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‎examples/4a_averages_and_ses.ipynb

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"name": "4a_averages_and_ses.ipynb",
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"provenance": [],
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"collapsed_sections": [],
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"authorship_tag": "ABX9TyP+mgtJZoqPKv7k/JkZPGz4",
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"authorship_tag": "ABX9TyN0MCV9CSEvVqalgvPpkNxv",
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"include_colab_link": true
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},
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"kernelspec": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "qyrssun2kgSi",
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"outputId": "f07f1e2e-9055-42aa-c770-474996ab25a2"
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"outputId": "15bf8f9f-666a-4cd4-ff0f-131f9e75b5dd"
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},
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"source": [
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"import pandas as pd\n",
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"\n",
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"from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt"
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],
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"execution_count": 156,
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"execution_count": 162,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 477 100 477 0 0 3785 0 --:--:-- --:--:-- --:--:-- 3785\n",
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"100 477 100 477 0 0 3755 0 --:--:-- --:--:-- --:--:-- 3726\n",
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 629 100 629 0 0 4952 0 --:--:-- --:--:-- --:--:-- 4992\n",
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"100 629 100 629 0 0 4250 0 --:--:-- --:--:-- --:--:-- 4278\n",
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 3867 100 3867 0 0 37182 0 --:--:-- --:--:-- --:--:-- 37182\n",
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"100 3867 100 3867 0 0 37911 0 --:--:-- --:--:-- --:--:-- 37911\n",
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 456 100 456 0 0 3931 0 --:--:-- --:--:-- --:--:-- 3931\n",
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"100 456 100 456 0 0 5010 0 --:--:-- --:--:-- --:--:-- 5010\n",
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 1456 100 1456 0 0 13866 0 --:--:-- --:--:-- --:--:-- 13866\n",
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"100 1456 100 1456 0 0 18200 0 --:--:-- --:--:-- --:--:-- 18200\n",
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" % Total % Received % Xferd Average Speed Time Time Time Current\n",
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" Dload Upload Total Spent Left Speed\n",
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"100 151 100 151 0 0 1659 0 --:--:-- --:--:-- --:--:-- 1659\n"
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"100 151 100 151 0 0 1556 0 --:--:-- --:--:-- --:--:-- 1556\n"
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],
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"name": "stdout"
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}
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"height": 541
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},
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"id": "mbtL6K0tIPOM",
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"outputId": "899b4e3a-aaab-48ec-e33f-9a24abe8d1e2"
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"outputId": "877583d9-a0b9-4f39-ed54-2b965a792991"
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},
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"source": [
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"can_openers.plot()"
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],
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"execution_count": 5,
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"execution_count": 163,
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7f0bb96716a0>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7f0b9d3c1908>"
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]
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},
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"metadata": {
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"tags": []
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},
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"execution_count": 5
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"execution_count": 163
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},
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{
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"output_type": "display_data",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 228
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"height": 0
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},
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"id": "Wy5VyH48klYK",
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"outputId": "dc7cea7d-c76f-40bd-f6d2-c2984cfa812b"
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"outputId": "6c9ac18a-7131-4aa1-cf8b-703d20a9cf30"
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},
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"source": [
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"can_openers['mean_forecast'] = can_openers.expanding().mean().shift(1)\n",
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"can_openers.head()"
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],
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"execution_count": 6,
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"execution_count": 164,
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"outputs": [
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{
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"output_type": "execute_result",
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"metadata": {
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"tags": []
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},
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"execution_count": 6
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"execution_count": 164
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}
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]
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},
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 541
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"height": 0
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},
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"id": "fsK3fqIIktfJ",
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"outputId": "aba0cb1d-d729-4fd1-8360-41b7dc506d92"
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"outputId": "23f58cb3-4d64-4f08-b6e2-d73c29c09d7f"
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},
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"source": [
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"can_openers['mean_forecast'].plot()\n",
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"can_openers['mean_value'].plot(color='red', ax=ax)\n",
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"plt.legend()"
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],
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"execution_count": 9,
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"execution_count": 165,
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.legend.Legend at 0x7f0bb937d940>"
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"<matplotlib.legend.Legend at 0x7f0b9ba1a2e8>"
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]
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},
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"metadata": {
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"tags": []
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},
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"execution_count": 9
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"execution_count": 165
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},
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{
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"output_type": "display_data",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 378
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"height": 0
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},
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"id": "xWRta9Dzk-Tg",
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"outputId": "4fedca51-cbb5-4c9f-cf89-f13441457292"
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"outputId": "734d7aa2-f1c8-4c66-a3ab-656b77b82260"
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},
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"source": [
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"can_openers = pd.read_csv('can_openers.csv', parse_dates=['month']).set_index('month')\n",
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"can_openers['MA5_forecast'] = can_openers['shipments'].rolling(5, center=True).mean().shift(3)\n",
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"can_openers.head(10)"
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],
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"execution_count": 44,
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"execution_count": 166,
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"outputs": [
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{
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"output_type": "execute_result",
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"metadata": {
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"tags": []
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},
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"execution_count": 44
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"execution_count": 166
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}
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]
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},
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 541
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"height": 0
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},
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"id": "5Rnf3YpLLtt-",
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"outputId": "edfe6411-1da6-4c26-9583-23a53d7a47b9"
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"outputId": "affb0ae3-c083-4978-bde7-9c85bae0dc4e"
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},
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"source": [
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"can_openers['MA3_forecast'].plot()\n",
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"\n",
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"plt.legend()"
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],
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"execution_count": 45,
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"execution_count": 167,
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.legend.Legend at 0x7f0bb11f36a0>"
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"<matplotlib.legend.Legend at 0x7f0b9b9d2748>"
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]
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},
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"metadata": {
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"tags": []
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},
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"execution_count": 45
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"execution_count": 167
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},
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{
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"output_type": "display_data",
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"height": 699
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},
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"id": "ZdpzoBlwcO6s",
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"outputId": "cd35cf75-d706-4665-e675-54f2619d18a0"
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"outputId": "f7b5cbce-5be3-402c-8e5b-eb752bf0dab0"
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},
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"source": [
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"# Reload a fresh copy of our data\n",
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"\n",
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"can_openers.plot()"
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],
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"execution_count": 160,
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"execution_count": 168,
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"outputs": [
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{
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"output_type": "stream",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7f0b9bc4e6d8>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7f0b9b90f780>"
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]
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},
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"metadata": {
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"tags": []
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},
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"execution_count": 160
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"execution_count": 168
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},
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{
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"output_type": "display_data",
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}
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "Hh5S264iJFG5",
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"outputId": "6098d250-7255-4e1e-946e-b016b913fa74"
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},
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"source": [
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"can_openers.shape"
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],
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"execution_count": 169,
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"(12, 4)"
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]
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},
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"metadata": {
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"tags": []
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},
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"execution_count": 169
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "NY8QCfKkIoIM"
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},
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"source": [
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"We can calculate the MSE to determine the goodness of fit for each of the smoothed fit values. Remember that we'll want to use a **test set** to perform our evaluation.\n",
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"\n",
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"For our purposes, we'll consider the last four observations to be the test set, and we can access this part of the `pandas` `DataFrame` with the `.tail(N)` function (`.tail(4)`).\n",
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"\n",
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"We can then calculate the MSE between each of the fits and the original data as follows:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "cj8petGxJctJ",
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"outputId": "ad7a5e17-fe65-4209-c074-bff1983723f4"
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},
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"source": [
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"test = can_openers.tail(4)\n",
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"test.head()\n",
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"\n",
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"mse_1 = ((test['alpha_0.1'] - test['shipments'])**2).mean()\n",
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"mse_5 = ((test['alpha_0.5'] - test['shipments'])**2).mean()\n",
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"mse_9 = ((test['alpha_0.9'] - test['shipments'])**2).mean()\n",
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"\n",
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"print(mse_1, mse_5, mse_9)"
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],
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"execution_count": 174,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"2228.2308984507677 3050.129555940628 3431.988106158692\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"\n",
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"can_openers.plot()"
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],
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"execution_count": 161,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",

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