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Move updated SARIMA notebook
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‎SARIMA.ipynb

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This file was deleted.

‎notebooks/SARIMA.ipynb

+54-49
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@@ -5,6 +5,7 @@
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"colab": {
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"name": "SARIMA.ipynb",
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"provenance": [],
8+
"collapsed_sections": [],
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"include_colab_link": true
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},
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"kernelspec": {
@@ -39,6 +40,7 @@
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" - autoregression model i.e. regression of the time series onto itself. The basic assumption is that the current series values depend on its previous values with some lag (or several lags). The maximum lag in the model is referred to as p\n",
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" . To determine the initial p\n",
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" , you need to look at the PACF plot and find the biggest significant lag after which most other lags become insignificant.\n",
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" \n",
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"MA(q)\n",
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" - moving average model. Without going into too much detail, this models the error of the time series, again with the assumption that the current error depends on the previous with some lag, which is referred to as q\n",
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" . The initial value can be found on the ACF plot with the same logic as before.\n",
@@ -102,7 +104,7 @@
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"from sklearn.metrics import r2_score, median_absolute_error, mean_absolute_error\n",
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"from sklearn.metrics import median_absolute_error, mean_squared_error, mean_squared_log_error"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": []
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},
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{
@@ -142,26 +144,26 @@
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" smt.graphics.plot_pacf(y, lags=lags, ax=pacf_ax)\n",
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" plt.tight_layout()"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "j4sj2_tL78Ia",
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"colab_type": "code",
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"outputId": "5620b1e5-6bd5-4ab2-852f-9753e6d738dd",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 398
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}
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},
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"outputId": "5620b1e5-6bd5-4ab2-852f-9753e6d738dd"
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},
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"source": [
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"# Get datasets from github repository\n",
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"!wget https://raw.githubusercontent.com/Yorko/mlcourse.ai/master/data/ads.csv\n",
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"!wget https://raw.githubusercontent.com/Yorko/mlcourse.ai/master/data/currency.csv"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
@@ -205,7 +207,7 @@
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"ads = pd.read_csv('ads.csv', index_col=['Time'], parse_dates=['Time'])\n",
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"currency = pd.read_csv('currency.csv', index_col=['Time'], parse_dates=['Time'])"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": []
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},
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{
@@ -215,19 +217,21 @@
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"colab_type": "text"
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},
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"source": [
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"## Plot time series data"
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"## Plot time series data\n",
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"\n",
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"- ACF and PACF functions will be very useful for estimate the ARMA parameters, keep in mind."
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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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"id": "uzqzlw938luZ",
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"colab_type": "code",
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"outputId": "c6405669-db46-4387-83ef-722bd10c1b0b",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 389
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}
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},
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"outputId": "c6405669-db46-4387-83ef-722bd10c1b0b"
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},
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"source": [
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"plt.figure(figsize=(18, 6))\n",
@@ -236,7 +240,7 @@
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"plt.grid(True)\n",
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"plt.show()"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
@@ -257,11 +261,11 @@
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"metadata": {
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"id": "IlPQn7kB8oI7",
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"colab_type": "code",
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"outputId": "d997efb0-4c93-4015-bde5-a1225e390a5d",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 389
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}
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},
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"outputId": "d997efb0-4c93-4015-bde5-a1225e390a5d"
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},
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"source": [
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"plt.figure(figsize=(18, 6))\n",
@@ -270,7 +274,7 @@
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"plt.grid(True)\n",
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"plt.show()"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
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"metadata": {
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"id": "zKL_VIbl8vRL",
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"colab_type": "code",
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"outputId": "f82f11ab-0bee-4e04-8797-409d5e2fca1b",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 513
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}
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},
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"outputId": "f82f11ab-0bee-4e04-8797-409d5e2fca1b"
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},
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"source": [
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"tsplot(ads.Ads, lags=60)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
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"metadata": {
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"id": "mpHij1ef803k",
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"colab_type": "code",
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"outputId": "94876629-05d5-4964-d734-de279c0ae720",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 513
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}
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},
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"outputId": "94876629-05d5-4964-d734-de279c0ae720"
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},
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"source": [
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"# The seasonal difference\n",
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"ads_diff = ads.Ads - ads.Ads.shift(24)\n",
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"tsplot(ads_diff[24:], lags=60)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
@@ -363,17 +367,17 @@
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"metadata": {
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"id": "HIbu5nM688tm",
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"colab_type": "code",
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"outputId": "215d3ffb-8a6d-4665-826a-dfe8378daaeb",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 513
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}
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},
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"outputId": "215d3ffb-8a6d-4665-826a-dfe8378daaeb"
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},
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"source": [
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"ads_diff = ads_diff - ads_diff.shift(1)\n",
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"tsplot(ads_diff[24+1:], lags=60)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
@@ -398,12 +402,12 @@
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"source": [
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"## SARIMA parameters\n",
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"\n",
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"- p\n",
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" is most probably 4 since it is the last significant lag on the PACF, after which, most others are not significant.\n",
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"- **p**\n",
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" is most probably 4 since it is the last significant lag on the **PACF**, after which, most others are not significant.\n",
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"- d\n",
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" equals 1 because we had first differences\n",
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"- q\n",
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" should be somewhere around 4 as well as seen on the ACF\n",
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"- **q**\n",
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" should be somewhere around 4 as well as seen on the **ACF**\n",
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"- P\n",
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" might be 2, since 24-th and 48-th lags are somewhat significant on the PACF\n",
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"- D\n",
@@ -417,11 +421,11 @@
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"metadata": {
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"id": "nFqLgQgB9FAR",
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"colab_type": "code",
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"outputId": "9468b952-e6dd-46e3-e9d4-c237843e7c9c",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 34
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}
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},
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"outputId": "9468b952-e6dd-46e3-e9d4-c237843e7c9c"
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},
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"source": [
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"# setting initial values and some bounds for them\n",
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"parameters_list = list(parameters)\n",
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"len(parameters_list)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "execute_result",
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"colab": {}
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},
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"source": [
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"def optimizeSARIMA(parameters_list, d, D, s):\n",
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"def optimizeSARIMA(y, parameters_list, d, D, s):\n",
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" \"\"\"Return dataframe with parameters and corresponding AIC\n",
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" \n",
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" y - time series\n",
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" parameters_list - list with (p, q, P, Q) tuples\n",
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" d - integration order in ARIMA model\n",
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" D - seasonal integration order \n",
@@ -477,7 +482,7 @@
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" for param in tqdm_notebook(parameters_list):\n",
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" # we need try-except because on some combinations model fails to converge\n",
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" try:\n",
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" model=sm.tsa.statespace.SARIMAX(ads.Ads, order=(param[0], d, param[1]), \n",
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" model=sm.tsa.statespace.SARIMAX(y, order=(param[0], d, param[1]), \n",
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" seasonal_order=(param[2], D, param[3], s)).fit(disp=-1)\n",
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" except:\n",
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" continue\n",
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" \n",
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" return result_table"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "n2D_Pzxc9mtr",
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"colab_type": "code",
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"outputId": "a5cf28d8-2693-494f-dead-d3b533333265",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 69,
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"referenced_widgets": [
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"26fb1f95b0414c88a650b00f7dd7743c"
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]
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}
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},
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"outputId": "a5cf28d8-2693-494f-dead-d3b533333265"
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},
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"source": [
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"%%time\n",
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"warnings.filterwarnings(\"ignore\") \n",
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"result_table = optimizeSARIMA(parameters_list, d, D, s)"
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"result_table = optimizeSARIMA(ads.Ads, parameters_list, d, D, s)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
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"metadata": {
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"id": "9GbyTEDb_y2m",
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"colab_type": "code",
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"outputId": "6cce2a2e-69c4-41aa-e570-41a844688c07",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 206
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}
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},
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"outputId": "6cce2a2e-69c4-41aa-e570-41a844688c07"
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},
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"source": [
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"result_table.head()"
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],
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"execution_count": 0,
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"execution_count": null,
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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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"id": "_vr3oGkxBarW",
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"colab_type": "code",
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"outputId": "c1f5b667-92da-4845-e29d-952889f3ca0f",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 537
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}
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},
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"outputId": "c1f5b667-92da-4845-e29d-952889f3ca0f"
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},
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"source": [
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"# set the parameters that give the lowest AIC\n",
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" seasonal_order=(P, D, Q, s)).fit(disp=-1)\n",
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"print(best_model.summary())"
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],
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"execution_count": 0,
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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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"metadata": {
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"id": "XqqXdHQ-BoDa",
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"colab_type": "code",
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"outputId": "737f202d-1161-401d-80c2-eac91701f1b0",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 513
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}
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},
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"outputId": "737f202d-1161-401d-80c2-eac91701f1b0"
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},
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"source": [
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"tsplot(best_model.resid[24+1:], lags=60)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",
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" plt.legend()\n",
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" plt.grid(True)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "9Iyjz_IfBtqU",
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"colab_type": "code",
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"outputId": "f21b389e-538e-440c-98d9-2f642722c15e",
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"colab": {
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"base_uri": "https://localhost:8080/",
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"height": 444
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}
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},
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"outputId": "f21b389e-538e-440c-98d9-2f642722c15e"
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},
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"source": [
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"plotSARIMA(ads, best_model, 50)"
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],
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"execution_count": 0,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "display_data",

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