{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[online booklet](https://media.readthedocs.org/pdf/a-little-book-of-r-for-time-series/latest/a-little-book-of-r-for-time-series.pdf)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "%load_ext rmagic\n", "\n", "%R library(forecast)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "metadata": {}, "output_type": "display_data", "text": [ "This is forecast 4.8 \n", "\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Reading TS**" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## King's ages\n", "kings <- scan(\"http://robjhyndman.com/tsdldata/misc/kings.dat\",skip=3)\n", "kings <- ts(kings)\n", "\n", "# NY city birth data\n", "births <- scan(\"http://robjhyndman.com/tsdldata/data/nybirths.dat\")\n", "births <- ts(births, frequency = 12, start = c(1946, 1))\n", "\n", "## monthly sale for souvenir shop\n", "## trend, seasonality non-additive\n", "## but its LOG transform can be modelled as trend, seasonality and additive\n", "souvenir <- scan(\"http://robjhyndman.com/tsdldata/data/fancy.dat\")\n", "souvenir <- ts(souvenir, frequency = 12, start = c(1987, 1))\n", "\n", "## london rainfall in inches from 1813 to 1912\n", "## constant-level, non-seasonality, additive\n", "rain <- scan(\"http://robjhyndman.com/tsdldata/hurst/precip1.dat\",skip=1)\n", "rain <- ts(rain, start = c(1813))\n", "\n", "## women's skirts diameter at the hem from 1866 to 1911\n", "## linear trend, non-seasonality and addtive\n", "skirts <- scan(\"http://robjhyndman.com/tsdldata/roberts/skirts.dat\",skip=5)\n", "skirts <- ts(skirts, start = c(1866))\n", "\n", "## Vocanic Dust Veil in Northern Hemisphere\n", "## 1500 to 1969\n", "dusts <- scan(\"http://robjhyndman.com/tsdldata/annual/dvi.dat\", skip=1)\n", "dusts <- ts(dusts, start = c(1500))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Read 42 items\n", "Read 168 items\n", "Read 84 items\n", "Read 100 items\n", "Read 46 items\n", "Read 470 items\n" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Plotting TS**" ] }, { "cell_type": "code", "collapsed": false, "input": [ "## the plot suggests an additive model \n", "## as random fluctuations in the data are constant\n", "%R plot.ts(kings)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IY5XFIbgq8o8HF1Fy2MIYprhRDgl+4qJQE8zpakZ45t3e440R9Y+j5byikTyCi5omSzDg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\nY3vjeIybeQXdkq4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} ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "## We can see from this time series that there seems to be seasonal variation in the number of births per month:\n", "## there is a peak every summer, and a trough every winter. Again, it seems that this time series could probably be\n", "## described using an additive model, as the seasonal \ufb02uctuations are roughly constant in size over time and do not\n", "## seem to depend on the level of the time series, and the random \ufb02uctuations also seem to be roughly constant in\n", "## size over time.\n", "%R plot.ts(births)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wzJ9z7HSuR3IJI0fTZzY67ZSA2uJKAycVPCkD+44C7H2PvAtso+Q7efIBcc+Q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\n9UaCHcSE1bU5naGwAMPzBB8Nl6SQQq4M1apvT49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} ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## In this case, it appears that an additive model is not appropriate for describing this time series, since the size of\n", "## the seasonal \ufb02uctuations and random \ufb02uctuations seem to increase with the level of the time series. Thus, we may\n", "## need to transform the time series in order to get a transformed time series that can be described using an additive\n", "## model. For example, we can transform the time series by calculating the natural log of the original data\n", "par(mfrow = c(2, 1))\n", "plot.ts(souvenir)\n", "## Here we can see that the size of the seasonal \ufb02uctuations and random \ufb02uctuations in the log-transformed time\n", "## series seem to be roughly constant over time, and do not depend on the level of the time series. Thus, the log\n", "## transformed time series can probably be described using an additive model.\n", "plot.ts(log(souvenir))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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} ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Decomposing TS**\n", "\n", "(1) First make sure that the sereis can be described as an additive model by checking its fluctutation is roughly constantly sized. Otherwise making a transformation first. (2) Then check there is a frequency > 1 in the data\n", "\n", "Decomposing a time series means separating it into its constituent components, which are usually a trend component and an irregular component, and if it is a seasonal time series, a seasonal component.\n", "\n", "The seasonal component is better described as a weakly stationary series. (constant mean function and auto-covariance functions that only depends on the distance of lag)\n", "\n", "To estimate the trend component of a non-seasonal time series that can be described using an *additive model*, it is common to use a *smoothing* method (**sepcially for non-seasonal series**), such as calculating the simple moving average of the time series. The smoothing step is filtering out how frequency noise and useful to find trend and seasonal components." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## for example, to find the trend of the king ages, \n", "## we use the moving average to smooth the curve, \n", "## the order of the smoothing depends on trial and error\n", "\n", "## we can see the trend is roughly that going up first\n", "## and then going down\n", "plot.ts(kings, col = 1)\n", "lines(filter(kings, sides = 2, \n", " method = \"convolution\", \n", " filter = rep(1./3, 3)),\n", " col = 2)\n", "lines(filter(kings, sides = 2, \n", " method = \"convolution\", \n", " filter = rep(1./9, 9)),\n", " col = 3)\n", "legend(\"topleft\", \n", " c(\"original\", \"3-moving average\", \"9-moving average\"),\n", " col = 1:3, lty = 1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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BAx6PN3/+/IyMDMp1KC9NuRQJVKiiijlz5vD58k/dhg0b7ty5Y9796ElcXFx2djb+dPjw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\nQUFBbJ4abNiMoG2bAmdmUnW1dSWG/Qj62rVrTgM6KIiCg0mjsT5ms5g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cYvoloYcRgEMI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\nHv1LhAAAAABJRU5ErkJggg==\n" } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## decomposition of trend + sesonal + irregular\n", "## for birth data\n", "births.stl <- decompose(births)\n", "plot(births.stl)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Jhgy+bf7jh0ecr+qcpYAOg59oN/N8NbH43xmqI0++A3joI/ghb+u//BlEqLrlQZ4w+ecK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\nc9p7TDs89232pp2Nf2aSEt9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F4DikCzU5LZfYnnjrNw9Dp+3uKLtFTsqBTeYodFrlPFmL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\nD94Mkpw445T7sSItFP/G8TBrsMIafh0y8Yjlku6UDa13CictF+edHku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pU7D2anXWLCa5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\ngg==\n" } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## and use the Acf to check the quality of the decomposition\n", "par(mfrow = c(2, 2))\n", "Acf(births.stl$x, lag.max = 24)\n", "Acf(na.omit(births.stl$trend, lag.max = 24))\n", "Acf(na.omit(births.stl$seasonal, lag.max = 24))\n", "Acf(na.omit(births.stl$random, lag.max = 24))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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jTe9yefJExZ05dGT06P/dAkSavaOGvYxyZNy4oL/++ktxt4limfnzt7700jfs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\nFW/f8aEE5sMPP1ywYIHWm01KSlq5ciU7/tVXX12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} ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Forecasts by Exponential Smoothing**\n", "\n", "Mostly used to make short-term forecasts for time series\n", "\n", "- **Simple Exponential Smoothing (constant-level, non-seasonality, additive) **: If you have a time series that can be described using an **additive model with constant level** and **no seasonality**, you can use simple exponential smoothing to make short-term forecasts. The SES provides a way of estimating the constant level at the current time point. Control parameter $\\alpha$ (between 0 and 1) controls the weight placed on the most recent observations when making forecasts of future values. $\\alpha = 1$ means very little weight is placed on most recent observations and small $\\alpha$ means the forecast depends on both recent and less recent observations\n", "\n", " Simple Exponential Smoothing is implemented as HoltWinters() smoothing in R. set `beta = F` and `gamma = F` in HoltWinters to choose the \"SIMPLE\" smoothing. The forecasts made by HoltWinters() are stored in a named element called \"fitted\"\n", "\n", "- **Holt's Exponential Smoothing (increasing/decreasing trend, non-seasonality, additive)**: it estimates the level and scope. Smoothing is controlled by two parameters, $\\alpha$, for the estimate of the level at the current time point, and $\\beta$ for the estimate of the slope b of the trend component at the current time point. As with simple exponential smoothing, the paramters $\\alpha$ and $\\beta$ have values between 0 and 1, and values that are close to 0 mean that little weight is placed on the most recent observations when making forecasts of future values\n", "\n", "- **Holt Winters Exponential Smoothing (trend, seasonality, additive)**: Holt-Winters exponential smoothing estimates the level, slope and seasonal component at the current time point. Smoothing is controlled by three parameters: $\\alpha$, $\\beta$, and $\\gamma$, for the estimates of the level, slope b of the trend component, and the seasonal component, respectively, at the current time point. The parameters alpha, beta and gamma all have values between 0 and 1, and values that are close to 0 mean that relatively little weight is placed on the most recent observations when making forecasts of future values." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## the rain data:\n", "## 1. it is roughly at constant level - the mean stays at 25 inches\n", "## 2. the random flucutations seem to be roughly constant in size over time\n", "## so it is approporiate to describe it as an additive model\n", "## 3. no obvious seasonality (frequency = 1)\n", "## THUS, we use SES to do short time forecast\n", "plot.ts(rain)\n", "\n", "rain.hw <- HoltWinters(rain, beta = F, gamma = F)\n", "print(rain.hw)\n", "## alpha = 0.024 (close to zero) means forecasts are based on \n", "## both recent and less recent observations\n", "plot(rain.hw)\n", "\n", "## measure of fitting errors\n", "print(paste(\"SSE\", rain.hw$SSE))\n", "\n", "## use Holt Winters to predict on the future\n", "rain.future <- forecast.HoltWinters(rain.hw, h = 8)\n", "plot(rain.future)\n", "\n", "## if there is still correlaton between forecast error \n", "## for successive predictions, the model can still be\n", "## improved on - usually it means that the simple SES\n", "## should be replaced by other more sphotistcated models\n", "Acf(residuals(rain.hw))\n", "## it is also a good idea to check if the residuals follow\n", "## a zero mean and constant variance Gaussian, to see if the\n", "## prediction can be further improved\n", "plot(density(residuals(rain.hw)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Holt-Winters exponential smoothing without trend and without seasonal component.\n", "\n", "Call:\n", "HoltWinters(x = rain, beta = F, gamma = F)\n", "\n", "Smoothing parameters:\n", " alpha: 0.02412151\n", " beta : FALSE\n", " gamma: FALSE\n", "\n", "Coefficients:\n", " [,1]\n", "a 24.67819\n", "[1] \"SSE 1828.8548918638\"\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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3bs8++6xeA/NdaB00OmgEcTsmk6kdG8Pi4mKNl5+2traAgAAAWLx48a5du3Qalw9DJgnR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nZ6euN8wukskkRBxi5KlA49tVXR1ztKQi2RJxYIG2zEEbm0FjB62X9AWa3EIZ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\nsSgeiF3OelMDlKyATqM+/fTTYDD45ptv9vT0XH/99Xg8fe3atbNnz/6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}, { "metadata": {}, "output_type": "display_data", "png": 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WdPvSVNMgPHqbJnS1y06yva6ybMPNhBtAzb1wC8XfIv3fHgV8/iiU4QdjohLB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\nolmiwQXZiojguOiSiLtAtiMiOMUREZziiAhOcUQEpzgiglM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R0AAgKQIaACRFQAOApAhoAJAUAQ0AkiKgAUBSBDQASIqABgBJEdAAICkCGgAk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\n7mHfvn0PPfSQTqd74oknSkp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} ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## linear trend, non-seasonality and addtitive forecast\n", "## by Holt's exponential smoothing\n", "\n", "## non-seasonal, roughly additive (constant flucutation), \n", "plot.ts(skirts)\n", "\n", "## high values of alpha and beta meaning that\n", "## the forecast is heavily on most recent values\n", "## it is intuitive since both the level and slope \n", "## change quite a lot over time\n", "skirts.holt <- HoltWinters(skirts, gamma = F)\n", "print(skirts.holt)\n", "print(skirts.holt$SSE)\n", "\n", "## predict on the fit\n", "plot(skirts.holt)\n", "\n", "## predict on the future\n", "plot(forecast(skirts.holt, h = 10))\n", "\n", "## check residuals\n", "plot(density(residuals(skirts.holt)))\n", "## lag 5 exceeds significance bounds, however its odds\n", "## is 1 out of 20 for 95% interval\n", "Acf(residuals(skirts.holt))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Holt-Winters exponential smoothing with trend and without seasonal component.\n", "\n", "Call:\n", "HoltWinters(x = skirts, gamma = F)\n", "\n", "Smoothing parameters:\n", " alpha: 0.8383481\n", " beta : 1\n", " gamma: FALSE\n", "\n", "Coefficients:\n", " [,1]\n", "a 529.308585\n", "b 5.690464\n", "[1] 16954.18\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ChW0bv7nMzs3Nzc3NrUPj2rVrCwsL2R+RkzTfIayqAlFRoFDIjsMFHBwcDh48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\nVlRUBAYGJicnsxrlpRmZ3WCjuWdnjI5fWlpqa2t78eLFysr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2fPjwAQMGqNXqyMjI8PBwFkbn0L59+/z9/Xn9q4+wcuVKPz+/Pn364OtIM61c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\nrP6JV65ccXNza9GixaRJk0pLS1kNXUt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} ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "\n", "## log of souvenir - trend, seasonality and additive\n", "log.souvenir <- log(souvenir)\n", "\n", "## seasonal, and roughly constant fluctuation\n", "plot.ts(log.souvenir)\n", "\n", "## holt winter fit\n", "## relatively small value of alpha means the level prediction\n", "## depends on both recent and further past values.\n", "## big value of gamma means \n", "## the seasonality is based on very recent values\n", "## 0 beta means the trend (slope) is not updated with time series\n", "log.souvenir.hw <- HoltWinters(log.souvenir)\n", "print(log.souvenir.hw)\n", "print(log.souvenir.hw$SSE)\n", "\n", "## plot the fit\n", "plot(log.souvenir.hw)\n", "## plot the forecast on the future\n", "plot(forecast(log.souvenir.hw, h = 24))\n", "\n", "## plot the residuals\n", "plot(density(residuals(log.souvenir.hw)))\n", "Acf(residuals(log.souvenir.hw))\n", "\n", "\n", "## plot future fit on original\n", "souvenir.forecast <- exp(forecast(log.souvenir.hw, h=50)$mean)\n", "par(mfrow=c(1, 2))\n", "plot(souvenir, col = 1)\n", "plot(souvenir.forecast, col = 2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Holt-Winters exponential smoothing with trend and additive seasonal component.\n", "\n", "Call:\n", "HoltWinters(x = log.souvenir)\n", "\n", "Smoothing parameters:\n", " alpha: 0.413418\n", " beta : 0\n", " gamma: 0.9561275\n", "\n", "Coefficients:\n", " [,1]\n", "a 10.37661961\n", "b 0.02996319\n", "s1 -0.80952063\n", "s2 -0.60576477\n", "s3 0.01103238\n", "s4 -0.24160551\n", "s5 -0.35933517\n", "s6 -0.18076683\n", "s7 0.07788605\n", "s8 0.10147055\n", "s9 0.09649353\n", "s10 0.05197826\n", "s11 0.41793637\n", "s12 1.18088423\n", "[1] 2.011491\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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OiYkJDAxU71ZXVwcHB3/22WdRUVEajA4ADkqLgNbpdLfddlvD3YiIiEcffbSgoGD79u3j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\nMk2cOHH48OH79++3YvVjx47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YbKzZbGbaoNDo9XpZTAzw2dWeiF3WIBCI2wG9Xg/QLNBxcWaTiWmDQqPX6+UiEdNW+IIE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QQmhcxezZs8vLy3ft2hUdHU0ISUlJ2b9///r1648ePerhXWvXrn3ttdccDtbV1eXn5wfx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\n/73Dtz777LPFixcHeD0s7mNp7969V19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TQyfw3DJrDq8Jn7ahCsBH3InA/P3RpkOrJVV8hDvRjryewkLl6USOc9s8LJ18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\njzhUMXCmoukLDF81vYhQb++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YGxur0Wj4nghCA7IOWuoOuofP26RJk9566y1/f//Vq1efPn1ap9NxPy1EOJg6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\njZWVlYNNAjhTgQ4JCelXoE37ePTmoI1G45dffrl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} ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**ARIMA Models**\n", "\n", "- About `Exponential Smoothing`: Exponential smoothing methods are useful for making forecasts, and *make no assumptions about the correlations\n", "between successive values of the time series.* However, if you want to make prediction intervals for forecasts made using exponential smoothing methods, the prediction intervals *require that the forecast errors are uncorrelated and are normally distributed with mean zero and constant variance.*\n", "- While exponential smoothing methods do not make any assumptions about correlations between successive values of the time series, in some cases you can make a better predictive model by taking correlations in the data into\n", "account. Autoregressive Integrated Moving Average (ARIMA) models include an explicit statistical model for the irregular component of a time series, that allows for non-zero autocorrelations in the irregular component.\n", "- In summary, *Exponential Smoothing* is more like a traditional statistics model, where the irregular part is supposed to be uncorrelated. On the other hand, *ARIMA* allows for non-zero autocorrelations in the irruglar component.\n", "- **ARIMA models are defined for stationary time series.** It means that the time series has a constant mean function and an auto-covariance function that depends only on time difference. **So, if you start off with a non-stationary time series, you will first need to \"difference\" the time series until you obtain a stationary time series.** If you have to difference the time series `d` times to obtain a stationary series, then you have an `ARIMA(p, d, q)` model, where `d` is the order of differencing used. Use `diff()` in R to difference a time series. \n", "- After find the appropriate `d` by `diff()` the time sereis to be stationary, the next step is to find the parameters `p` and `q` in the ARIMA model. To do this, you usually need to examine the **correlogram** and **partial correlogram** of the stationary time series. To plot them, use `acf()` and `pacf()` in R, or `Acf()` and `Pacf()` in forecast, to get the value estimates instead of plotting, use `plot = F` as the parameters to these functions.\n", "- **Intuitive Interpretation of ARIMA parameters**: \n", " - `d` is the order of differences that is needed to make a series stationary (constant mean and roughly constant autocorrelation). \n", " - `p` and `q` determine the type of the fitted model (two main types: autoregression and moving average): a nonzero `p` indicates an autoregression model, the order of which is determined by partial autocorrelation.\n", " - a nonzero `q` indicates a moving average model, the order of which is determined by correlogram (Acf)\n", " - We should try to select the SIMPLEST model, which gives the smallest sum of p + q. The `forecast` package comes up with a function `auto.arima` which can estimate `p, q, d` automatically from data\n", "- The two main types of models that ARIMA describes:\n", " - autogression (with a nonzero p), e.g., for `p = 2`\n", " $$x_t - \\mu = \\beta_1*(x_{t-1}-\\mu) + \\beta_2*(x_{t-2}-\\mu) + z_t$$\n", " where $x_t$ is the **stationary** time series under sudying, $\\mu$ is the mean of the time series, $\\beta_1$ and $\\beta_2$ are parameters to be estimated, and $z_t$ is white noise with mean zero and constant variance\n", " - moving average (with a nonzero q), e.g., for `q = 1`\n", " $$x_t - \\mu = z_t - \\theta*z_{t-1}$$\n", " where $x_t$ is the **stationary** time series, $\\mu$ is the mean of time series $x_t$, $z_t$ is the white noise with mean zero and constant variance, and $\\theta$ is the parameter to be estimated\n", " - mix of the two types" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "\n", "## Skirt series is not stationary (its mean is not constant), after \n", "## 2nd difference, it seems to be stationary\n", "par(mfrow = c(3, 1))\n", "plot(skirts)\n", "plot(diff(skirts, differences = 1))\n", "plot(diff(skirts, differences = 2))\n", "## Now the 2nd differences does appear to be stationary\n", "## in mean and variance, as the level of the series\n", "## stays roughly constant over time, and the variance\n", "## of the series appears roughly constant over time.\n", "## so d = 2 in ARIMA\n", "\n", "par(mfrow = c(2, 1))\n", "Acf(diff(skirts, differences = 2)) ## q ~ 0 considering 5% odds\n", "Pacf(diff(skirts, differences = 2)) ## p ~ 1\n", "## so it indicates a ARIMA(p = 1, d = 2, q = 0) model\n", "skirts.arima <- auto.arima(skirts)\n", "print(skirts.arima)\n", "## gives ARIMA (1, 2, 0), which is a autoregression model\n", "\n", "## use ARIMA to fit \n", "plot.ts(skirts, col = 1)\n", "lines(skirts - skirts.arima$residuals, col = 2)\n", "## use ARIMA to predict\n", "plot(forecast(skirts.arima, h = 10))\n", "\n", "## check whether residuals are Normal with zero mean\n", "## check whether residuals are Acf uncorrleated\n", "par(mfrow = c(2, 1))\n", "Acf(skirts.arima$residuals)\n", "plot(density(skirts.arima$residuals))\n", "abline(v = 0, col = 2) \n", "## does look a very good fit - so better check the assumption \n", "## for ARIMA model" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Series: skirts \n", "ARIMA(1,2,0) \n", "\n", "Coefficients:\n", " ar1\n", " -0.2997\n", "s.e. 0.1424\n", "\n", "sigma^2 estimated as 388.7: log likelihood=-193.66\n", "AIC=391.33 AICc=391.62 BIC=394.9\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Cvm1paalUKuVyOfOyrODtFsHi5kDY3iL0Z5CXBW6wsgdNUZRMJpsyZcrw4cNz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\naAAAnkJAAwDwFAIaAICnENAAADz1/wFP3xbXx27kdgAAAABJRU5ErkJggg==\n" 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N9YyMhMePISuL6opQLYgjoN3d3SMjI319fdPT0wUCwcePH/39/WNjY93d3cXQ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\nxsbGxvPnzxcKhbdv3967d29CQkKfPn1Gjx7drdt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guA4lEIFzFnLSDWsLmZoOPIGbhH4t10aRwACcnsJYwVRgg/g7sQ67aXbWXo3s\nKhSYhYsJ/AiRnfU5opsy/lWzF6JlHNHGLkzgY9/Aj3UtgQ0f9aCx4+Em6q8LTvoFyTkE+Ns8bezC\nBJbCtQRu/M1PSOyUzZt9XmST3nubVo68pqBgbQzjI/Bp91VI7EQ1/JIssumXtCtfIDkHn91bvLTp\nnIUIfKc59zj0WNcSeHVxhPRO0jwxWvF6J7yteEdnCIpzCJB0L7VOE8MQgeOqVqVBj0Us8KtfVR2e\nctcHxT2w+CgAa0QexNNqgTeCUwjhDrbu1cQwROBJWfeTocciFnj1kG41h/v2Tr2pPhO97sZ68osw\n4Y1+vSChQf05BPhlArg6SxPLEIF/WFf9LfRYxAKPXqfqX9SBAwjcEN8spT5HCj5MugOMV+Ex9ecQ\nYP0B0O3PSbt0CoVliMDZ0TsOcLewGhCIBdaBVHiZD+VZLPg1Vn0mwp5TnwfzhLZR99jZxZImRvFS\npJ0YI5sB8OG0sWfzwi3sASJweo6B013I6fBHK3BTNPjg3Wj34T8sMVaOVGfi/mjTV4en0MaC/QC8\n+VTKRN0/tHOT/MTaXVa6qZxP4ZQw3sOkTiUHiMAT59VyyiJOhz9agY8b75pbwXZ77NaXAjDuvtpM\nzDln/k69JrBxPGVe8iLa/G9XuUmDvF7Bj6mgvBw7i1hpb0PHo6hXQwSuT03h+G04Hf5oBV5Qafwo\nnmvv4VQro3iHyjx80FkWqqYJbPWiCqjPJLQCny7fxUl5PvrmcLiLcwF1Xd1iPy9PrNi3SeJUcoAI\nfLT8WBk7vTEjKdPs8W0NDgwM/BPS6I6QD9Rnkr2VGGMNFzxMVpmH4o3WJfcu3sa3I6jPJWW8DSx6\ndZWZnKSzOWD9CuhBvlT7oc+HlTbnYhO/NFcOrB3c0zORnc4JtFR1B4/l1BEN5hZmm3uTffZM957a\nQjigxbq0mF/fO2/qezm6Gm7iyoyXUZykLQeAIeIy5JiW4aYvf1Yz0bcLeCJo2EMEjmhqGsFO5wRa\nqhG4xHMGO+Gu5WL6aYRd/9WLGOpztDpfSe142+LDGN7W/KPUZ4NE3XblMaDjJE27DsBLj1bxY46Y\nK+0zmYX3uyBjtes6/FxygAh8LTb6CjudE2ipQuDnQ9s4P8Ou7ZaFvC/tMXguh/rczGvXKWIy4zYL\nbOFuHW1qQUn5skLbTKUFk6AOKoOQNtxks5B7mKMMvs8BoHStyAHv5Pd5wNrBUbGcTHECLe0X2DDy\nEoh8yUpKr7VuC79oh8WNh6jPG1NZiUuVucbe+jBWvuKN6bA8/0M6YDY6/SinKTvNfCkvFB8k4m52\nL9QxQ5IX/gjAKzHvesn/S5X7r0EEniGwhYUCgTnX9LYFxnbNQVaSr22Xl8PeyLZrY/It6lPPur2e\n/ndlHYhbvmKstHEdS82fmb/nQI2eywJg9VFWUlu46as38IbIMQ8tlVU9swrhT11H3iKtxqR7xYEv\nhTe1cur/EIEnH6quFsmSGbkC31oz4pMFTB/YfS/j9XeD1ZPRGUgvH+NWQ2UQYL6iI5jXxqKkNYps\neL1nro2pZ289ZSk69m2D2VhQDsDJlayk6jnm7wYPm33DbWZFY5u1ARz0wZbWYbq+Phe+mPo8jXUV\nt58Fty3k9FlABM7Pzc8XtGFFjsBNe5OHpRx8BVal0Bdjn/9t46eB5S2y/goUvXZUhi0leh6jldXj\n1sitz0K5wH5knc5ib15saR/9Au1i8zM2rx4ks5KKdloWvh1n+nq+K2FYELOJG/3UsjD3ki3tnKnK\nfpx9qdhySvVKPw84KLCpyZ1TR1Xoi2YhKXB7lm7kRos7Ztdntsvzy3Wmr9FPGbtuKGGsxCrusrE2\nTZjXSelyoChGLuEOa7XXjf1ThVuqwX2+EButVLuD06CdW2Vdmrb7w5nZnp9uuWe8xp/btvfZrvSS\nDbbEnO+pz7fDBc+SYXJ9dk1cwG9wTOc27xT5ojlICXxs0F5GmNTpIMvj83qoOV9bmR4fVjfc14oH\nrZZbbrcePzot5AVIeCDfRDO3L/+Lctaq7bHCrSQzOZrH2tXESFt9vNPPd9FF89FXaCfRZduT41Gi\nLTHIHHPgx/e3GNFZcrA56i1ny2Pe1afIF80BLvCv0RPYlaWfvExdCV06S49C/TjGRtZv8jISel4B\ntuy3LITYgjHqxgBQwPUaQhZc8S0AAA1rSURBVJjPDWu8MZ659sT240++LW5kmsmHzW6Oc5vFZqb+\nYF1afsKWaLuXuyxCZVYIHPowzrp03ofjfU/mdWso8kVzgAms3zqUd646T+qnmbPHuu5Bb3rNltSv\nE3piPrZG1mLb7zar3KjRJNkWro/kJXl9YKzQj8/CPbw9behMD6ecc4wkZvWRQavO+j8G0b1Pw613\nZGWG+fuHHIFDN9Ct4CdurMr0bf4dCRG4SGALC4jAt/2yBTT61eciqBhjW02iH6BnlrN2XHxG6twc\nAq1nO5dtWfjgYay36z3EDuDS68Mv99fuZqzQJSkk8O5Xs/+LFXnAaZvb2JNj/n4fQKctLLcsLLM4\ncj8ECRwZyvDBVIcwC4woficYROAJR+xtJnVm+wnf+60hez1e29aKt9sWOS78K5JtcA62x6DtF9lp\nuuOG8/xRIqzcwk9r82T0AQXZLtgO8QDX3eYm1HVmW/SgSJ+QYfg90/eppXTaUWugQYj1Vg76ALi8\nZYleOJtevjyafxqFzSQ5ER0NX3psFfMnd8Z9x9iRvpnD2Z5a+Xeemdd0N7y1WuJtsrhUZtjL3WCh\nHOfttC3qfehkcWdlslkz1iWQc1Zk5zrz83QW4y56ZlGox3Y2usixUcpWZSLd1Am5y91XYTNJRkRH\nU+6wSRfkdhd4Wq8XA7flK1H6czlPD7KZX2n6qja3Vsvnyzq+z/+xUHKXm+3+ucUYlDVWcGfAaNoz\n/52YF2JnzTFVAXXMrmKLgYu21t5F/oCHRHbToCfI2kdxRqjRo6iZREd0dKzJzc39G6c3EbzbFRpZ\noqB+NNkapHJ/PGfLEbiLhUsBfdmdMpfmY821ro4Awf25rFknnL7Tlo0iRo1kndiQnjvWHySsjU4U\nv9+7PF4B0BjNTLI46FfYKta9XI8p6HXnJLxwN891pXd7zt0XKGwm0REd3YdLSkp0HJ/O8iE5Ctqd\nRg5Yi6cD3BKwLVSRoem0267FlOcWH8uql5wBS098RZq2PR7WGu5UhiP5xxwRO1us19nndDccx+vB\n4oSxrN5VwExZai7BRtBVhxFt7GPApc+5Zn6MMD0yj8zmbqAQF7jrFq+Z1JiZlMmobHIf0c1KJ1lq\nsroSZ/HCmIJ5kWswghk9PF7UI2+ttfScwe5oXyVYPQ8X6wYA+5dYFnwZD9IWsU6eUdan8Xa6/c17\nOLEOuAoSWS3Z06bnD9NXyxtdMv8c4LJmkfGjb5hgMJG4wOGf7dkDafEBFDFZ1vE4/rzOrzyJkY1s\nmL4EytdgsBWeh1hdqj3DAphNHwvF2fw0C3pvc6W/i/WoF/GV99mexoyoneOCEbgWGnw4D9xmU22R\n2Yi4wr1hPQWeSXHGq6A4R/AU4gJfSj1x4oTARhr1Ak83t9uYDkYLt7nlO4wWppPi0HoAztpC6J+x\n4ppOLO6M4pXuL3SC/kAzJ83VnSusx59I4N0V21mtXYtGVkF/w7xJHFeMqfmQz3CqcR/xjwSaQuC9\nrr5rsPAzz7l38LfmAKdrAoY8FDzvL2YwVp4bJY2hA05Z/Q1x90Bf2myO5Rhoaz/I1CWyhdWeEAm8\ny6W1pB8p8FDenv8qZSeMoipKEcwZQj9lX00bBR5BxoLAc4VI16i4wDXp2t/BLea+8AKBCJSpwt2d\ngmxnuZw9Db8y2qHM/oZ205MiJ5H1kDvMq7SwqDTdYsms2qPIY3c4fQ/52U7BHa/AoYlTOFFFrp7l\nvV7PvgSGvwZCnPoPkdaLuMD1141AM4cgLtpcfRW6yk8uk2+FXUebULeY0fe4hXHF7zLX2reOYAwP\nfePB6ubnE0E5L7xYd/1TwXhhptN5ou0RorBv+6yxPvAzy7nJdnW285pNEogLXLTSCPRYBAKbPbxe\nAo/jD4ItWL1gT3EIS6PigiGMW7SW0ZYbYfHMH/GyPAMfbo3yqJTI4vU448/KCS8VVO3cInp5jXXY\n3jOF46WoDuV1h5gpbCfQ4Vxl9iACxw7628c+0GMRCGxqFrwV7JUMF6jJPA/+v6sFLgZ2h9zD/8ms\nFdPd6eCFrS52fugj0PbNZLe4ImbQgQhx10E5p54dyvcQA7CA0bVnje8BZdKD1dgYa1mfsX1frM7H\nZEhfpSAQR0e8wQAfuoBA4HeUQ+NsjtCmzfwB0Sf/XtGTOYIXGd/GuUD+zBrCRvc3rKOL+huD/IJz\nr8lzqd6LAHmcxuhcoXoZs633cKxlYeMhgT1hxD1mxzIB1shwveIBaRCBA968Ee7KtIJibFKAsW7w\n5WmhLY+4V1fXrGhKqx8Hfc/ZUMUZ0MSOM1his+7LeJK3Cd2DIkyq5PqT9xfw97IET5qx9U1whwxK\nsrb0JqflVD+BXq5S2s0GE7gibOQF6LEoBM4q5zUErOjY9c96naV38XXUXHZbf0cx7AxnrR0Rd5Ps\nyB/F0yBuUEZdKn8v9pgWa7UiUGnoQmXGZm6bglEIZ/I7lyRw9iw7P2aLxbSAOawA+GId3bbd5sNq\ntcyGjfsB76yPoezvYLvBmMMdBSYUeDed1eSIfWb+FvnfxHkXFMOtFyTRU7x5KJ7lwtkCG9sWjXHC\nm35cQC+/Tfic6W76RccsoIfD/daW/gaDJ7xFCqGlhpvCD7zrYo8UW2zuBRZ1W4vjyesLL15gdbU/\njuZukwQu8HboEGQk44ND3x9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9E+WopuAWUbWagltEtZmm4OZQ1/xRfIuQG/agP4L+Pu/OnTvfunXL2dlZwWqR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\n7kNtIB9zc3Nzc3MVDCQWixuvOE6zAwBgKdzNDgC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} ], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "%%R\n", "## age of kings\n", "par(mfrow = c(3, 1))\n", "plot(kings)\n", "plot(diff(kings, differences = 1))\n", "plot(diff(kings, differences = 2))\n", "## so d = 1\n", "\n", "## estimate p and q by acf and pacf\n", "par(mfrow = c(1, 1))\n", "Acf(diff(kings), lag.max = 20) # q = 1\n", "#print(Acf(diff(kings), lag.max = 20, plot = F))\n", "Pacf(diff(kings), lag.max = 20) # p = 3\n", "#print(Pacf(diff(kings), lag.max = 20, plot = F))\n", "## so the esitmated ARIMA is either (p = 3, d = 1, q = 0)\n", "## or (p = 0, d = 1, q = 1) or a mix (p = x, d = 1, q = x)\n", "## so the simplest would be (p = 0, d = 1, q = 1)\n", "kings.arima <- auto.arima(kings)\n", "print(kings.arima) # (p = 0, d = 1, q = 1) an moving average model\n", "\n", "## check the residuals\n", "par(mfrow = c(2, 1))\n", "Acf(kings.arima$residuals)\n", "plot(density(kings.arima$residuals))\n", "abline(v = 0, col = 2)\n", "## looks good enough\n", "\n", "## see the forecast on the future\n", "plot(forecast(kings.arima, h = 5))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "Series: kings \n", "ARIMA(0,1,1) with drift \n", "\n", "Coefficients:\n", " ma1 drift\n", " -0.7463 0.3882\n", "s.e. 0.1294 0.6603\n", "\n", "sigma^2 estimated as 233.9: log likelihood=-165.76\n", "AIC=337.53 AICc=338.17 BIC=342.67\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ASiGgAQAohYAGAKAUAhoAgFIIaAAASiGgAQAohYAGAKAUAhoAgFIIaAAASik1oBmG+fr1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\nRHvJNmzY8Ouvv6qwVaAS9Aa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PHq1Ba0CF06dP/+tf/3L0FIAwaNDjgQceOH78eGZmpqenpxAiICBg165dqampBw4c0KA7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\nYII=\n" 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Bgxwc+DwXALghjSLSwcFh6NCh5tvr1q2ruw0AuBErvFDlueee074pANgcPpMQ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\nf+ygcZsLDQ31/K9PP/30scc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}, { "metadata": {}, "output_type": "display_data", "png": 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359oxNEwqy+mX81gNUqroS9BIzxqqHDk6ntYgtd+8CKrqEZqgvhOocnbZOkNP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\nz9FPdn6i9Po0wVjmJLf+9JS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3pijqyJEjo0ePjo2Nlf2HhEaNGvX27dtx48aNHz9eljhSqXTSpEk//fRTE++i\n24ji4mJra+uvv/76+PHjXC531KhRMkY7evRot27djh8/3qZNGxmj0SiKmjt37qJFi2SM8+DBg2XL\nll26dOnt27cTJkyQcRcMGjTozz//vH79+suXL+fPn08IEQqFMmZICCkpKeHz+fRjfX19kUhUXl4u\ne1i5YO0ZIcfTgcj7jGg+Rv5bUAy59KApiiopKfH39+/evfv169dlDPXw4cPnz59Xh9XQ0KioqGh2\ntN9++y00NJSiqOLiYtnHoKuVl5erqakVFxc3O8KGDRvc3d3px0KhkMvlyhKNdu7cueqYsoiOjp44\ncSL9uKKiQlNT8/Xr17IE/PXXXy0tLdu0afPDDz9wudyqqqrmxal5uP7222/VNy0tKSnh8Xj0bxY2\nL1rjC5sRTcYzomY0Gc+IWhtNxtOhoe0j+xnRbOhB/wv6ft5dunS5evWqq6urjNESEhLWrFlDPxYK\nhWpqarL8TOiZM2eOHj1qYmLSsWNHiURiYmJy5cqV5oW6fv36+fPn6ccaGhpcLleWxKytrasfq6mp\ncTgc2X8N9fDhw6GhoTIGIYRIJBKJREI/piiKLnzNjlZeXu7r65ubm1tYWOjp6fnJJ5/I5eeSbW1t\nq2dH3L9/v3379iz5eWLC4jNCjqcDkfcZ0XyK/z9BYeTSg46Pj3dycnpWQ7O7SBRFXb9+vXXr1lev\nXi0uLv7yyy9lvLV7SUlJTk5OTk7O7du31dTUcnJymt0fv3DhgqGhYUpKSklJydy5c728vGRJrKKi\nok2bNnv27CkpKZk9e7bsPV+pVGptbV3d1ZLFvXv3DAwM/v7775KSkunTp8s4iyMjI0NXV/fChQvP\nnz/v37//xo0bmx2q5uEqFostLCwOHDhQXl4+bNiwyMhIWaI1vvBDo8l+RtSMJuMZUTOU7KdDzWjy\nPSOaDQX6X8ybN6/Wf2kyftLZtm3bJ598YmBgMHLkSHl9aJJ9iEMqlW7atMne3l5fX9/f3z8/P1/G\nlK5everi4qKnp/fFF1/k5OTIGC0tLc3CwkL2r2dpf/75Z6dOnfh8Pt35lTHahg0bTE1NLS0tIyMj\nZcmw1uF6/fp1JyenVq1ajRs3rhn/77ZcgZb9jKiVhixnRL1rJJchDrmfEc2DH+wHAGAptgxsAQBA\nLSjQAAAshQINAMBSKNAAACyFAg0AwFIo0CAjZlkAACAASURBVAAALIUCDQDAUijQAAAshQINAMBS\nKNAAACyFAg0AwFIo0AAALIUCDQDAUijQAAAshQINAMBSKNAAACyFAg0AwFIo0AAALIUCDQDAUijQ\noLIEAgGHwykpKWE6EYBmQoEGAGApFGj46MTFxdnY2Ghra/fu3fvhw4f0wh07drRv3759+/Y7d+5s\n3749owkC/AcKNHxccnJypk2btnPnzpycnC5duqxZs4YQcvfu3W+//Xb//v2XLl3asmUL0zkC/AcK\nNHxcTE1NMzMz+/fvr62tbWJi8ubNG0JIfHz8+PHje/bsaWFh8e233zKdI8B/8JhOAECheDzeli1b\nEhMTDQwMNDU1+Xw+ISQvL69Hjx70C9q1a8doggD/gx40fFwOHDhw4sSJU6dOJScnh4SE0AvNzc2z\ns7Ppxzk5OcxlB/Ae9KBBxb1584bH+89xrq2t/fLlSz09PW1t7aKiop9//tnMzIwQEhgY+MUXXwQF\nBVlaWv7000+M5gvwP+hBg4rr0KGD0X/t3r177NixmpqaVlZW/v7+ixYtunr16u7du7t3775s2bJh\nw4Z5eHiEhITo6ekxnTUAIehBgwrT09OjKKru8qSkpOrHhYWFhJAHDx507tw5Pz+fftbU1FRhSQI0\nAj1oAFJaWhoSElJUVPTu3buff/55yJAhTGcEQAgKNAAhpE+fPjNmzOjWrZu9vb25ufnUqVOZzgiA\nEEI49X4GBAAAxqEHDQDAUijQAAAshQINAMBSKNAAACyFAg0AwFIo0AAALIUCDQDAUijQAAAshQIN\nAMBSKNAAACyFAg0AwFIo0AAALIUCDQDAUijQAAAshQINAMBSKNAAACyFAg0AwFIo0AAALIUCDQDA\nUijQAAAshQINAMBSKNAAACyFAg0AwFIo0AAALIUCDQDAUijQAAAshQINAMBSKNAAACyFAg0AwFIo\n0AAALIUCDQDAUijQAAAshQINAMBSKNAAACyFAg0AwFIo0AAALIUCDQDAUijQAAAshQINoDqWLl26\ncuVKprMAuUGBbhH37t3jcDidO3eWb9iKigoOh8Pj8eQSrYlJ3rx5s2PHjlwud/369c1o5V9z3rVr\nF4fDuX//fjOC1+vBgwccDqdDhw4fmomCyTefpKQkJyenyMjIJUuWdO/e/fTp03IJ20iSMh7kTVn9\n5cuX6+vrFxYWNq8JFYACrUw4HM6nn3766aef0n+6urpyOJwrV660aKPr1q3LzMzs27evs7Oz7NFq\n5fz27dsFCxYMGDCgS5cusgdvXK2txzg55vP06dNhw4a9ePGib9++rq6uT548GT58eH5+PquSbIaw\nsLB37959//33jLTOBmzpTUBTaGpq3rt3T8GNvnr1ihAye/bs/v37yz34zp078/Pzm9c3/1CMbL1G\nyDGfc+fOVVZWRkREvHr1isfjeXp6rlix4syZM2PGjGFPks1gZmY2YsSInTt3RkVFWVpaMpUGg9CD\nlpuioqKAgAAjIyMnJ6davdqsrKzhw4ebmJiYmJgEBwfn5uYSQgoLCzkcjomJyeHDhx0cHPh8vq+v\n74sXL+i3nD9//rPPPuPz+aampr6+vvRJUvNToaur640bNwghffr0iY+P9/X15XA4S5cupd++cuVK\nDoczbdo0GZN0dXU9ceIEISQgIGDhwoWEkOTk5D59+vD5fCMjIy8vr5s3b5L/ftqtHlW4cuUKh8Nx\ndXWt1XqtnAkhv/32m5mZ2bBhwwghmzdv5nA4pqam5eXlxcXFfD6fw+Hs379flp1SUFBgaWnJ4/ES\nExNrbr3GN35paWlISEirVq169eqVmJhYc13q3S+11LuJqlu8fPmyq6vrwYMHa+bz+PFjDodjZ2e3\ndu1aKysra2vr2NjYK1euuLi46OnpeXh4PH36tJHgRkZGhJCkpKQ3b94QQpYtWyYWi0ePHl230YZ2\ndEOrVmsgoqHjp/EDoN6ca2low3799dcSiWTLli3N2PuqgAJ5qKqq6tq1KyHEysrK2dlZTU2NENKp\nUyeKosrLy83NzXk8nq+vr7e3NyHExsZGIBAUFBQQQrhcLp/Pd3Fxod8SFhZGUVRhYaGuri6Hw/Hz\n86P7rRYWFm/fvn337h39FoqiTpw40b59e0LIkiVLnj17tm/fPkJI9+7d6Xzod128eFHGJE+cOOHk\n5EQImTlzZlpaWnZ2tra2NpfL9fDw6NWrFyHE2tpaKpXevXuXEGJnZ0c3dPny5epkGsmZ/gw+ZswY\n+l0SiYROe9myZXPmzCGE+Pr6SqXSD90X9HC2nZ3du3fvevbsSQiJi4urlUkjG18qlbq5uRFCzM3N\nnZ2d+Xx+9bo0tF9qtt7QJqJb1NXVbdu2LSHkwIEDNfPJzMykz0cNDY1OnTpVP7azs9PV1SWE+Pv7\nNxK8oqKC3rOEkJ49eyYkJEgkkurVrNloQzu6KYdcI8dPIwdAQznXjNzIhhWLxTo6On369PnQw0A1\noEDLR0JCAiGkS5cuAoFAKpVOnDix+tiNjY0lhEyYMKG4uLi4uNjT05MQ8scff9AnDyHk1q1bFEXt\n3LmTEOLo6EhRVFJSEn24P3/+nKKoWbNmBQQEZGZm1jymKYrq3r07IeTy5csURb19+1ZPT48Qkpub\n+/r1ax6P17ZtW/oslSVJiqKGDh1KCDl8+DBFUefOnfP29o6KiqIoqrS0lO5YFRcXN7FA18r56NGj\nhJAff/yxOsMHDx5oamrq6+tramry+fycnJxa2zkxMbFuJ8PPz6/ma+gCbWtrS3/AX7hwIb28boGu\nd+OnpKQQQtq1a/f69WupVEp/CqHXpaH9UrP1hjZRdYsrV64sKSmpqKiot0Dfv3+f+u//ryEhIVKp\n9MyZM9XbtqHgFEWVlZVFRERYWFjQcdzd3YVCYd1GG9rRTTnkGjl+GjkAGsq5ZuTGN2zPnj3V1dVr\nHcwfCQxxyEdaWhohJDAwkO4IjB07tvop+tjdtm2bqampqanp2bNnCSEPHjygn6U/LRJCevToQQgR\nCoWEEBcXF2tr6ydPnlhbWzs6Oqqpqa1evbrutISadHR0RowYQQg5fvz46dOnq6qqgoOD6T6O7ElW\nc3d3j46OFggEAwYMaNu2bVVVFSGE/rcZioqKCCEmJibVSzp16rR48eKysrLKyspVq1ZZWVnVeoux\nsbFXHdWdx5qePn26Z88eQoijo2NDCdS78emt5OfnZ2BgwOFwJk+eXP36puyXxjeRlpbWvHnzjI2N\nNTU16+ZjaWlJT4qgO7wDBgzgcDj0YzpCI8H5fP4PP/wwadKksWPHOjk5paSkVA8L1Gy0oR3dlFVr\n5PhpRFOOmcZbNzExEYvF9OjNxwZfEsqHRCIhhHA4HPrPmpVRJBIRQmbOnOnj41O9sF27drVeWf1e\nQoixsfHDhw/3799/5MiRpKSkNWvW/PLLLzdu3LCzs2skh9DQ0F27dh07dszc3JwQEhwcLK8kq/3z\nzz/u7u76+vrjxo2bOnXqlClTSkpKqp+lKIp+IJVKG8mzWs1VrkZXSUII3cOqpUePHsnJyU0JTghx\ncXG5efPmvHnzhg0bpqWlVfcF9W58elNwuVz6z5rzwBraLzUnOTS+iXR1dWv9r1lTrTlndaegNRQ8\nMjLy+PHj0dHRhJCOHTv269dvypQpOTk5dRttaEc35ZBr5Pih1XsANL5Bmr5hq4N/VNCDlg+6I3bw\n4EGhUEhRFN13o9ETyAQCwcCBAwcOHPjkyZOTJ08KBIJGoiUkJEydOlVTU/PgwYPFxcXe3t6VlZXn\nzp2r98XVnZEBAwaYmZmdPn36xIkTHTt27NatGyFEIpFkZWVlZWVJJBLZkzx8+LBEIpk8efKaNWt6\n9uz58uVLejld/rKzs1+9ekVRVEOp1sq5devWhJCap+udO3dWr17dqlUrXV3dRYsWVX8zVu369esD\n61i8eHHdJszMzC5dutSzZ8/nz5+vXbu28Xxqovuwx44do1d/27Zt1U81tF9qbuSGNpFcNBTczMzs\nxo0bUVFRBQUF+fn5v//+OyGk7pe0pOEd3ZRDrpHjp5EDoCkbpPHWX758qa6ubmhoKMOWU1rMja6o\nFJFIZGtrSwhp164dXRnJf4fniouL6S/ZAwMD6fFcW1vbsrIyenzQ2NiYjlD91RZFUXQnUUtLa8iQ\nIX5+fhoaGmpqajdv3qw1nuvu7k4I8fLyunHjBr1k1qxZdNOLFy+mlxQXF9NLiouLm5Ek9f4YdExM\nDCFET0/Px8fHzMyMjpCXlycSieiRCkNDQ1tbW7pvVe8YdM2c6S8JQ0ND6afEYjFdU2JiYuipr15e\nXrW+JGz6GHTNLamnp1dQUFB3DLrejS8Siezt7Qkhbdu2dXFxoTuM9Lo0tF9qbuSGNlGtFmttGXoM\n2tramn4qNDSUELJ9+/ZaTzUUXCwW+/r61twmI0aMqKqqqttoQzu6KYdcI8dPIwdAQznXjNxQ6xRF\nVVVV6erq4ktCkFVOTo6vr6+BgUGnTp1WrVpVfexSFJWRkeHt7W1oaGhqajp27Njc3Fyq0RpBUdS+\nfft69Oihr6+vo6PTrVu3P//8k6pT7OjRDF1d3aNHj9JLUlNT6RMgIyODXlKzdjQjSer9Ai0QCEJD\nQ/l8vp2dXWxsbN++favrSHJy8ieffKKjo9O3b9+tW7c2VKBr5ezk5NSmTRuRSERR1E8//UQIsbS0\nFAqFpaWldB3ZunXrh+6IWlvSy8uL/PeSh6YUaIqinj175u3tzefzHR0da02PqXe/1NzIDW0iuRTo\nRra/VCo9ffq0t7e3r69veno6/R9b3UYb2dFNOeQaOX4aOgAayrlW5Hpbp/7bGY+MjPzQw0A1oECr\nFHpOq5OTE9OJNNXGjRsJIfv372c6kf/Jy8s7fPhwcnIy/Sf9NZq3tzezWTXRkiVLli1bxnQW8jRq\n1Cgul1v9v8jHBgVadfz888/0jIV169YxnUtTCQQCCwsLT09PphP5n8ePH2toaBBCFixYsHXrVnq4\noxkdeZBdQUEBj8ebOHEi04kwBgVadXh4eLRu3Xr06NG1Lp1gOXoOMj3/lyXOnTvn7u5uZGSkq6vr\n7OwcFxfXjOtlQHbLli3j8/kFBQVMJ8IYDvVRTl4BAGA/TLMDAGApFGgAAJZCgQYAYCkUaAAAlkKB\nBgBgKRRoAACWQoEGAGApFGgAAJZCgQYAYCkUaAAAlkKBBgBgKRRoAACWQoEGAGApFGgAAJZCgQYA\nYCkUaAAAlkKBBgBgKRRoAACWQoEGAGApHtMJfJiXL18eOnQI91EEAJbQ1NQcPXq0urp6SwRXsh70\n6dOnz507x3QWoCIMior679nDdBag3OLi4rKzs1souJL1oAkh/fr1mzx5MtNZgErIzCTZ2Z1xOIEM\nrl271nLBlawHDQDw8WBvD/rx48dpaWm1Fp49e9bQ0JCRfECplZaWPnr0qKioqKioiMvltm7d2tzc\nvJOamg7TiQE0gr0Fury8vLS0tNbCzMxMLS0tRvIBpSOVSi9cuHD48OHU1FRDQ8MOHTrY2Nhoa2tL\nJJIHDx6cPn267MaNYQ8f/h4cPGDAAG9vb2tra6ZTBngPewt0t27dunXrVmvh/fv3CwoKGMkHlIhY\nLN66dev27dt79+795Zdfrl27lsPh1PO6zEzy44/dFi9OSUlZtmxZRkZG//79AwICevToofCUAerB\n3gIN0DwHDx6MjY0dOXLk+fPnNTU1//X1VlZWoaGhoaGhVVVVly5d2rp16/Tp04cNGzZixIjOnTsr\nIGGAhqBAg+rIzc2dPn16p06dTp06paPzwcPLPB6vf//+/fv3F4lEf//995IlSwoKCoKDg0NCQoyM\njFoiYYDGoUCDijh+/PiqVas2bNjg7OwsYygNDY2hQ4cOHTq0tLR07969ISEhfD4/ICDAz89PW1tb\nLtkCNAUKNCg9qVS6YMGC3NzckydP6unpyTGykZHR1KlTp06dmpubu2vXrkGDBllYWIwYMcLX11dX\nV1eODQHUC/OgQblVVlYGBgaamJj8/vvv8q3ONVlZWUVERFy8eHHFihVFRUXDhg3z9vaOiYlJT09v\noRYBCHrQoNRev349atSor776asSIEYppsUOHDjNmzJgxY8arV6+Sk5N/+umn9PR0JycnT09PDw8P\nc3NzxaQBHwkUaFBWxcXFgYGBy5cv/+yzzxTfeqtWrUaOHDly5EiKou7evXv27Nnw8PDi4uK+ffsO\nHjzYzc1NQ0ND8VmBikGBBqX06tWrgICA6Ojo3r17M5sJh8Pp2rVr165dZ86cKRaL//nnn5MnTy5e\nvLhdu3b+/v4+Pj74XhGaDQUalM+bN29GjBjxww8/MF6da1FXV/fw8PDw8CCE5OTk7N+/39vbu337\n9l9//XWfPn2Yzg6UD74kBCXz9u1bf3//77//npGRjaZr27bt3Llzz58/P2/evJ07d7q7u+/fv18i\nkTCdFygTFGhQJhKJZOzYsdOmTRs0aBDTuTSVg4PDpk2bjhw5cu/evUGDBiUlJTGdESgNFGhQJuHh\n4X5+fgqbsyFHhoaGUVFR8fHxhw4dGj16dG5uLtMZgRJAgQalsWzZsrZt2/7f//0f04k0X+vWrTdt\n2hQeHu7v73/w4EGm0wG2Q4EG5bBz586nT58uXLiQ6UTkwM3N7fz580lJSdOmTROJREynA+yFAg1K\n4OLFi3v37t20aRPTiciNtrb25s2bu3fvPnTo0JKSEqbTAZbCNDtgu8ePH8+ZMycxMbEpvx2qXMaP\nH29jY+Pn5xcfH9+2bVum0wHWQQ8aWK2srGz8+PF79uwxNjZmOpcW4eHhERcXN2rUqMzMTKZzAdZh\nbw/61q1bp06dqrWQvncRI/mA4kml0nHjxi1ZsqRjx45M59KCPvnkk927d48ZM2b37t0dOnRgOh1g\nEfYWaD09PVtb21oLDQwMuFwuI/mA4i1cuNDd3X3gwIFMJ9Li7Ozsdu7cGRoa+ueff1pZWTGdDrAF\newt0hw4d6vYmLl26hHsSfiT27Nnz4sWLFStWMJ2IgnTs2HHTpk0jR45MTEw0MDBgOh1gBYxBAxtd\nunRp27ZtGzduZDoRherWrdvixYtHjx5dVVXFdC7ACijQwDrZ2dkzZszYu3ev6k3b+FeDBw/28/P7\n5ptvmE4EWIGBAl1cXPz69WvFtwtKQSgUjh49etOmTWZmZkznwozJkyeLxeIdO3YwnQgwTxEFevDg\nwS9evCCE5OXl9evXz8zMrHXr1gMHDsRoMtRCUdTEiRNnzZrl6urKdC5MWrdu3a5du27fvs10IsAw\nRRToU6dOvXv3jhAyd+5cW1vbsrIygUDg5OQ0bdo0BbQOSmTlypUODg6BgYFMJ8IwdXX17du3T5ky\nRSAQMJ0LMEmhsziuX7/+119/0bdDXrBgAaZ8Qk1Hjx69d+/e77//znQirGBtbb1o0aIZM2Zs27aN\n6VyAMQoag87Pz6+qqvr000+zsrLoJenp6W3atFFM68B+d+/eXbNmzZYtWzgcDtO5sMWQIUP09fV3\n797NdCLAmHoK9IwZM86fPy/HWz/0798/ODhYT0/vwoUL3333HSHk/Pnzw4cPnzt3rryaAKVWWFg4\nZcqUvXv36ujoMJ0Lu6xatWrz5s348eiPVj1DHEZGRtOnT3/x4sWIESMCAwP79+/P48k0EpKSkkII\nEYlE2dnZxcXFhBBtbe1jx465ubnJEhZUAz1tY8OGDRYWFkznwjpaWlobNmyYMmXKsWPH8NniI1RP\nD3rp0qW3b9++dOlShw4dIiMjraysJk+enJSUJBaLZWlJQ0OjQ4cO9K0ze/TogeoMhBCKosaPH//1\n119369aN6VxYysnJqV+/fqr0U6vQdA2OQbdq1apt27Z2dnYikejSpUuRkZE2NjZHjhxRZHKg8hYs\nWNCrV6+goCCmE2G1b7/9dv/+/dXf38DHo56xix9//PHEiROpqan9+vXz8fFZvHixjY0NIeTcuXMh\nISF+fn4f2saDBw8aeqpz584fGg1UxsaNGysrK+fMmcN0ImzH4/HWr18/derU48ePY6Djo1JPgU5N\nTZ0xY8agQYP4fD695O3bt7q6uj169GjebyPQv7auo6NjZGRU6yl8+/HRSkhIOHXq1KFDh5hORDk4\nOjr26tVr8+bNX331FdO5gOK8V6Dpn2i5cuUKPReV/lMgELRr166srExXV9ff378Zbfz111+TJk3S\n1NTcsGGDPHIGpXf58uV169YdP34cPx7bdAsWLBgwYMCwYcPMzc2ZzgUU5L0xaC0tLS0trezsbK0a\nTExMhgwZImMzwcHB7du3lzEIqIaHDx8uWLDg8OHDenp6TOeiTNTV1VevXj179mymEwHFea9AV1VV\nVVVVDRo0qOp98fHxMjbj5eWFH+gCQkh2dvaXX365a9euuuNd8K/69u1raGiYmJjIdCKgIPXM4khK\nSmqhxiiKKisrk0qlLRQfWK6oqGjUqFGbN29u164d07koq1WrVi1dulQoFDKdCCjCe2PQrq6uUVFR\nixcvrvu61NTUZrchFArXrVu3Y8eO58+fi0QiLpdrY2MzZsyY+fPnN/KDv1euXElISKi18OLFi61b\nt252JsCg8vLykJCQNWvWODk5MZ2LEjM0NJw5c2ZkZGR0dDTTuUCLe69Ab9q0ycbGRu5T4sPDw/Py\n8uLi4hwcHPT19cvKyu7fvx8dHR0eHr5169aG3mVjY1N3emx2dnZlZaV80wMFEAqFAQEBERER9JVK\nIIuQkJDff//97t27jo6OTOcCLat2D5oQYmxs/Pjx43bt2kkkkq1bt+ro6IwdO1aWNhISEjIyMqov\n5DU2NnZzc3NycrKxsWmkQLdp06burym1adMGvyKtdCorK4OCgr7++msvLy+mc1ERsbGx06dPP3Hi\nBKZFq7Z6xqCjoqIcHBzKyspiYmJ2794dGxs7c+ZMWdqwsbGp+7XGyZMnMRD5MRCLxcHBwWPHjm3e\nHE2ol52dXa9evXbt2sV0ItCy6rlQJTY29sqVK8bGxhs3brx69WpVVVXPnj1luX1nXFxcYGBgTEyM\no6Mjn88XCATp6emlpaVHjx6VIXNQAiKRKDQ01M/PLzg4mOlcVM28efMGDBjg4+NjbGzMdC7QUuop\n0BKJxNDQ8Pr1623atGnXrl1hYaFIJJKlDVdX18ePH6ekpGRlZZWUlBgZGU2ePNnd3V3GH8kDlqus\nrBw5cuTIkSNDQ0OZzkUFaWtrR0ZGRkRE/Pbbb0znAi2lnhIZHBw8ePBgsVj8/fffP3v2LCQkZNCg\nQbI2w+PVGn/My8tLS0vz8fGRMTKwk0gkCgoKCg0NHTVqFNO5qCxvb+8tW7ZcvXq1V69eTOcCLaKe\nAr1hw4bDhw8TQkaMGPH06dOgoKCWuPz/8uXL48aNwy3XVNK7d+9CQkKCgoJQnVva2rVrR48effbs\nWVw0r5Lq+ZKQx+MFBQUFBQVxuVx7e/u5c+e2xCW5gYGBqM4qqby83N/ff9y4cTJO/oGmsLKy8vPz\n++WXX5hOBFpEPQX69OnTffv27fw+uTSGKwlV3qtXr4YOHTp9+vThw4czncvHYsaMGfv378f0U5VU\nzxDHhAkTQkJCxowZI68v8Zp3JSEoncLCQn9//6ioKNm/tICmq/4RJdl/MwfYpp4etFgsXrJkiYOD\ng7x60OHh4WfPno2Li8vPzxeJRC9evNi+ffuNGzfCw8NlCQuskpWVFRgYuH79elRnxevXr5+BgcFf\nf/3FdCIgZ/UU6Dlz5qxfv16Od/VOSEjYuXOnu7u7sbGxuro6fSXh77//jhtoqYy0tLRRo0Zt27at\nR48eTOfykVq1atXy5cvxI0oqpp4CnZCQsGzZslatWnXq1EkuPWhcSajakpKSZs2adfjw4Y4dOzKd\ny8fLyMho5syZUVFRTCcC8lTPKPOWLVvk2wauJFRhO3bsOHDgwJEjRwwNDZnO5WM3atSovXv3Xrt2\nrWfPnkznAvJRT4Gm+8sSiaSoqMjMzEz2X2PBlYQqiaKopUuXFhYWJiQkqKurM50OEELIhg0bQkJC\nzpw5o6GhwXQuIAf1lMi8vLwxY8Zcu3ZNQ0Pj77//nj179q5du+gbeze/mTpXEoJSe/fu3VdffdWt\nW7fIyEimc4H/adu27ahRo6KjoxcuXMh0LiAH9YxBjx8/3sHB4eXLlwYGBs7Ozr179540aZLiMwPW\nys7O/vzzz0eOHIn747HQ1KlTz58/n5GRwXQiIAf19KAvXry4f/9+LS0tQgiPx/vuu++sra0Vnhiw\n1JkzZyIiIjZv3ty1a1emc4F6qKmp/fLLLxMmTDhz5gyGnpRdPT1oe3v7ixcvVv959epVW1tbBaYE\nLEVRVExMTGxs7KlTp1Cd2cze3j40NHTVqlVMJwKyqqcHvX79+oCAAA8Pj1evXgUEBFy4cGHPnj2K\nz+zUqVOHDh2qtfDy5cvm5uaKTwZevXo1ceLE7t27Hz58WE2tnv/XgVW++uqrYcOG3bhxo3v37kzn\nAs1XT4F2d3d/+PDhsWPHnJ2dzc3Nf/nlFzMzM8Vn1qdPH3t7+1oLly9fXl5ervhkPnJnzpxZtGjR\nDz/84OHhwXQu0CQcDmfTpk0jR448depUS/zYGShG/RPdjI2Nx40bp9hMatPX19fX16+10MDAANdK\nKdK7d+8WLVqUn5//119/GRgYMJ0OfABLS8vZs2fPmjVL7lc2gMLU/qyampoaGBhoa2urpaVlZ2c3\ncuTImzdvMpIZMO6ff/5xd3fv1q3b3r17UZ2VUWBgoFQqPXjwINOJQDO9V6DPnDnj4eHRsWPHPXv2\n3Lt3b/fu3XZ2dv37909JSWEqP2BEaWnpjBkzfvrpp0OHDuGGVUrt559/Xrt27ZMnT5hOBJrjvSGO\niIiI1atXT506lf6zQ4cOffv2tbCwWLBgwaVLl5hIDxSNoqjff/9906ZN8+fPxw3JVICuru7WrVvH\njRt38uRJXV1dptOBD/NeD/rWrVu+d2fShQAAFwRJREFUvr61XjFs2DCMcnwkLl265Onp+eDBg7//\n/hvVWWV07tz5m2++CQsLoyiK6Vzgw7zXg66srKz3e7nKykoFpgQMSEtLi4yMNDIy2rVrF35lUPX4\n+fndu3dv5cqVERERTOcCH6D2LI67d+/y+fyaSzCtTbXdvn176dKlOjo60dHRnTp1YjodaCkRERFj\nxow5dOjQiBEjmM4Fmuq9Am1gYFB3iINerqh8QEEoijpx4kRsbKy5uXlUVJSDgwPTGUHL4nA4W7Zs\nGTJkiImJSf/+/ZlOB5rkvQL9+vVrpvIAhXn58uVvv/128uRJT0/PnTt3WlhYMJ0RKIi2tvaBAwd8\nfX03bdrk5OTEdDrw7/CLzB8LiURy6tSpXbt2CYXCkJCQ5ORk/GTwR8jExOTAgQNBQUHbtm3r0qUL\n0+nAv0CBVn0PHjzYsWNHcnKyp6dnZGSkjDcwA2VnZWW1b9++kJCQHTt24FsHlkOBVll5eXm7d+8+\nevSog4PD//3f/61cuVL2m+OAamjfvv2+ffvGjBmzYcMGZ2dnptOBBqFAq5rXr1/Hx8cfP35cXV09\nMDDw9OnT2traTCcFrNO+ffuDBw8GBgZGREQMGTKE6XSgfijQKkIikfz99987d+7MyckJDg7etWtX\nq1atmE4KWM3MzOzEiROhoaGZmZkzZ85kOh2oB37YV+kVFBSsXLmyd+/eSUlJERERFy9enDZtGqoz\nNIWBgUFCQkJhYWFwcDCueGAh9KCV2OnTp3/99deKiopJkyZ98803uL8RNAOPx1u5cuXJkye9vb2j\no6Pd3NyYzgj+BwVa+VRUVOzcuXP37t1ubm6rV6+2s7NjOiNQeoMHD3Z0dJwyZcrBgwdXrFiho6PD\ndEZACIY4lEtZWdnq1au9vLwkEslff/21atUqVGeQF0tLy2PHjvXu3fvzzz//448/8MtKbMDeHvTR\no0fr3gvx1q1bH+dP+bx48SI2NvbixYtTpkxJSUnh8di740CpBQcHDxkyJDo6Oi4ubvbs2UOGDMHs\nTAax9zwfPHjwZ599Vmvh999///LlS0byYUpJScmaNWvOnDmzcOHCH374AWcLtDR9ff3ly5cXFhbG\nxsZGR0d//fXXgYGB6BMwgr0bXUNDo+61yJqamh9PhXr9+vWaNWvOnj377bffojSDgpmZma1cubKs\nrGzTpk29evXy9vaeOnWqpaUl03l9XDAGzUaVlZUxMTFDhw51dHRMSUkZNmwYqjMwQl9ff968eVev\nXu3bt++cOXOGDRu2efPmV69eMZ3XxwIFml0kEsn27dv79++vp6eXkpISFBSkpoZ9BAzj8Xg+Pj5/\n/PHH9u3bRSJRUFCQr6/vjh07PrbxRsVT6MlPUVRZWZlUKlVko0rkyJEj/fv3LygoOHPmzJQpUzDq\nB2xjbGw8bdq006dPb9u2raKiIiwsjP5GMT09nenUVJMiCrRQKFyxYkXHjh21tLQMDAw0NDTs7e2X\nLl2KO2lVS01NHThw4MWLF48cORIREYGbewLLmZqaTpky5fDhw3v37rWxsVm9enWfPn3owRDMz5Mj\nRfTRwsPD8/Ly4uLiHBwc9PX1y8rK7t+/Hx0dHR4evnXrVgUkwGYPHz5cuHAhl8vdvHmzra0t0+kA\nfBhDQ8OgoKCgoCCxWHz+/PmdO3dOnz7dyckpICBg4MCB+BQoI0VsvoSEhIyMjOo7dxgbG7u5uTk5\nOdnY2HzMBTo3NzcqKiovL2/lypVdu3ZlOh0Amairq3t5eXl5eRFCbt26lZCQsGrVKltb24CAgM8/\n/xy/Q9A8iijQNjY2iYmJEydOrLnw5MmTH+clJ4SQoqKi6Oho+kbaded6Ayg7Z2dn+memHz58uH//\nfvqS1xEjRnzxxReo1B9EEQU6Li4uMDAwJibG0dGRz+cLBIL09PTS0tKjR48qoHVWKS4uXrdu3aVL\nl7755puYmBim0wFoWZ06dVq0aNGiRYsyMzN37doVFRXl6uoaEhLSv39/zBxtCkUUaFdX18ePH6ek\npGRlZZWUlBgZGU2ePNnd3f2jGp/Kzs6OiYnJyMiYPn368uXLcXTCR8Xe3n7ZsmVRUVFXr149cODA\n4sWLXVxcxo0bh3vXNk5BJZLH43l5eVEUVV5erqen91HN7b179+6aNWtevnw5d+7c9evXM50OAGM4\nHE7v3r179+4tlUrPnz//66+/Pnz40N3d/csvv8Q35PVSRIEWCoXr1q3bsWPH8+fPRSIRl8u1sbEZ\nM2bM/PnzNTU1FZAAIyQSyaFDh7Zs2WJsbDxv3jzc+Q2gmpqamoeHh4eHh0gkSkpKWrJkybNnz/z8\n/IKCgtq3b890diyCaXby9+jRo507d168eNHLy2vXrl1t2rRhOiMAltLQ0PDx8fHx8SkvLz927Nj8\n+fOLi4s///zz4cOH447jBNPs5Cg7O3v//v1Hjx7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} ], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }