q0bbt68icKFC8PDwwNPnz6Fj48P9PT0cjQ2IqLckOUnPJs2bYo3b94gLi4ORkZGsu1DhgzhByMREf1UwsPDsWbNGqxfvx5v3rwB8HndpdTUVHh5eSEtLQ1z587NlYVmhRDw8vICAIwePTrX1mVq0qQJbt68iSVLluC3337DqVOnZJNSGRoaYvTo0RgzZgzvWiGiAkehdaSEELh27RrWrFmD+Ph4AICWlhYLKSIi+ilcvXoV7du3R5kyZeDt7Y03b96gRIkS8PLyQkREBJYvXw4AmD9/PqZMmZIrV6aOHDkiu/ozZsyYHB/vv7S0tDBlyhTcuXMHnTp1QvHixeHl5YVnz55hzpw5LKKIqEDK8hWpZ8+eoXXr1nj+/DmSkpJgb28PfX19LFy4EImJibIF+4iIiAqi+Ph4tGjRAnFxcQAABwcHjBgxAu3atZNN5T169Gioqalh1KhR8Pb2RlpaGhYuXJhjV6aEEPjtt98AACNGjFBZ4WJtbY39+/erZGwiotyW5UJqzJgxqF27Nv7++2+5D+ouXbpg0KBBSg2OiIgor9m+fTvi4uJQtmxZBAcHo1y5chm2c3Nzg5qaGkaOHInFixcjLS0NS5YsyZFi6sSJE7LJHMaPH6/0/omIKL0sF1Lnz5/HhQsXoKWlJbe9VKlSePnypdICIyIiyovWrVsHABg2bNg3i6gvRowYAXV1dQwbNgxLly6FVCrF0qVLlV5MfbkaNWTIEJiZmSm1byIiyliWn5GSSqVIS0tLt/3FixfQ19dXSlBERER50c2bN3H16lVoampiwIABmTpm6NChWLt2LQBg+fLlGDNmDKRSqdJi2rFjB86dOwctLS1MnDhRaf0SEdH3ZbmQsre3x7Jly2TvJRIJEhISMGvWLLRt21aZsREREeUpAQEBAIDOnTvD1NQ008cNHjwYAQEBkEgkWLlyJezt7fH8+fNsx7Nlyxb07dsXwOdbCYsXL57tPomIKHOyXEgtXboUZ86cQaVKlZCYmIg+ffqgdOnSePnyJby9vXMiRiIiIpX7+PEjgoKCAHwujLLK1dUVmzdvhp6eHk6ePIkqVapg48aNCs/ot2bNGjg5OUEqlWLgwIFYuHChQv0QEZFislxIWVpa4ubNm5gwYQKGDh2KGjVqYMGCBbhx4wbvyyYiogJr9+7diI2NhbW1NVq0aKFQH/369cPff/8NOzs7xMXFYeDAgejcuTNevXqVpX58fHwwbNgwCCHg5uaGgIAAqKurKxQTEREpRqF1pHR1deHi4gJfX1/4+flh0KBB0NXVVXZsREREecaXSSZcXV2hpqbQj08AQNmyZXH27FksWLAAWlpaOHjwIGxtbbFnz54fHiuEwJw5c2Qz802ePBkrVqzIVjxERKSYLM/at3nz5u/uz+zDt0RERPnFvXv3cP78eaipqWHgwIHZ7k9dXR0eHh5o06YN+vfvj1u3bqFbt27o06cPevfujSpVqqBkyZJys/sJIeDh4YFFixYBALy8vDBt2rRsx0JERIpRaB2p/0pJScHHjx+hpaUFPT09FlJERFTgrF+/HgDQrl07WFpaKq3fqlWrIjQ0FJ6enliwYAG2bduGbdu2AQD09fVha2sLW1tbVKlSBbdu3ZJNdrF06VK4u7srLQ4iIsq6LBdS7969S7ft4cOHGD58OKddJSKiAicpKQmbNm0CoNgkEz+ipaWFuXPnokOHDvD19cXt27dx7949xMfH49KlS7h06ZKsrUQiwZo1a3IkDiIiyposF1IZKVeuHBYsWIB+/frh/v37yuiSiIgoTzhw4ADevHkDS0tLtGnTJsfGqVevHurVqwfg890e//zzD8LCwnD79m2EhYXh9evXcHd3R/fu3XMsBiIimeQP394nUQc0dTLZVg3Q1M1cW61CmY8vD1BKIQV8vt87MjJSWd0RERHlCV8mmXBxcYGGhtJ+bH6XpqYmKleujMqVK6Nnz565MiYRkZx537mNuZwD0HfX/94vKgukfMy4bamGwMAj/3u/rArw8W3GbWfHZj1OFcryT4SDBw/KvRdCICoqCr6+vmjQoIHSAiMiIlK1J0+e4MSJE5BIJHB1dVV1OERElIdkuZDq3Lmz3HuJRAJTU1M0b94cS5YsUVZcRET0k4mNjcWxY8eQmJiItLQ02UsqlSItLQ2pqamIj4/P8JWSkoLp06ejVatWSo1pw4YNAAB7e3uULl1aqX0TEeVpU79zp5nkq3XrJj76Ttuvlmdwv614THlMlgspqVSaE3EQEdFPrk+fPggODlb4+NGjR+PevXtKW1MpNTUVgYGBAHJmkgkiojwtK88r5VTbPC53bvYmIiL6jqNHjyI4OBiamppo3rw51NTUoK6uLnupqalBQ0MDhQsXhr6+PgwMDKCvrw99fX0ULlwYw4cPxz///IMTJ07AwcFBKTEFBwcjMjISpqam6Nixo1L6JCKigiNThdS4ceMy3aGPj4/CwRAR0c8nNTUV48ePBwCMGjVKodvEL1++jBUrVmDlypVKK6S+TDLh5OQELS0tpfRJREQFR6YKqRs3bmSqs/+uwE5ERJQZa9euxd27d1G0aFHMmDFDoT5GjhyJFStW4MiRI3jy5AlsbGyyFdMff/whu81w0KBB2eqLiIgKpkwVUqdOncrpOIiI6Cf0/v17zJw5EwDg6emJIkWKKNTPL7/8glatWuHYsWPw8/PD4sWLFY7pxo0b6N69O6RSKVxdXVG+fHmF+yIiooJLOU/kKujs2bPo0KEDLC0tIZFIsH//frn9QgjMnj0blpaW0NXVRdOmTXHnzh25NklJSRg1ahRMTExQqFAhdOzYES9evMjFsyAiIkV5eXnh7du3qFixIoYOHZqtvtzc3AAA69evx8eP31jP5AeeP3+Odu3a4cOHD2jRogX8/PyyFRMRERVcChVSoaGhmDRpEnr16gVHR0e5V1Z8+PAB1apVg6+vb4b7Fy5cCB8fH/j6+iI0NBQWFhawt7dHfHy8rI27uzv27duHHTt24Pz580hISED79u2RlpamyKkREVEuefToEVasWAEAWLJkSbYXu23Tpg1sbGzw/v17bN26NcvHx8bGol27doiKioKtrS327NnDZ6OIiOibslxI7dixAw0aNMDdu3exb98+pKSk4O7duzh58iQMDQ2z1FebNm3g5eWVYQEmhMCyZcswbdo0ODo6wtbWFps2bcLHjx+xbds2AJ9/6K1fvx5LlixBy5YtUaNGDQQFBeH27ds4ceJEVk+NiIhy0aRJk5CSkoJWrVqhTZs22e5PXV0dI0eOBAD4+vpCCJHpY5OTk9G1a1eEhYWhWLFiCA4OzvLPNCIi+rlk+c9/8+bNw9KlSzFy5Ejo6+tj+fLlsLa2xtChQ1GsWDGlBRYeHo7o6Gi52Ze0tbXRpEkTXLx4EUOHDsW1a9eQkpIi18bS0hK2tra4ePHiNxdmTEpKQlJSkux9XFwcgM9rZKl6nSypVAohhMrjoPyFeUOKUlXunD59Gvv27YO6ujoWLVqktPGdnJwwY8YM3Lp1C2fOnEHjxo1/eIwQAkOGDMGff/6JwoUL49ChQyhevDj/PX0HP3NIEcwbUlRu505mx8lyIfX48WO0a9cOwOfC5sOHD5BIJBg7diyaN28OT0/PrHaZoejoaACAubm53HZzc3M8e/ZM1kZLSwtGRkbp2nw5PiPz58/PMM7Xr18jMTExu6Fni1QqRWxsLIQQSltUkgo+5g0pShW5k5aWhjFjxgAA+vXrB1NTU8TExCitf0dHRwQFBcHHxwcVKlT4YXsfHx9s2rQJ6urq8Pf3R/HixZUaT0HEzxxSBPOGFJXbufPfx4i+J8uFlLGxsazz4sWLIywsDFWqVMH79+8Vfrj3e76eUl0I8cNp1n/UZsqUKXJrY8XFxcHKygqmpqYwMDDIXsDZJJVKIZFIYGpqyg8ZyjTmDSlKFbkTGBiIsLAwGBoawtvbG6ampkrtf8KECQgKCkJwcDCSk5NRokSJb7bdvHkzFi1aBODz7YC9e/dWaiwFFT9zSBHMG1JUbueOjo5OptplupC6efMmqlevjkaNGiEkJARVqlRBjx49MGbMGJw8eRIhISFo0aKFwgF/zcLCAsDnq07/vWUwJiZGdpXKwsICycnJePfundxVqZiYGNjZ2X2zb21tbWhra6fbrqamlif+YUskkjwTC+UfzBtSVG7mTkJCAqZPnw4AmD59erq7DpShWrVqaNKkCc6cOYN169bht99+S9dGKpVi8eLFmDZtGgDAw8MDw4YNU3osBRk/c0gRzBtSVG7mTmbHyHQkNWvWRK1atVCxYkXZX+ymTJmCCRMm4NWrV3B0dMT69esVizYD1tbWsLCwQEhIiGxbcnIyzpw5IyuSatWqBU1NTbk2UVFRCAsL+24hRUT0s7h//z7q1auH/v3748KFC1magEHZ/v33X4wYMQLR0dEoU6YMRo0alWNjfZkKfe3atXLPxAKf/0DXqlUreHh4IDU1Fc7Ozpg3b16OxUJERAWUyKSLFy+KQYMGCQMDA6Grqyv69u0rTp48mdnDMxQfHy9u3Lghbty4IQAIHx8fcePGDfHs2TMhhBALFiwQhoaGYu/eveL27duid+/eolixYiIuLk7Wx7Bhw0SJEiXEiRMnxPXr10Xz5s1FtWrVRGpqaqbjiI2NFQBEbGxsts5HGdLS0kRUVJRIS0tTdSiUjzBvKCPJycmiVq1aAoDsZWtrK3x9fcX79++FELmTO3FxceK3334TBgYGsjj279+fY+MJIURKSoooUaKEACA2b94s2x4cHCxMTU0FAKGrqyvWrVsnpFJpjsZSEPEzhxTBvCFF5XbuZLY2yHQh9cXHjx/Fxo0bRZMmTYSampqwsbERXl5eIiIiIstBnjp1Su4H/JeXk5OTEEIIqVQqZs2aJSwsLIS2trZo3LixuH37tlwfnz59Em5ubsLY2Fjo6uqK9u3bi+fPn2cpDhZSlN8xbygjXl5eAoAoUqSIGDhwoNDV1ZV9zurp6QlXV1dx+fLlHMudT58+CR8fH2FiYiIbt2rVquLIkSNKHysjX87/119/FYmJiWLcuHFycdy9ezdX4iiI+JlDimDekKLyaiElEULx+zweP36MwMBAbN68GVFRUbC3t0dwcLCi3alMXFwcDA0NERsbmycmm4iJiYGZmRnvH6ZMY97Q127fvo1atWohJSUFmzdvRv/+/fH+/XsEBQXB398fd+7ckbXt1q0bduzYAXV1daWMnZKSgsDAQMyZMwcvX74EAJQrVw5z5sxBjx49ci1HY2JiYGVlheTkZJQvXx4PHjwA8Pm2v0WLFmX6YWJKj585pAjmDSkqt3Mns7VBtiIpU6YMJk+ejGnTpsHAwADHjh3LTndERKQEKSkpcHZ2RkpKCjp27Ih+/foBAIoUKQI3Nzfcvn0b586dQ9++faGhoYHdu3dj9erVShlbCIGOHTti6NChePnyJaysrBAQEIC7d++iV69eufrLk5mZGXr27AkAePDgAYyNjXHgwAGsXLmSRRQREWWbwj/Rzpw5AycnJ1hYWGDSpElwdHTEhQsXlBkbEREpwNvbG9evX4eRkRH8/f3TLQchkUjQsGFDBAUFyab+Hj9+PG7evJntsS9duoSjR49CW1sby5cvx8OHD+Hq6goNjSyvtqEUHh4eMDExgb29PW7duoWOHTuqJA4iIip4svSTLSIiAhs3bsTGjRsRHh4OOzs7rFy5Ej169EChQoVyKkYiIsqkW7duYc6cOQCAlStXyi0fkZFRo0YhODgYISEh6NWrF65du5atz/Ply5cDAPr27YvRo0cr3I+yVK5cGa9eveJtREREpHSZ/slib28Pa2tr+Pn5oVu3brh37x7Onz+PgQMHsogiIsoD/ntLX+fOndGnT58fHiORSLB06VJYWlriwYMH2ZqS/MWLF9izZw8A5Iki6gsWUURElBMy/dNFV1cXe/bswYsXL+Dt7Y3y5cvnZFxERJRF8+fPx40bN2BsbIzVq1enu6XvW4oWLYqgoCCoqakhMDAQ27ZtU2h8Pz8/pKWloUmTJqhWrZpCfRAREeUXmS6kDh48iE6dOiltViciIlKemzdv4rfffgMA+Pr6wsLCIkvHN2nSBDNmzAAADBs2DI8ePcrS8Z8+fcLatWsBAGPGjMnSsURERPkR73cgIsrnkpOT4ezsjNTUVDg6OqJXr14K9TN9+nQ0atQI8fHx6N27N5KTkzN97LZt2/D27VuUKlWKEzoQEdFPgYUUEVE+JoTA2LFj8ffff6No0aLw8/PL9C19X9PQ0MDWrVthbGyMq1evYurUqZmO4cskE25ubrxzgYiIfgospIiI8rG5c+fKiqeAgACYm5tnqz8rKyts2LABALBkyZJMLbJ+5swZ3L59G3p6enB1dc3W+ERERPkFCykionwqICBA9lzT8uXL0blzZ6X026lTJ9nsff369UNYWNh323+5GuXk5AQjIyOlxEBERJTXsZAiIsqHDh06hKFDhwIApkyZkq1pyzOycOFC1KtXD+/evYODgwPCw8MzbBceHo4DBw4AgNJjICIiystYSBER5TMXL15Ejx49IJVKMXDgQMydO1fpY+jo6ODIkSOwtbVFVFQU7O3tER0dna7dqlWrIISAg4MDKlasqPQ4iIiI8ioWUkRE+ci9e/fQoUMHJCYmol27dli7dq3Ck0v8iLGxMY4dOwZra2s8fvwYrVq1wrt372T7ExISEBAQAIBTnhMR0c+HhRQRkRI9ffoU8+bNw7x585CamqrUvl+8eIFWrVrh33//Rd26dbFz505oaGgodYyvWVpaIiQkBBYWFrh16xbat2+PDx8+AAA2b96M2NhYlCtXDq1bt87ROIiIiPKanP0JTET0E4iNjcXu3buxefNmnD17Vrb97t272LRpk1KmA3/37h3atGmDiIgIlC9fHocPH0ahQoWy3W9mlClTBseOHUOTJk1w8eJFdO3aFQcOHMDKlSsBfH42Sk2Nf5cjIqKfC3/yEREpIDU1FX/88Qd69+4NCwsLDBo0CGfPnoVEIkGjRo1kazK5uLggLS0tW2NFR0ejefPmCAsLQ7FixXDs2DGYmJgo6Uwyp2rVqjhy5Aj09PRw7Ngx2NnZ4f79+9DX14ezs3OuxkJERJQXsJAiIsqCtLQ0BAYGokyZMmjbti127NiBxMREVKxYEQsWLMDz589x9uxZbN++Herq6ti8eTMGDx4MqVSq0HgPHz6EnZ0dbt68CTMzMxw7dgylSpVS8llljp2dHfbu3QtNTU1cv34dAODi4gJ9fX2VxENERKRKLKSIiDJBCIGDBw+iWrVqcHFxwfPnz2FiYoLRo0fj6tWruHPnDjw8PFCiRAkAQLdu3bB161aoqakhMDAQQ4cOzXIxdfXqVTRo0ADh4eEoU6YMLl68iCpVquTE6WVaq1atEBQUBIlEAjU1Nbi5uak0HiIiIlXhM1JERD9w4cIFeHh44MKFCwAAIyMjTJ06FSNHjoSuru43j+vZsyfS0tLQv39/BAQEQENDA35+fpmaZe/48eNwdHTEhw8fULNmTQQHB8Pc3Fxp55QdPXr0gLm5OaRSKcqWLavqcIiIiFSChRQR0TfcvXsXU6ZMwcGDBwEAurq6GDNmDDw8PFCkSJFM9dGnTx+kpaXByckJ/v7+UFdXx8qVK79bTG3duhXOzs5ITU1Fy5YtsXfv3jx3+1yTJk1UHQIREZFKsZAiIsrApUuX0LRpUyQnJ0NdXR0uLi6YNWsWihcvnuW++vfvj7S0NLi4uGDVqlX49OkTWrduDWNjY9nLyMgI+vr6WLp0KcaPHw8A6NWrFzZt2gQtLS1lnx4RERFlEwspIqKvvH79Gj169EBycjKaNWsGPz8/VKhQIVt9Ojs7Iy0tDYMGDcKGDRuwYcOGdG00NDRka0+NGTMGPj4+nFaciIgoj2IhRUT0H2lpaejTpw9evHiB8uXL48CBA0q7rc7V1RVGRkbYvHkz/v33X7lXUlISUlNToaamhrlz58LDwyNTz1IRERGRarCQIiL6j9mzZ+PEiRPQ09PDnj17lP5skqOjIxwdHdNt//TpE/79919oa2vn+hpRRERElHUspIgoT5BKpdi1axeOHDmC2NhYxMfHp3upq6tj+/btaN26dY7EEBwcDC8vLwDA2rVrUbly5RwZJyO6uroKPX9FREREqsFCiohU7sSJE/Dw8JAt8vo9vXr1wtWrV5U+7fbTp0/Rr18/AMDw4cPRt29fpfZPREREBQsLKSJSmZs3b8LDwwPHjx8HAOjr62PEiBGwtraGvr6+7GVgYIBChQrBxcUFFy9eRJcuXXDp0iUULlxYKXEkJSWhe/fuePfuHerUqYOlS5cqpV8iIiIquFhIEVGue/r0KWbMmIGtW7dCCAFNTU0MHz4c06dPh6mp6TeP27VrF2rVqoWwsDC4urpix44dSpmQwd3dHVevXoWxsTF27doFbW3tbPdJREREBRvn1SWiXOXr64vy5csjKCgIQgj06tUL9+7dw/Lly79bRAGApaUldu/eDQ0NDfz+++9YsmRJtuMJCgqCv78/JBIJgoKCUKpUqWz3SURERAUfCykiyjVv377F+PHjkZycjObNmyM0NBTbt29HmTJlMt1HgwYNsHz5cgCAh4cH/vzzT4XjuXv3LoYMGQIAmD59Otq0aaNwX0RERPRzYSFFRLlm69atSE5ORvXq1XHixAnUrl1boX6GDx8OZ2dnSKVS9OzZE8+ePctyH8nJyejbty8+ffqEli1bYtasWQrFQkRERD8nFlJElCuEEFi/fj2AzwvTZufZJolEgtWrV6NWrVp4+/YtHB0d8enTpyz1MXPmTNy8eRNFixbFpk2boK6urnA8RERE9PNhIUVEueLatWu4desWtLW1lTK1uI6ODvbu3QsTExNcv34dw4cPhxAiU8eePXsWCxcuBPB5vShLS8tsx0NEREQ/FxZSRJQrvlyNcnR0hJGRkVL6LFmyJHbu3Ak1NTVs2rQJs2fP/mExFRsbi/79+0MIARcXFzg6OiolFiIiIvq5sJAiohz38eNHbNu2DcDn2/qUqXnz5rLZ++bMmQNXV1ekpKR8s72bmxueP38OGxsbLFu2TKmxEBER0c+DhRQR5bg9e/YgLi4O1tbWaNasmdL7d3d3h5+fH9TU1BAYGIi2bdsiNjY2XbudO3ciKCgIampq2LJlC/T19ZUeCxEREf0cWEgRUY77clvfwIEDoaaWMx87w4cPx6FDh1CoUCGcOHECDRo0wPPnz2X7X7x4gWHDhgEApk2bBjs7uxyJg4iIiH4OLKSICrhr166hXr16WLdunUrGf/ToEc6cOQOJRAJnZ+ccHatt27Y4d+4cihUrhjt37qBu3bq4fv06pFIpnJyc8P79e9SpUwczZszI0TiIiIio4NNQdQBElHOkUikGDx6MGzdu4PLly4iPj8e4ceNyNYYNGzYAAFq3bg0rK6scH69GjRq4fPky2rZti7CwMDRu3BhdunTByZMnoaenh6CgIGhqauZ4HERERFSw8YoUUQG2detW3LhxAxoan/9mMn78eMyfPz/Xxk9NTcXGjRsBKH+Sie+xsrLC+fPnYW9vjw8fPiAoKAgA4OPjg19++SXX4iAiIqKCi4UUUQH16dMnTJs2DQDg5eWFOXPmAACmTp0KT0/PTK+5lB1Hjx5FVFQUTE1N0aFDhxwf778MDQ1x5MgRuLi4AAA6d+6MIUOG5GoMREREVHDx1j6iAmrFihWIiIiAlZUVRo8eDV1dXWhpaWHy5MmYPXs2kpOT4eXlBYlEkmMxfJlkon///tDS0sqxcb5FU1MTAQEBmDx5MmxsbHL0XImIiOjnwitSRAXQmzdvMG/ePACfr0bp6uoCADw8PODj4wMAmDdvHiZOnJhjV6ZevXqFw4cPA8jd2/q+JpFIUK5cOairq6ssBiIiIip4WEgRFUBeXl6Ii4tD9erV0a9fP7l9Y8eOha+vLwBgyZIlGDNmTI4UU5s3b0Zqairq1auHSpUqKb1/IiIiIlViIUVUwDx+/Bh+fn4AgEWLFmW4btPIkSOxZs0aSCQSrFy5EtOnT8/yOFKpFGlpaRnuE0LIbutT5dUoIiIiopzCQoqogJkyZQpSUlLQunVrtGzZ8pvthgwZgoCAAACfC67w8PBMj/HmzRvY2NjA0NAQDg4O+O2333DmzBl8+vQJAHDx4kU8ePAAhQoVQs+ePbN3QkRERER5ECebICpA/vrrL+zatQtqampYuHDhD9u7uLhgx44dCAkJwcyZM7Fly5ZMjTNr1iw8e/YMABASEoKQkBAAgJaWFn799VdZQdWjRw/o6+sreDZEREREeRevSBEVEEIITJo0CQDg7OyMKlWqZOq4L+tKbd26Fbdu3fph+7CwMPj7+wMAAgMD4evri549e6JYsWJITk7G+fPnce3aNQC8rY+IiIgKrjxdSM2ePRsSiUTuZWFhIdsvhMDs2bNhaWkJXV1dNG3aFHfu3FFhxESq88cff+DChQvQ1dWVrRmVGbVq1UKPHj0ghMDUqVO/21YIgXHjxkEqlaJLly5wdnbGyJEjsWPHDrx8+RIPHz7Ehg0bMHDgQMyaNQt2dnbZPS0iIiKiPClPF1IAULlyZURFRclet2/flu1buHAhfHx84Ovri9DQUFhYWMDe3h7x8fEqjJgo96WkpGDu3LkAgHHjxqF48eJZOt7Lywvq6uo4cuQIzp079812R44cQUhICLS0tLBo0SK5fRKJBGXLlsXAgQOxYcMG2R9CiIiIiAqiPF9IaWhowMLCQvYyNTUF8Pkv48uWLcO0adPg6OgIW1tbbNq0CR8/fsS2bdtUHDVR7klLS8PkyZPx5MkTmJqaym7vy4py5cph0KBBAD6vNZXRdOjJyckYP348AMDd3R1lypTJXuBERERE+VieL6QePnwIS0tLWFtbo1evXnjy5AkAIDw8HNHR0XBwcJC11dbWRpMmTXDx4kVVhUuUq6Kjo2Fvb49ly5YBAObOnQsDAwOF+po5cyZ0dXVx6dIlHDp0KN3+VatW4Z9//oGZmRmmTZuWnbCJiIiI8r08PWtf3bp1sXnzZvzyyy949eoVvLy8YGdnhzt37iA6OhoAYG5uLneMubm5bDaxb0lKSkJSUpLsfVxcHIDP6+JIpVIln0XWSKVSCCFUHgd9du3aNRgaGqJs2bKqDiWd06dPo2/fvoiOjkahQoXg7e2NgQMHKpw7FhYWGDNmDBYsWICpU6eiTZs2UFdXB/B5unNPT08AwG+//YbChQszRwsIfuaQIpg3pAjmDSkqt3Mns+Pk6UKqTZs2sv+vUqUK6tevjzJlymDTpk2oV68eAKR7BkMI8cPnMubPny/7pfC/Xr9+jcTERCVErjipVIrY2FgIITJcSJVyz/79+zF8+HAAgI2NDZo3b44WLVqgfv360NbWVllcUqkUK1euxMKFCyGVSlG+fHmsXbsWpqamiImJyVbeODs7w9/fH3fu3MHq1avRo0cPAJ/XpoqNjYWtrS3atWuHmJgYZZ0OqRg/c0gRzBtSBPOGFJXbuZPZ+RYkIqOHIfIwe3t7lC1bFhMnTkSZMmVw/fp11KhRQ7a/U6dOKFKkCDZt2vTNPjK6ImVlZYV3794pfFuUskilUrx+/Rqmpqb8kFGhly9fomrVqnj//j0kEoncM0N6enpo0aIF2rRpgy5dusDMzCzX4nr79i0GDBiAo0ePAgAGDBgAX19f6OrqKi1vFi9eDA8PD5QsWRL37t3Do0ePUKNGDUilUpw8eRJNmjRRxqlQHsHPHFIE84YUwbwhReV27sTFxcHIyAixsbHfrQ3y9BWpryUlJeHevXto1KgRrK2tYWFhgZCQEFkhlZycjDNnzsDb2/u7/Whra2d4RUFNTS1P/MOWSCR5JpafkRACgwYNwvv371GnTh0cO3YMp0+fRnBwMIKDgxEZGYlDhw7h0KFDmDx5MhYvXoxBgwbl+Ax1165dQ5cuXRAREQEdHR2sWrUKLi4uAD5/wCgrb0aNGoUVK1bg+fPnWLNmDYKDgyGVStG1a1c0a9ZMGadCeQw/c0gRzBtSBPOGFJWbuZPZMfJ0Fk+YMAFnzpxBeHg4Ll++jG7duiEuLg5OTk6QSCRwd3fHvHnzsG/fPoSFhcHZ2Rl6enro06ePqkOnfGz16tU4fvw4dHR0sHnzZhgZGaFLly5Yt24dXrx4gZs3b2Lu3LmoWrUq4uLiMGTIELRs2VI2EUpOePHiBdq2bYuIiAiUK1cOly9flhVRyqarq4vZs2cDAKZOnYoTJ05AS0sLCxcuzJHxiIiIiPKjPF1IvXjxAr1790b58uXh6OgILS0t/PXXXyhVqhQAYNKkSXB3d8eIESNQu3ZtvHz5EsePH4e+vr6KI6f86uHDh5gwYQIAwNvbGxUqVJDbL5FIUK1aNUydOhXXr1+Hj48PdHV1cfLkSVSpUgXLly9HWlqaUmNKSkpCt27dEBMTg6pVq+Lq1auoWrWqUsf4mrOzMypUqCB7ZnDcuHGwsbHJ0TGJiIiI8pN894xUToiLi4OhoeEP74PMDVKpFDExMTAzM+Nl71yWmpqKhg0b4vLly2jRogWOHz+eqe/B48ePMXjwYJw6dQoAUL9+faxfvx4VK1ZUSlxDhgzBunXrYGRkhKtXr2ZY0ORE3uzbtw+Ojo4wNzfHP//8o/J/G5Qz+JlDimDekCKYN6So3M6dzNYGzGKi/+ft7Y3Lly/D0NAQgYGBmf6HWqZMGZw4cQJr1qyBvr4+Ll26hOrVq8vWdsqOtWvXYt26dZBIJNi+fXuuXhXq0qULDh06hDNnzrCIIiIiIvoKCykiANevX5c9F7Ry5UpYWVll6Xg1NTUMGTIEd+7cQdu2bZGcnIyxY8fKrlIp4tKlS3BzcwMAzJs3D61atVK4L0W1b98e5cuXz/VxiYiIiPI6FlL000tMTET//v2RmpqKrl27ol+/fgr3ZWVlhcOHD2Po0KEAgBEjRiA5OTnL/URFRaFr165ISUlBt27d4OHhoXBMRERERKR8LKTopzd9+nTcvXsX5ubmWL16dbanMZdIJJg/fz7MzMxw//59LF26NEvHJycno3v37oiKikLlypURGBiY41OrExEREVHWsJCin9q5c+fg4+MDAAgICICpqalS+jUyMsKiRYsAAHPmzMHz588zfezYsWNx4cIFGBoaYt++fShcuLBSYiIiIiIi5WEhRT+t5ORkDB06FEIIuLi4oH379krtv3///mjUqBE+fvwId3f3TB0TEBAAPz8/SCQSbN26FeXKlVNqTERERESkHCyk6Ke1ePFi3Lt3D6amprKrR8okkUjg5+cHdXV17Nu3D8HBwd9tHxAQgCFDhgAAPD090a5dO6XHRERERETKwUKKfkpPnjzBb7/9BgDw8fGBsbFxjoxja2uLsWPHAgBGjRqFT58+Zdhu6dKlGDx4MIQQGDZsGKZNm5Yj8RARERGRcrCQop+OEAIjR45EYmIimjdvjr59++boeLNmzULx4sXx5MkTLFiwIF0sc+bMwbhx4wAAkyZNgp+fHxcqJCIiIsrj+Nsa5TqpVAohhMrG3717N44ePQotLS3Z80g5qXDhwrLFeb29vfHo0SMAn4uoiRMnYtasWQAALy8vLFiwgDP0EREREeUDLKQoV0VERKBmzZooWrQoRo4cidDQ0FwtquLi4jBmzBgAwJQpU3JtsdmuXbvCwcEBSUlJcHNzQ1paGoYNG4YlS5YAAJYtW4Zp06axiCIiIiLKJ1hIUa65f/8+GjRogL///hvv3r2Dn58ffv31V1SuXBkLFy5EZGRkjscwffp0REVFoVy5cpg8eXKOj/eFRCKBr68vtLS0cOzYMdjZ2WHt2rWQSCRYv369rLgjIiIiovyBhRTliitXrqBhw4aIiIhA+fLlsXv3bvTt2xe6urq4d+8ePDw8YGVlhTZt2uDQoUM5EsPVq1exatUqAICfnx90dHRyZJxvKVeuHDw8PAB8/npoaGhg+/btcHFxydU4iIiIiCj7WEhRjgsJCUHz5s3x9u1b1KlTB+fPn0fXrl0RFBSE6OhoBAQEoGHDhpBKpTh69Cg6duyIbdu2KTWGL7fSSaVS9OnTBy1btlRq/5k1ZcoU2NraQldXF/v370fPnj1VEgcRERERZQ8LKcpRO3fuRLt27fDhwwfY29vj5MmTMDExke03MDCAq6srzp07h4cPH2LgwIEAgOHDhyM8PFxpcfj5+eHatWswNDSEj4+P0vrNKl1dXVy5cgWvXr3iOlFERERE+RgLKcoxq1atQu/evZGSkoKePXvi0KFDKFy48Dfbly1bFmvXroWdnR3i4uLQr18/pKamZjuOiIgI2bpMCxYsgLm5ebb7zA5dXV3o6+urNAYiIiIiyh4WUpQj5syZAzc3N9maTVu3boW2tvYPj9PQ0EBQUBAMDAxw8eJFzJs3L1txnD9/HvXq1UN8fDzq1auHIUOGZKs/IiIiIiKAhRTlgG3btsnWRvL09MTKlSuhrq6e6eOtra3h5+cH4HNBdunSpSzHIITA4sWL0bRpU0RGRqJixYoICgriQrdEREREpBT8rZKU6uHDhxg6dCgAYNq0aZg5c6ZCayP17dsXffv2RVpaGvr27Yu4uLhMH/v+/Xt06dIFEydORFpaGvr06YMrV66gTJkyWY6DiIiIiCgjLKRIaZKSktCzZ08kJCSgSZMm8PT0zFZ/q1atQunSpREeHo6RI0dm6phr166hZs2aOHDgALS0tLB69WoEBQV999ksIiIiIqKsYiFFSjNx4kTcuHEDJiYm2Lp1a5Zu58uIoaGhrJ+goKDvTokuhIC/vz/s7OwQHh4Oa2trXLx4EcOGDVPoihgRERER0fewkCogjh07hkGDBiEoKAjv37/P9fH37duHlStXAgA2bdqE4sWLK6VfOzs7zJgxA4D8lOipqam4fv06Vq5ciV69eqFkyZIYPnw4kpOT0bFjR1y7dg21atVSSgxERERERF/TUHUAlD3JycmYOnUqlixZAgBYv349NDQ00KxZMzg6OqJTp04oVqxYjsbw9OlTuLi4AAAmTJiAtm3bKrX/adOmISQkBBcuXEDHjh1hZmaGy5cv48OHD3LttLW18dtvv2HChAm8CkVEREREOYqFVD4WHh6OXr164cqVKwCArl274v79+7hz5w5CQkIQEhKCESNGoF69eujWrRtGjBgBHR0dpcaQkpKC3r174/3796hbty7mzp2r1P6B/02JXq1aNYSFhcm2Gxoaws7ODnZ2dmjQoAF+/fVXFCpUSOnjExERERF9jYVUPrV7924MGjQIsbGxMDIyQmBgIDp16gTg88x5+/btw969e3H58mVcunQJly5dwsWLF7Fr1y6lXq2ZPn06/vrrLxgaGmLHjh3Q0tJSWt//Vbp0aezfvx87d+5EjRo10KBBA1SqVInTmRMRERGRSkiEEELVQahaXFwcDA0NERsbCwMDA5XGIpVKERMTAzMzswyLhE+fPmHcuHHw9/cH8PkZou3bt6NkyZIZ9vfy5Uvs2bMHEyZMQEpKCvz8/DB8+HClxPrHH3/IbuPbs2cPHB0dldIvZd2P8oboW5g7pAjmDSmCeUOKyu3cyWxtwCzORx48eIB69erB398fEokEU6dOxenTp79ZRAFA8eLFMXr0aHh7ewMAxo4di7///jvbsbx9+xYDBgwAAIwcOZJFFBERERH9VFhI5RMPHjxAo0aNcOvWLZiZmeHYsWOYO3cuNDU1M3W8u7s72rdvL7fWU3asX78eb968QaVKlbB48eJs9UVERERElN+wkMoHnj59ipYtW+L169eoUaMG/v77b9jb22epD4lEgsDAQBQvXhwPHjyAm5ubwvFIpVKsWbMGADBu3DilT2BBRERERJTXsZDK46KiotCyZUu8ePECFStWxLFjx2BhYaFQXyYmJti+fTvU1NSwadMmbNmyRaF+jh8/jidPnsDQ0BC9evVSqA8iIiIiovyMhVQe9vbtW9jb2+Px48ewtrZGSEgITE1Ns9Vno0aNMHv2bACfF7h98OBBlvtYvXo1AMDJyYnTjRMRERHRT4mFVB4VFxeH1q1b486dO7C0tMSJEydQvHhxpfQ9depUNGvWDB8+fEDPnj2RmJiY6WOfP3+Ow4cPAwCGDRumlHiIiIiIiPIbFlJ50MePH9GpUydcvXoVJiYmCAkJgY2NjdL6V1dXR1BQEExNTfH3339jwoQJmT523bp1kEqlaNq0KSpWrKi0mIiIiIiI8hMWUnlMcnIyBg0ahLNnz8LAwADHjh1DpUqVlD6OpaUlNm/eDABYtWoV9u3b98NjUlJSEBAQAABKW4uKiIiIiCg/YiGVh6SmpqJfv344deoU9PT0EBwcjJo1a+bYeK1bt8bEiRMBAIMHD0ZUVNR32x84cADR0dEwNzdH586dcywuIiIiIqK8joVUHhIdHY3Lly9DS0sLe/bsQYMGDXJ8TC8vL9SoUQNv376Fi4sLhBDfbPtlkolBgwZBS0srx2MjIiIiIsqrWEjlISVKlMDZs2exYcMGODg45MqYWlpaCAoKgo6ODo4ePSorlr724MEDnDx5EmpqahgyZEiuxEZERERElFexkMpjSpUqhRYtWuTqmJUqVYK3tzcAYMKECRlOie7v7w8AaNeuHUqWLJmr8RERERER5TUspAgA4ObmBnt7e3z69An9+vVDSkqKbN/Hjx+xceNGAJxkgoiIiIgIYCFF/09NTQ2BgYEwMjLC1atXMWfOHNm+nTt34v3797C2tkarVq1UGCURERERUd7AQopkihcvLruFb968ebh48SKA/00yMXToUKipMWWIiIiIiPhbMcnp0aMH+vXrB6lUiv79++PMmTMIDQ2FlpYWXFxcVB0eEREREVGewEKK0vH19UXJkiXx5MkTtG/fHgDQrVs3mJqaqjgyIiIiIqK8gYUUpWNoaIhNmzZBIpEgISEBADBs2DAVR0VERERElHewkKIMNW3aFOPHjwcAVKlSBQ0bNlRxREREREREeYeGqgOgvGvevHn45Zdf0LhxY0gkElWHQ0RERESUZ7CQom/S1NTE4MGDVR0GEREREVGew1v7iIiIiIiIsoiFFBERERERURYVmELKz88P1tbW0NHRQa1atXDu3DlVh0RERERERAVUgSikdu7cCXd3d0ybNg03btxAo0aN0KZNGzx//lzVoRERERERUQFUIAopHx8fuLq6YtCgQahYsSKWLVsGKysrrF69WtWhERERERFRAZTvZ+1LTk7GtWvXMHnyZLntDg4OuHjxYobHJCUlISkpSfY+Li4OACCVSiGVSnMu2EyQSqUQQqg8DspfmDekKOYOKYJ5Q4pg3pCicjt3MjtOvi+k3rx5g7S0NJibm8ttNzc3R3R0dIbHzJ8/H56enum2v379GomJiTkSZ2ZJpVLExsZCCAE1tQJxwZByAfOGFMXcIUUwb0gRzBtSVG7nTnx8fKba5ftC6ouvF4wVQnxzEdkpU6Zg3LhxsvdxcXGwsrKCqakpDAwMcjTOH5FKpZBIJDA1NeWHDGUa84YUxdwhRTBvSBHMG1JUbueOjo5Optrl+0LKxMQE6urq6a4+xcTEpLtK9YW2tja0tbXTbVdTU8sT/7AlEkmeiYXyD+YNKYq5Q4pg3pAimDekqNzMncyOke8LKS0tLdSqVQshISHo0qWLbHtISAg6deqUqT6EEAD+96yUKkmlUsTHx0NHR4cfMpRpzBtSFHOHFMG8IUUwb0hRuZ07X2qCLzXCt+T7QgoAxo0bh/79+6N27dqoX78+1q5di+fPn2PYsGGZOv7LfZBWVlY5GSYREREREeUT8fHxMDQ0/Ob+AlFI9ezZE2/fvsWcOXMQFRUFW1tbBAcHo1SpUpk63tLSEhEREdDX1//mc1W55cvzWhERESp/XovyD+YNKYq5Q4pg3pAimDekqNzOHSEE4uPjYWlp+d12EvGja1aUq+Li4mBoaIjY2Fh+yFCmMW9IUcwdUgTzhhTBvCFF5dXc4Q2qREREREREWcRCioiIiIiIKItYSOUx2tramDVrVobTsxN9C/OGFMXcIUUwb0gRzBtSVF7NHT4jRURERERElEW8IkVERERERJRFLKSIiIiIiIiyiIUUERERERFRFrGQIiIiIiIiyiIWUnmMn58frK2toaOjg1q1auHcuXOqDonykPnz56NOnTrQ19eHmZkZOnfujAcPHsi1EUJg9uzZsLS0hK6uLpo2bYo7d+6oKGLKi+bPnw+JRAJ3d3fZNuYNZeTly5fo168fihYtCj09PVSvXh3Xrl2T7WfeUEZSU1Mxffp0WFtbQ1dXFzY2NpgzZw6kUqmsDXOHzp49iw4dOsDS0hISiQT79++X25+ZHElKSsKoUaNgYmKCQoUKoWPHjnjx4kWunQMLqTxk586dcHd3x7Rp03Djxg00atQIbdq0wfPnz1UdGuURZ86cwciRI/HXX38hJCQEqampcHBwwIcPH2RtFi5cCB8fH/j6+iI0NBQWFhawt7dHfHy8CiOnvCI0NBRr165F1apV5bYzb+hr7969Q4MGDaCpqYk//vgDd+/exZIlS1CkSBFZG+YNZcTb2xv+/v7w9fXFvXv3sHDhQixatAgrV66UtWHu0IcPH1CtWjX4+vpmuD8zOeLu7o59+/Zhx44dOH/+PBISEtC+fXukpaXlzkkIyjN+/fVXMWzYMLltFSpUEJMnT1ZRRJTXxcTECADizJkzQgghpFKpsLCwEAsWLJC1SUxMFIaGhsLf319VYVIeER8fL8qVKydCQkJEkyZNxJgxY4QQzBvKmIeHh2jYsOE39zNv6FvatWsnXFxc5LY5OjqKfv36CSGYO5QeALFv3z7Z+8zkyPv374WmpqbYsWOHrM3Lly+FmpqaOHr0aK7EzStSeURycjKuXbsGBwcHue0ODg64ePGiiqKivC42NhYAYGxsDAAIDw9HdHS0XB5pa2ujSZMmzCPCyJEj0a5dO7Rs2VJuO/OGMnLw4EHUrl0b3bt3h5mZGWrUqIF169bJ9jNv6FsaNmyIP//8E//88w8A4O+//8b58+fRtm1bAMwd+rHM5Mi1a9eQkpIi18bS0hK2tra5lkcauTIK/dCbN2+QlpYGc3Nzue3m5uaIjo5WUVSUlwkhMG7cODRs2BC2trYAIMuVjPLo2bNnuR4j5R07duzA9evXERoamm4f84Yy8uTJE6xevRrjxo3D1KlTceXKFYwePRra2toYMGAA84a+ycPDA7GxsahQoQLU1dWRlpaGuXPnonfv3gD4mUM/lpkciY6OhpaWFoyMjNK1ya3fnVlI5TESiUTuvRAi3TYiAHBzc8OtW7dw/vz5dPuYR/RfERERGDNmDI4fPw4dHZ1vtmPe0H9JpVLUrl0b8+bNAwDUqFEDd+7cwerVqzFgwABZO+YNfW3nzp0ICgrCtm3bULlyZdy8eRPu7u6wtLSEk5OTrB1zh35EkRzJzTzirX15hImJCdTV1dNV0DExMemqcaJRo0bh4MGDOHXqFEqUKCHbbmFhAQDMI5Jz7do1xMTEoFatWtDQ0ICGhgbOnDmDFStWQENDQ5YbzBv6r2LFiqFSpUpy2ypWrCibAImfN/QtEydOxOTJk9GrVy9UqVIF/fv3x9ixYzF//nwAzB36sczkiIWFBZKTk/Hu3btvtslpLKTyCC0tLdSqVQshISFy20NCQmBnZ6eiqCivEULAzc0Ne/fuxcmTJ2FtbS2339raGhYWFnJ5lJycjDNnzjCPfmItWrTA7du3cfPmTdmrdu3a6Nu3L27evAkbGxvmDaXToEGDdMsr/PPPPyhVqhQAft7Qt338+BFqavK/Yqqrq8umP2fu0I9kJkdq1aoFTU1NuTZRUVEICwvLvTzKlSktKFN27NghNDU1xfr168Xdu3eFu7u7KFSokHj69KmqQ6M8Yvjw4cLQ0FCcPn1aREVFyV4fP36UtVmwYIEwNDQUe/fuFbdv3xa9e/cWxYoVE3FxcSqMnPKa/87aJwTzhtK7cuWK0NDQEHPnzhUPHz4UW7duFXp6eiIoKEjWhnlDGXFychLFixcXhw8fFuHh4WLv3r3CxMRETJo0SdaGuUPx8fHixo0b4saNGwKA8PHxETdu3BDPnj0TQmQuR4YNGyZKlCghTpw4Ia5fvy6aN28uqlWrJlJTU3PlHFhI5TGrVq0SpUqVElpaWqJmzZqyaa2JhPg8PWhGr8DAQFkbqVQqZs2aJSwsLIS2trZo3LixuH37tuqCpjzp60KKeUMZOXTokLC1tRXa2tqiQoUKYu3atXL7mTeUkbi4ODFmzBhRsmRJoaOjI2xsbMS0adNEUlKSrA1zh06dOpXh7zROTk5CiMzlyKdPn4Sbm5swNjYWurq6on379uL58+e5dg4SIYTInWtfREREREREBQOfkSIiIiIiIsoiFlJERERERERZxEKKiIiIiIgoi1hIERERERERZRELKSIiIiIioixiIUVERERERJRFLKSIiIiIiIiyiIUUERH9NGbPno3q1aurOgwiIioAuCAvEREVCBKJ5Lv7nZyc4Ovri6SkJBQtWjSXoiIiooKKhRQRERUI0dHRsv/fuXMnZs6ciQcPHsi26erqwtDQUBWhERFRAcRb+4iIqECwsLCQvQwNDSGRSNJt+/rWPmdnZ3Tu3Bnz5s2Dubk5ihQpAk9PT6SmpmLixIkwNjZGiRIlsGHDBrmxXr58iZ49e8LIyAhFixZFp06d8PTp09w9YSIiUikWUkRE9FM7efIkIiMjcfbsWfj4+GD27Nlo3749jIyMcPnyZQwbNgzDhg1DREQEAODjx49o1qwZChcujLNnz+L8+fMoXLgwWrdujeTkZBWfDRER5RYWUkRE9FMzNjbGihUrUL58ebi4uKB8+fL4+PEjpk6dinLlymHKlCnQ0tLChQsXAAA7duyAmpoaAgICUKVKFVSsWBGBgYF4/vw5Tp8+rdqTISKiXKOh6gCIiIhUqXLlylBT+9/fFc3NzWFrayt7r66ujqJFiyImJgYAcO3aNTx69Aj6+vpy/SQmJuLx48e5EzQREakcCykiIvqpaWpqyr2XSCQZbpNKpQAAqVSKWrVqYevWren6MjU1zblAiYgoT2EhRURElAU1a9bEzp07YWZmBgMDA1WHQ0REKsJnpIiIiLKgb9++MDExQadOnXDu3DmEh4fjzJkzGDNmDF68eKHq8IiIKJewkCIiIsoCPT09nD17FiVLloSjoyMqVqwIFxcXfPr0iVeoiIh+IlyQl4iIiIiIKIt4RYqIiIiIiCiLWEgRERERERFlEQspIiIiIiKiLGIhRURERERElEUspIiIiIiIiLKIhRQREREREVEWsZAiIiIiIiLKIhZSREREREREWcRCioiIiIiIKItYSBEREREREWURCykiIiIiIqIsYiFFRERERESURf8HZVwVt7GctLQAAAAASUVORK5CYII=", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = run_sequence_plot(time[:-5], train, title=f\"Simple average - MSE: {simple_mse:.2f}\")\n", "ax.plot(time[-5:], test, color='tab:blue', linestyle=\"--\", label=\"test\")\n", "ax.plot(time[-5:], simple_avg_preds, color='tab:orange', linestyle=\"--\", label=\"preds\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Single Exponential" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictions: [196.61657923 196.61657923 196.61657923 196.61657923 196.61657923]\n", "MSE: 136.2446911548019\n" ] } ], "source": [ "from statsmodels.tsa.api import SimpleExpSmoothing\n", "\n", "single = SimpleExpSmoothing(train).fit(optimized=True)\n", "single_preds = single.forecast(len(test))\n", "single_mse = mse(test, single_preds)\n", "print(\"Predictions: \", single_preds)\n", "print(\"MSE: \", single_mse)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = run_sequence_plot(time[:-5], train, title=f\"Simple exponential smoothing - MSE: {single_mse:.2f}\")\n", "ax.plot(time[-5:], test, color='tab:blue', linestyle=\"--\", label=\"test\")\n", "ax.plot(time[-5:], single_preds, color='tab:orange', linestyle=\"--\", label=\"preds\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- This is certainly better than the simple average method but it's still pretty crude. \n", "- Notice how the forecast is just a horizontal line. \n", "- Single Exponential Smoothing cannot pick up neither trend nor seasonality." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Double Exponential" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictions: [198.62600614 200.63543303 202.64485991 204.6542868 206.66371368]\n", "MSE: 82.95678016291609\n" ] } ], "source": [ "from statsmodels.tsa.api import Holt\n", "\n", "double = Holt(train).fit(optimized=True)\n", "double_preds = double.forecast(len(test))\n", "double_mse = mse(test, double_preds)\n", "print(\"Predictions: \", double_preds)\n", "print(\"MSE: \", double_mse)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = run_sequence_plot(time[:-5], train, title=f\"Double exponential smoothing - MSE: {double_mse:.2f}\")\n", "ax.plot(time[-5:], test, color='tab:blue', linestyle=\"--\", label=\"test\")\n", "ax.plot(time[-5:], double_preds, color='tab:orange', linestyle=\"--\", label=\"preds\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "- Double Exponential Smoothing can pickup on trend, which is exactly what we see here. \n", "- This is a significant leap but no quite yet the prediction we would like to get." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "### Triple Exponential" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predictions: [204.468726 207.03255819 215.74668895 209.88430558 202.24064983]\n", "MSE: 28.93848905442322\n" ] } ], "source": [ "from statsmodels.tsa.api import ExponentialSmoothing\n", "\n", "triple = ExponentialSmoothing(train,\n", " trend=\"additive\",\n", " seasonal=\"additive\",\n", " seasonal_periods=13).fit(optimized=True)\n", "triple_preds = triple.forecast(len(test))\n", "triple_mse = mse(test, triple_preds)\n", "print(\"Predictions: \", triple_preds)\n", "print(\"MSE: \", triple_mse)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 1000x350 with 1 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = run_sequence_plot(time[:-5], train, title=f\"Triple exponential smoothing - MSE: {triple_mse:.2f}\")\n", "ax.plot(time[-5:], test, color='tab:blue', linestyle=\"--\", label=\"test\")\n", "ax.plot(time[-5:], triple_preds, color='tab:orange', linestyle=\"--\", label=\"preds\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "- Triple Exponential Smoothing pickups trend and seasonality. \n", "- Clearly, this is the most suitable approach for this data.\n", "- We can summarize the results in the following table:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " MSE\n", "simple 9549.121874\n", "single 136.244691\n", "double 82.956780\n", "triple 28.938489\n" ] } ], "source": [ "data_dict = {'MSE':[simple_mse, single_mse, double_mse, triple_mse]}\n", "df = pd.DataFrame(data_dict, index=['simple', 'single', 'double', 'triple'])\n", "print(df)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" }, "tags": [] }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Summary\n", "\n", "In this lecture we learned\n", "\n", "1. What is smoothing and why it is necessary.\n", "2. Some common smoothing techniques.\n", "3. A basic understanding of how to smooth time series data with Python and generate forecasts.\n", "---" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Exercises\n", "\n", "Load the following two time series." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "144\n", "1000\n" ] } ], "source": [ "# Load the first time series\n", "response = requests.get(\"https://zenodo.org/records/10897398/files/smoothing_ts1.npy?download=1\")\n", "response.raise_for_status()\n", "smoothing_ts1 = np.load(BytesIO(response.content))\n", "print(len(smoothing_ts1))\n", "\n", "# Load the second time series\n", "response = requests.get(\"https://zenodo.org/records/10897398/files/smoothing_ts4_4.npy?download=1\")\n", "response.raise_for_status()\n", "smoothing_ts2 = np.load(BytesIO(response.content))\n", "print(len(smoothing_ts2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using on what you learned in this and in the previous lectures, do the following.\n", "\n", "1. Create two time variables called `mytime1` and `mytime2` that starts at 0 and are as long as each dataset.\n", "2. Split each dataset into train and test sets (as the test, use the last 5 observations).\n", "3. Identify trend and seasonality, if present.\n", "4. Identify if trend and/or seasonality are additive or multiplicative, if present.\n", "5. Create smoothed model on the train set and use to forecast on the test set.\n", "6. Calculate MSE on test data.\n", "7. Plot training data, test data, and your model's forecast for each dataset." ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.16" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }