{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Module 8\n", "\n", "## Video 37: Predictive Modelling II\n", "**Python for the Energy Industry**\n", "\n", "In the previous lesson, we fit a first order autoregressive model onto floating storage data. Here, we will discuss finding the most appropriate type of ARIMA model for fitting to a time series. \n", "\n", "Start by getting the data:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# initial imports\n", "import pandas as pd\n", "import numpy as np\n", "from datetime import datetime\n", "from dateutil.relativedelta import relativedelta\n", "import vortexasdk as v\n", "from statsmodels.tsa.arima.model import ARIMA\n", "\n", "# The cargo unit for the time series (barrels)\n", "TS_UNIT = 'b'\n", "\n", "# The granularity of the time series\n", "TS_FREQ = 'day'\n", "\n", "# datetimes to access last 7 weeks of data\n", "now = datetime.utcnow()\n", "seven_weeks_ago = now - relativedelta(weeks=7)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Find crude ID\n", "crude = [p.id for p in v.Products().search('crude').to_list() if p.name=='Crude']\n", "assert len(crude) == 1\n", "\n", "search_result = v.CargoTimeSeries().search(\n", " timeseries_frequency=TS_FREQ,\n", " timeseries_unit=TS_UNIT,\n", " filter_products=crude,\n", " filter_time_min=seven_weeks_ago,\n", " filter_time_max=now,\n", " # Filter for cargo in floating storage\n", " filter_activity=\"storing_state\",\n", " # Only get floating storage that lasted longer than 21 days\n", " timeseries_activity_time_span_min=1000 * 60 * 60 * 24 * 14,\n", ")\n", "\n", "df_floating_storage = search_result.to_df()\n", "df_floating_storage = df_floating_storage.rename(columns = {'key': 'date', 'value': 'quantity'})[['date','quantity']]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important question to ask about time series data before fitting an ARIMA model is whether the data is [stationary](https://en.wikipedia.org/wiki/Stationary_process). Non-stationary data should be differenced, using an ARIMA(p,d,q) model with d > 0. \n", "\n", "We can test stationarity with the Augmented Dickey Fuller test:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ADF Statistic: -1.1815462355916246\n", "p-value: 0.6814832570453857\n" ] } ], "source": [ "from statsmodels.tsa.stattools import adfuller\n", "adfresult = adfuller(df_floating_storage['quantity'])\n", "print('ADF Statistic: ', adfresult[0])\n", "print('p-value: ', adfresult[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, we cannot reject the null hypothesis that the time series is non-stationary. What about the first order difference of the time series:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ADF Statistic: -7.164255346445803\n", "p-value: 2.914087126669944e-10\n" ] } ], "source": [ "adfresult = adfuller(df_floating_storage['quantity'].diff().dropna())\n", "print('ADF Statistic: ', adfresult[0])\n", "print('p-value: ', adfresult[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So it seems that we would only need 1 order of differencing, i.e. d=1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's also useful to look at the autocorrelation and partial autocorrelation (where the contribution of intervening lags is removed). We will do this using the below functions from the statsmodels module, for both the original and 1-order-differenced data:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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tyfoJ++3b0dFTo/x04LjvKmVmbSOVC68iYguwpWJZ1aCPiHekUWezFArBsy+cZP/RoWY3xcxsSnyl7RQcH86x5+Bx3wzczNqSA38SIoL+F0/x3JFTvoDKzNqWA38CJ0dy/PTgCY4P55rdFDOzujjwxzGSK/DD/qMU2vyovlAItu09wtOHT7B+2RkecdMsoxz4VQyN5jkxkiNfiFkR9h98aCd7fF9cs8xLZbTM2eTg4BDb+4+Sb/ekT2zbe4Q9yX1xg7H3xTWzbHHgJ0ZyBX78/CA/HTgxa8Iexr8vrplli7t0gEPHh3n60AlGZ+EYOL4vrpmVZPoIfzRfYPeBY+w+cHxWhj28fF9cJd31vi+uWXZl9gh/cGiU3QeOzfoBz3xfXDMryWzgHz05OuvDvsT3xTUzyHiXjplZljjwzcwywoFvZpYRDnwzs4xw4JuZZUQqgS/pWkm7JO2RdGeV9W+TtD35+zdJl6ZRr5mZTV7dgS+pE/g4cB2wAbhR0oaKYj8DfjUiLgH+HNhcb71mZjY1aZyHfwWwJyKeApB0P7AJeLJUICL+raz894G1KdRrDeZhls3aWxqBvwbYWzbfD1w5TvlbgIdSqNcayMMsm7W/NPrwq/1vr3oJq6Rfoxj4d9TcmHSrpD5JfQMDAyk0z9LgYZbN2l8agd8PrCubXwvsqywk6RLgHmBTRByutbGI2BwRvRHRu2LFihSaZ2nwMMtm7S+NwH8MuEDSeZK6gRuAB8sLSDoHeAB4e0T8JIU6rcFKwyyX8zDLZu2l7sCPiBxwO/BNYCfwpYjYIek2Sbclxe4ClgF/L2mbpL5667XG8jDLZu0vldEyI2ILsKVi2d1l0+8C3pVGXdYcHmbZrP1ldnhkmzoPs2zW3jy0gplZRjjwzcwywoFvZpYRDnwzs4xw4JuZZYTP0rGG8gBsZs3jwLeG8QBsZs3lLh1rGA/AZtZcDnxrmDQHYCsUgsefeZEHHu/n8WdepFCoOkCrmZVxl441TGkAtuGy0J/OAGzuGjKbHh/hW8OkNQCbu4bMpseBbw1TGoBtzZIeVizo5r/++gXTOir32Pxm0+MuHWuoNAZgS6tryCxrHPjWdkpdQ0/uHyTCY/Pb+Frl2o9WaIcD39qOx+a3yWqVH/hbpR3uw7e2VOoaWr5wLpefu9Rhb1Wl9QN/vacBt8qJBqkc4Uu6Fvgo0AncExEfqlivZP31wEngHRHxeBp1m5nVMt4P/JP9DSmNo/M02pGGuo/wJXUCHweuAzYAN0raUFHsOuCC5O9W4BP11mtms1saF9eVfuAvN9Uf+NM4Ok+jHWlQRH1XKEp6DfCBiHhDMv+HABHxl2Vl/gF4JCK+kMzvAq6KiP3jbfvMcy+Ka95375Tb9OT+QQA2rFpUs8xwrsBwLl9z/TOHTwJw7rL5U64/7e20yjZmY1usNUUEz75wilOjeSJAgp45nZxzZg/S5LvvSts5OVL8vz6d7QwcG+bQ8ZHTlq9Y0M3yhXNnpB0L5nbRMYXXWe5Lt/3i1ojorbYujS6dNcDesvl+4MpJlFkDnBb4km6l+C2ABateOa0GjRf0k5VWiKSxnVbZRlrbaZW2RAQ/O3SSQgRnLZrHgrmdUwqTklb6AGuVbdS7nePD+ZfCHiACTo3mOT6cZ+G8yceWJM45s4fjw3mGR/PMndM55X/neXM6kaD82FiCuXM6G9qONKQR+NVaXPm1YTJligsjNgObAXp7e+OL/+U19bWuhr0vnKT/xVMzsm1rfaV+2ZF8gYjiUdzinumdNfFnX98BwF1vvLiuNqWxnVbZRqEQ3PHAdoZG87zxF1ZP+SyqBx7v58tb+8cuDHjNK5bxlsvXTrtd09GMM2w2rltCT/fkP1DKfem22uvSCPx+YF3Z/Fpg3zTKmDVMqV+2dNRW3i/byB/RZqNSQD535BQR8LHv7p5yQLbSxXWl04CbfQ59GtI4LfMx4AJJ50nqBm4AHqwo8yBwk4peDRydqP/ebCZ5eIaZM96H6WSVLq6b29WBaP7FdR0d4vJzl/KWy9e29WnAdR/hR0RO0u3ANymelnlvROyQdFuy/m5gC8VTMvdQPC3znfXWa1aPVjqCnG3SOAVxNh1Vt5JUzsOPiC0UQ7182d1l0wG8O426zNJQOoKs7Jf18Az1S+vDtHRU7S629HhoBcskH0HOHH+Yti4HvmWWjyBnhj9MW5cD38xS5w/T1uTB08xmiUIhODaUY+DYsO/za1U58M1aQL1hXX7u+6HjI3zsu7v54EM7Hfo2hgPfrA5pHFWnEdZpnPteaou/JcxeDnyzaUrrqDqNsE7jQjJ/S5j9HPhm05TWUXUaYZ3mMMD1vh5rXQ58s2lKa3iGNMI6jaEIPNzE7OfTMs2mKa0rStO4UCmNc9893MTs58A3m6a0rihN60Kles999xWys1/dd7yaSb29vdHX1zcj2/Z4+JaGQiFm1RWls+31tKt6xsOXNKN3vDLLrNl2Relsez02ln+0NTPLCAe+mVlGOPDNzDLCgW9mlhF1Bb6kMyV9W9Lu5PG0X3okrZP0L5J2Stoh6T311GlmZtNT7xH+ncDDEXEB8HAyXykH/EFEXAS8Gni3pA111mtmZlNUb+BvAu5Lpu8D3lxZICL2R8TjyfQxYCewps56zcxsiuoN/LMiYj8Ugx1YOV5hSeuBy4BHxylzq6Q+SX0DAwN1Ns/MzEomvPBK0neAs6usev9UKpK0APgK8N6IGKxVLiI2A5uheKXtVOowM7PaJgz8iHhdrXWSDkhaFRH7Ja0CDtYoN4di2H8+Ih6YdmvNzGza6u3SeRC4OZm+GfhaZQFJAj4J7IyIv6mzPjMzm6Z6A/9DwDWSdgPXJPNIWi1pS1Lml4C3A78uaVvyd32d9ZqZ2RTVNXhaRBwGrq6yfB9wfTL9r4CH2zMzazJfaWtmlhEOfDOzjHDgm5llRGYDf05nZl+6mWVUZu94dfbieXR1iqcPnWA07+u7zGz2y/Rh7vIFc7lk7RKWnjGn2U0xM5txmQ58gO6uDl519iJeueIMOn2zZjObxTIf+CUrF83jkrWLWdST2V4uM5vlHPhl5s3pZMOqRZy7bD4+2Dez2caBX0ESq5f08AtrF7Ngro/2zWz2cODXML+7i59fs4i1S3uQj/bNbBZw4I9DEuvOnM/Pr1lMT3dns5tjZlYXB/4kLJjbxSVrFrNq8bxmN8XMbNoc+JPU0SHWLz+DDasXMXeOd5uZtR8n1xQt7pnDJWsWs3LR3GY3xcxsShz409DV2cErVyzgVWcvpLvLv+iaWXuoK/AlnSnp25J2J49LxynbKekHkr5eT52tZOkZ3VyydgnLFnQ3uylmZhOq9wj/TuDhiLgAeDiZr+U9wM4662s5czo7+LmzFnL+ygV0dfpo38xaV72Bvwm4L5m+D3hztUKS1gK/AdxTZ30ta8XCuVyydjFL5nsgNjNrTfUG/lkRsR8geVxZo9xHgP8OFCbaoKRbJfVJ6hsYGKizeY01t6uTi1Yt4hUeiM3MWtCEYwdI+g5wdpVV759MBZLeCByMiK2SrpqofERsBjYD9Pb2tuVA9WctmsfinjnsOXicY0O5ZjfHzAyYROBHxOtqrZN0QNKqiNgvaRVwsEqxXwLeJOl6YB6wSNLnIuI/TrvVbWDenE4uXr2I/UeH2HfklG+yYmZNV2+XzoPAzcn0zcDXKgtExB9GxNqIWA/cAHx3tod9SWkgtsvOWcq6M3uY4x91zayJ6g38DwHXSNoNXJPMI2m1pC31Nm626OwQa5fOd/CbWVPVNf5vRBwGrq6yfB9wfZXljwCP1FNnOysF/6rFPTw/OMR+d/WYWQN5wPcm6OwQa5b0cPaieQ5+M2sYB34TOfjNrJEc+C3AwW9mjeDAbyEOfjObSQ78FuTgN7OZ4MBvYeXBf+TkCINDOY4NjXJyJE84/81sihz4baCzQyxbMJdlC4o3XcnlCxwbyjE4NMqxoRzHh3P+ADCzCTnw21BXZwdLz+hm6RnFcfjzheB48gFw9NQoJ4ZzFPwBYGYVHPizQGeHWDx/Dovnz2EdUCgEx4aL3T+Dp4rfAPL+BDDLPAf+LNTRIRb3zGFxzxxYChHB8eEcJ4bzDOfyjOYLDOcKjOQKjObDHwZmGeHAzwBJLJw3h4Xzqt+cJZcvBv9IrsBwPv/SdPEDofjhMJov+HcCszbnwDe6Ojvo6oSe7k6g+odCRBQ/CPIF8oWgUAgKEeQjiKA4XShO55N1hWR5+brS9MtfKiLZfvlc2XzEacvMbHoc+DYpkujuEt1d9Q6wWr+IsR8SLy2vUqbausrnxmlrp9uuikdizAfZaR9e8XLdES+Xebl8WfvGbKf29k97beXbKKuHGnVxWnvG1hUxtt6Xy8Zp2x673alq3U/3Rhx4aIYG1HXgW9tR8r9h/P8UHoLarFLzD9fMzKwhHPhmZhnhwDczy4i6Al/SmZK+LWl38ri0Rrklkr4s6ceSdkp6TT31mpnZ1NV7hH8n8HBEXAA8nMxX81HgGxHxKuBSYGed9ZqZ2RTVG/ibgPuS6fuAN1cWkLQI+BXgkwARMRIRR+qs18zMpqjewD8rIvYDJI8rq5R5BTAAfErSDyTdI+mMWhuUdKukPkl9AwMDdTbPzMxKJgx8Sd+R9KMqf5smWUcXcDnwiYi4DDhB7a4fImJzRPRGRO+KFSsmWYWZmU1kwguvIuJ1tdZJOiBpVUTsl7QKOFilWD/QHxGPJvNfZpzANzOzmVHvlbYPAjcDH0oev1ZZICKel7RX0oURsQu4GnhyMhvfunXrIUnPTLNty4FD03xuo7VTW6G92ttObYX2am87tRXaq731tPXcWitUOebIVEhaBnwJOAd4FvjtiHhB0mrgnoi4Pim3EbgH6AaeAt4ZES9Ou+LJta0vInpnso60tFNbob3a205thfZqbzu1FdqrvTPV1rqO8CPiMMUj9srl+4Dry+a3AW2xo83MZitfaWtmlhGzOfA3N7sBU9BObYX2am87tRXaq73t1FZor/bOSFvr6sM3M7P2MZuP8M3MrIwD38wsI9o68CVdK2mXpD2STruYS0UfS9Zvl3R5M9qZtGWdpH9JRgvdIek9VcpcJemopG3J313NaGtZe56W9MOkLX1V1rfE/pV0Ydk+2yZpUNJ7K8o0dd9KulfSQUk/Kls22dFmx32fN6itf52Mdrtd0j9LWlLjueO+ZxrY3g9Ieq7s3/v6Gs9thX37xbJ2Pi1pW43n1r9vI6It/4BO4KcUx+rpBp4ANlSUuR54iOL97l4NPNrE9q4CLk+mFwI/qdLeq4CvN3vflrXnaWD5OOtbZv9WvC+eB85tpX1LcQDBy4EflS37H8CdyfSdwF/VeD3jvs8b1NbXA13J9F9Va+tk3jMNbO8HgP82ifdK0/dtxfoPA3fN1L5t5yP8K4A9EfFURIwA91McvbPcJuAzUfR9YEkyBETDRcT+iHg8mT5GcYjoNc1oS4paZv+WuRr4aURM9wrtGRER3wNeqFg84WizTO59nqpqbY2Ib0VELpn9PrB2JtswFTX27WS0xL4tkSTgd4AvzFT97Rz4a4C9ZfP9nB6gkynTcJLWA5cBj1ZZ/RpJT0h6SNLFjW3ZaQL4lqStkm6tsr4V9+8N1P4P00r7FiY32mwr7uP/RPGbXTUTvWca6fakC+reGt1lrbZvXwsciIjdNdbXvW/bOfBVZVnlOaaTKdNQkhYAXwHeGxGDFasfp9gVcSnwt8BXG9y8Sr8UEZcD1wHvlvQrFetbav9K6gbeBPxTldWttm8nq9X28fuBHPD5GkUmes80yieAVwIbgf0Uu0oqtdS+BW5k/KP7uvdtOwd+P7CubH4tsG8aZRpG0hyKYf/5iHigcn1EDEbE8WR6CzBH0vIGN7O8PfuSx4PAP1P8ClyupfYvxf8Ij0fEgcoVrbZvEwdKXWAaf7TZltjHkm4G3gi8LZJO5UqTeM80REQciIh8RBSA/1WjHa20b7uAtwBfrFUmjX3bzoH/GHCBpPOSI7sbKI7eWe5B4KbkbJJXA0dLX6EbLemf+ySwMyL+pkaZs5NySLqC4r/P4ca1ckxbzpC0sDRN8Ue7H1UUa5n9m6h5hNRK+7ZMabRZqDHaLJN7n884SdcCdwBvioiTNcpM5j3TEBW/Jf1WjXa0xL5NvA74cUT0V1uZ2r6dyV+kZ/qP4lkiP6H4S/v7k2W3Abcl0wI+nqz/IdDbxLb+MsWvi9uBbcnf9RXtvR3YQfFsge8Dv9jE9r4iaccTSZtaff/Opxjgi8uWtcy+pfhBtB8YpXhkeQuwjOK9oHcnj2cmZVcDW8qee9r7vAlt3UOxv7v03r27sq213jNNau9nk/fkdoohvqpV922y/NOl92pZ2dT3rYdWMDPLiHbu0jEzsylw4JuZZYQD38wsIxz4ZmYZ4cA3M8sIB76ZWUY48M3MMuL/A9QhKqYdhJ/vAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n", "ax1 = plot_acf(df_floating_storage['quantity'])\n", "ax2 = plot_pacf(df_floating_storage['quantity'])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax1 = plot_acf(df_floating_storage['quantity'].diff().dropna())\n", "ax2 = plot_pacf(df_floating_storage['quantity'].diff().dropna())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From these plots, we can see that there is no autocorrelation in the differenced data, so if d=1 then we should use an ARIMA(0,1,0). \n", "\n", "In the original data, there is autocorrelation which is fully accounted by 1 day lag, so if using d=0 as in the previous lesson then ARIMA(1,0,0) should be optimal. \n", "\n", "Let's try an ARIMA(0,1,0) model, and see how it compares to our ARIMA(1,0,0) model:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "arima = ARIMA(df_floating_storage['quantity'].head(42),order=(0,1,0))\n", "res = arima.fit()\n", "\n", "pred = res.get_prediction(start=1,end=49)\n", "df_floating_storage['prediction'] = pred.predicted_mean\n", "df_floating_storage['lower'] = pred.conf_int()['lower quantity']\n", "df_floating_storage['upper'] = pred.conf_int()['upper quantity']\n", "\n", "ax = df_floating_storage.plot(x='date',y=['quantity','prediction'])\n", "ax.fill_between(df_floating_storage['date'].values,df_floating_storage['lower'],df_floating_storage['upper'],color='g',alpha=.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This models performs similarly to the ARIMA(1,0,0) model. Notably, since an ARIMA(0,1,0) model is equivalent to a random walk, the out-of-sample predicted mean is a constant value. \n", "\n", "Finally, we can also assess different model types numerically, testing a range of different models. There are a range of metrics we can use to measure model performance, here we will use mean-square-error (MSE) and the Akaike information criterion (AIC), whiuch penalises higher order models.\n", "\n", "Doing a loop over different sets of (p,d,q):" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:965: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n", " warn('Non-stationary starting autoregressive parameters'\n", "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:977: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.\n", " warn('Non-invertible starting MA parameters found.'\n", "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n", " warnings.warn(\"Maximum Likelihood optimization failed to \"\n", "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n", " warnings.warn(\"Maximum Likelihood optimization failed to \"\n", "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n", " warnings.warn(\"Maximum Likelihood optimization failed to \"\n", "C:\\Users\\Lloyd\\anaconda3\\lib\\site-packages\\statsmodels\\base\\model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n", " warnings.warn(\"Maximum Likelihood optimization failed to \"\n" ] } ], "source": [ "MSEs = {}\n", "AICs = {}\n", "\n", "for p in range(4):\n", " for d in range(2):\n", " for q in range(4):\n", " arima = ARIMA(df_floating_storage['quantity'].head(42),order=(p,d,q))\n", " res = arima.fit()\n", " mse = res.mse\n", " aic = res.aic\n", " MSEs[(p,d,q)] = mse\n", " AICs[(p,d,q)] = aic" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "results = pd.DataFrame({'MSE':MSEs.values(),'AIC':AICs.values()},index=MSEs.keys())" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", "
" ], "text/plain": [ " MSE AIC\n", "0 0 0 2.554974e+13 1535.782190\n", " 1 1.354841e+13 1397.341655\n", " 2 9.912498e+12 1383.094585\n", " 3 9.500133e+12 1385.256180\n", " 1 0 7.671702e+13 1343.099914" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.head()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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MSEAIC
0029.912498e+121383.094585
39.500133e+121385.256180
1008.525074e+121376.418360
18.501005e+121378.309353
28.435501e+121381.191926
38.402791e+121384.744361
2008.495810e+121378.286910
18.190029e+121378.465350
28.138664e+121381.179028
39.930077e+121391.063531
3008.404489e+121379.835533
18.147085e+121380.360607
27.587775e+121378.696377
37.555709e+121380.509978
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" ], "text/plain": [ " MSE AIC\n", "0 0 2 9.912498e+12 1383.094585\n", " 3 9.500133e+12 1385.256180\n", "1 0 0 8.525074e+12 1376.418360\n", " 1 8.501005e+12 1378.309353\n", " 2 8.435501e+12 1381.191926\n", " 3 8.402791e+12 1384.744361\n", "2 0 0 8.495810e+12 1378.286910\n", " 1 8.190029e+12 1378.465350\n", " 2 8.138664e+12 1381.179028\n", " 3 9.930077e+12 1391.063531\n", "3 0 0 8.404489e+12 1379.835533\n", " 1 8.147085e+12 1380.360607\n", " 2 7.587775e+12 1378.696377\n", " 3 7.555709e+12 1380.509978" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results[results['MSE'] < 1e13]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, only models with d=0 yield an MSE below 1e13. Of these, the model which minimizes AIC is ARIMA(1,0,0).\n", "\n", "### Exercise\n", "\n", "Determine which order of ARIMA model is best for the US crude exports data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }