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Chapter 1.ipynb
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"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('ggplot')\n",
"%config InlineBackend.figure_format = 'svg'\n",
"\n",
"import numpy\n",
"import pandas\n",
"from statsmodels.tsa.filters.filtertools import recursive_filter\n",
"import math\n",
"from statsmodels.tsa.stattools import ccovf\n",
"from statsmodels.tsa.stattools import acf\n",
"from statsmodels.formula.api import ols"
]
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"source": [
"# Figure 1.7"
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Figure 1.9"
]
},
{
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"metadata": {
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"cs = pandas.Series([2*math.cos(2*math.pi*x/50 + 0.6*math.pi) \n",
" for x in range(0, 500)])\n",
"w_1 = pandas.Series(numpy.random.normal(0, 1, 500))\n",
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"plt.plot(cs + w_1)\n",
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"plt.subplot(3, 1, 3)\n",
"plt.plot(cs + w_25)\n",
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{
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"source": [
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"x1 = 2 * pandas.Series(numpy.random.binomial(1, 0.5, 11)) - 1\n",
"x2 = 2 * pandas.Series(numpy.random.binomial(1, 0.5, 101)) - 1\n",
"y1 = (5 + x1 - 0.7*x1.shift(1))[1:]\n",
"y2 = (5 + x2 - 0.7*x2.shift(1))[1:]\n",
"plt.subplot(2, 1, 1)\n",
"plt.plot(y1)\n",
"plt.subplot(2, 1, 2)\n",
"plt.plot(y2)\n",
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"print(acf(y1, nlags=4))\n",
"print(acf(y2, nlags=4))"
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{
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"source": [
"# Figure 1.17"
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},
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"source": [
"num = 120\n",
"t = range(0, num)\n",
"\n",
"X = pandas.Series(2 * math.cos(2*math.pi*i/12) for i in t + numpy.random.normal(0, 1, num))\n",
"Y = pandas.Series(2 * math.cos(2*math.pi*(i + 5)/12) for i in t + numpy.random.normal(0, 1, num))\n",
"F1 = pandas.Series(math.cos(2*math.pi*i/12) for i in t)\n",
"F2 = pandas.Series(math.sin(2*math.pi*i/12) for i in t)\n",
"model = ols(formula='Y ~ F1 + F2', \n",
" data=pandas.DataFrame({'Y': Y, 'F1': F1, 'F2': F2}))\n",
"result = model.fit()\n",
"Yw = result.resid\n",
"\n",
"plt.subplot(3, 2, 1)\n",
"plt.plot(X)\n",
"plt.ylabel('X')\n",
"plt.subplot(3, 2, 2)\n",
"plt.plot(Y)\n",
"plt.ylabel('Y')\n",
"plt.subplot(3, 2, 3)\n",
"plt.acorr(X, maxlags=24)\n",
"plt.ylabel('acorr(X)')\n",
"plt.subplot(3, 2, 4)\n",
"plt.acorr(Y, maxlags=24)\n",
"plt.ylabel('acorr(Y)')\n",
"plt.subplot(3, 2, 5)\n",
"# again, we use cross correlation instead of\n",
"# cross covariance\n",
"plt.xcorr(X, Y, maxlags=24)\n",
"plt.ylabel('xcorr(X, Y)')\n",
"plt.subplot(3, 2, 6)\n",
"# note the much shorter ranges of the y axis\n",
"plt.xcorr(X, Yw, maxlags=24)\n",
"plt.ylabel('xcorr(X, Yw)')\n",
"plt.tight_layout()"
]
}
],
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