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@ChadFulton
Last active August 29, 2015 14:22
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Statespace Unobserved Components: Nile example
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Nile data"
]
},
{
"cell_type": "code",
"execution_count": 331,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"%matplotlib inline\n",
"import numpy as np\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"from statsmodels.tsa.statespace import structural\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 276,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Get dataset\n",
"nile = sm.datasets.nile.data.load_pandas().data\n",
"nile.index = pd.date_range('1871', '1970', freq='AS')\n",
"\n",
"\n",
"# Create exogenous array for intervention in 1899\n",
"# and for pulse in 1913\n",
"nile['intervention'] = 0\n",
"nile.ix['1899':, 'intervention'] = 1\n",
"nile['pulse'] = 0\n",
"nile.ix['1913', 'pulse'] = 1"
]
},
{
"cell_type": "code",
"execution_count": 327,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"AAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x114069650>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nile['volume'].plot(figsize=(10,3));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Local level model"
]
},
{
"cell_type": "code",
"execution_count": 330,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Statespace Model Results \n",
"================================================================================\n",
"Dep. Variable: volume No. Observations: 100\n",
"Model: UnobservedComponents Log Likelihood -617.221\n",
"Date: Tue, 02 Jun 2015 AIC 1242.441\n",
"Time: 16:00:02 BIC 1252.862\n",
"Sample: 01-01-1871 HQIC 1246.659\n",
" - 01-01-1970 \n",
"====================================================================================\n",
" coef std err z P>|z| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------------\n",
"sigma2.irregular 1.455e+04 2067.494 7.040 0.000 1.05e+04 1.86e+04\n",
"sigma2.level 1.988e-05 nan nan nan nan nan\n",
"beta.1 -242.4507 22.796 -10.635 0.000 -287.131 -197.771\n",
"beta.2 -387.6257 121.323 -3.195 0.001 -625.415 -149.836\n",
"===================================================================================\n",
"Ljung-Box (Q): 41.48 Jarque-Bera (JB): 0.82\n",
"Prob(Q): 0.41 Prob(JB): 0.66\n",
"Heteroskedasticity (H): 0.88 Skew: 0.18\n",
"Prob(H) (two-sided): 0.72 Kurtosis: 2.74\n",
"===================================================================================\n"
]
},
{
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"pDHGGGOMyZsVk8YYY4wxJm//D2Qrl3X5BHpHAAAAAElFTkSuQmCC\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x115120810>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod_ll = structural.UnobservedComponents(\n",
" nile['volume'], exog=nile[['intervention', 'pulse']],\n",
" level=True, stochastic_level=True,\n",
")\n",
"res_ll = mod_ll.fit()\n",
"print(res_ll.summary())\n",
"res_ll.plot_diagnostics(figsize=(11,6));"
]
},
{
"cell_type": "code",
"execution_count": 329,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x11510bcd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 1, figsize=(10,6))\n",
"\n",
"dates = nile.index._mpl_repr()\n",
"\n",
"# Filtered level\n",
"ax = axes[0]\n",
"ax.plot(dates, nile['volume'], 'k.')\n",
"ax.plot(dates, res_ll.filtered_state[0] + res_ll.obs_intercept[0])\n",
"ax.set_title('Filtered level');\n",
"\n",
"# Residuals\n",
"ax = axes[1]\n",
"ax.plot(dates, nile['volume'] - res_ll.filtered_state[0]- res_lc.obs_intercept[0])\n",
"ax.set_title('Filtered residuals');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Deterministic level + stochastic cycle"
]
},
{
"cell_type": "code",
"execution_count": 302,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Statespace Model Results \n",
"================================================================================\n",
"Dep. Variable: volume No. Observations: 100\n",
"Model: UnobservedComponents Log Likelihood -604.025\n",
"Date: Tue, 02 Jun 2015 AIC 1218.050\n",
"Time: 15:53:11 BIC 1231.076\n",
"Sample: 01-01-1871 HQIC 1223.322\n",
" - 01-01-1970 \n",
"===================================================================================\n",
" coef std err z P>|z| [95.0% Conf. Int.]\n",
"-----------------------------------------------------------------------------------\n",
"sigma2.cycle 1.435e+04 2062.830 6.955 0.000 1.03e+04 1.84e+04\n",
"frequency.cycle 0.5236 1.270 0.412 0.680 -1.966 3.013\n",
"damping.cycle 0.1370 0.112 1.228 0.219 -0.082 0.356\n",
"beta.1 -241.1206 30.793 -7.830 0.000 -301.473 -180.768\n",
"beta.2 -380.6163 121.617 -3.130 0.002 -618.981 -142.251\n",
"===================================================================================\n",
"Ljung-Box (Q): 37.78 Jarque-Bera (JB): 0.77\n",
"Prob(Q): 0.57 Prob(JB): 0.68\n",
"Heteroskedasticity (H): 0.80 Skew: 0.18\n",
"Prob(H) (two-sided): 0.52 Kurtosis: 2.76\n",
"===================================================================================\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x11407cd10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create the model\n",
"mod_lc = structural.UnobservedComponents(\n",
" nile['volume'], exog=nile[['intervention','pulse']],\n",
" irregular=False,\n",
" level=True, stochastic_level=False,\n",
" cycle=True, stochastic_cycle=True, damped_cycle=True\n",
")\n",
"# Fit the model\n",
"res_lc = mod_lc.fit()\n",
"print(res_lc.summary())\n",
"res_lc.plot_diagnostics(figsize=(11,6));"
]
},
{
"cell_type": "code",
"execution_count": 323,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x114f7d890>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(3, 1, figsize=(10,9))\n",
"\n",
"dates = nile.index._mpl_repr()\n",
"\n",
"# Plot the level\n",
"ax = axes[0]\n",
"ax.plot(dates, nile['volume'], 'k.')\n",
"ax.plot(dates, res_lc.filtered_state[0] + res_lc.obs_intercept[0])\n",
"ax.set_title('Filtered level');\n",
"\n",
"# Plot the cycle\n",
"ax = axes[1]\n",
"ax.plot(dates, res_lc.filtered_state[1])\n",
"ax.set_title('Filtered cycle');\n",
"\n",
"# Plot the filtered residuals\n",
"ax = axes[2]\n",
"ax.plot(dates, nile['volume'] - res_lc.filtered_state[0] - res_lc.filtered_state[1] - res_lc.obs_intercept[0])\n",
"ax.set_title('Filtered residuals')\n",
"ax.set_ylim(-300,400);"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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