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moskytw/lab_25_stationarity_spectrum_acf.ipynb

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lab_25_stationarity_spectrum_acf.ipynb
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"source": [
"%matplotlib inline\n",
"import funcy as fy\n",
"import numpy as np\n",
"import scipy as sp\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"import statsmodels.formula.api as smf\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import IPython as ip"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"mpl.style.use('ggplot')\n",
"mpl.rc('figure', figsize=(8.0, 5.5))\n",
"mpl.rc('font', family='Noto Sans CJK TC')\n",
"ip.display.set_matplotlib_formats('svg')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
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],
"source": [
"np.random.seed(20190518)\n",
"\n",
"t = np.arange(1, 2*365, 1)\n",
"e = np.random.randn(len(t))\n",
"p = 7\n",
"f = 1/p\n",
"\n",
"y_s = 500*e\n",
"y_ts = t + 250*e\n",
"y_cs = 250*np.sin(2*np.pi*f*t) + 250*e\n",
"\n",
"y = np.zeros(len(t))\n",
"y[0] = 50*e[0]\n",
"for i in range(1, len(y)):\n",
" y[i] = y[i-1] + 50*e[i]\n",
"y_ds = y\n",
"\n",
"fig, axes = plt.subplots(2, 2)\n",
"axes[0][0].plot(t, y_s)\n",
"axes[0][0].set_title('Stationarity')\n",
"axes[0][1].plot(t, y_ts)\n",
"axes[0][1].set_title('Trend Stationarity')\n",
"axes[1][0].plot(t, y_cs)\n",
"axes[1][0].set_title('Cyclostationary')\n",
"axes[1][1].plot(t, y_ds)\n",
"axes[1][1].set_title('Difference Stationarity')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
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],
"source": [
"Fs = p\n",
"scale = 'linear'\n",
"fig, axes = plt.subplots(2, 2)\n",
"axes[0][0].magnitude_spectrum(y_s, Fs=Fs, scale=scale)\n",
"axes[0][0].set_title('Stationarity')\n",
"axes[0][1].magnitude_spectrum(y_ts, Fs=Fs, scale=scale)\n",
"axes[0][1].set_title('Trend Stationarity')\n",
"axes[1][0].magnitude_spectrum(y_cs, Fs=Fs, scale=scale)\n",
"axes[1][0].set_title('Cyclostationary')\n",
"axes[1][1].magnitude_spectrum(y_ds, Fs=Fs, scale=scale)\n",
"axes[1][1].set_title('Difference Stationarity')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
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],
"source": [
"lags = 2*p\n",
"fig, axes = plt.subplots(2, 2)\n",
"sm.graphics.tsa.plot_acf(y_s, ax=axes[0][0], lags=lags)\n",
"axes[0][0].set_title('Stationarity')\n",
"sm.graphics.tsa.plot_acf(y_ts, ax=axes[0][1], lags=lags)\n",
"axes[0][1].set_title('Trend Stationarity')\n",
"sm.graphics.tsa.plot_acf(y_cs, ax=axes[1][0], lags=lags)\n",
"axes[1][0].set_title('Cyclostationary')\n",
"sm.graphics.tsa.plot_acf(y_ds, ax=axes[1][1], lags=lags)\n",
"axes[1][1].set_title('Difference Stationarity')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
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"text/plain": [
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"source": [
"lags = 2*p\n",
"fig, axes = plt.subplots(2, 2)\n",
"sm.graphics.tsa.plot_pacf(y_s, ax=axes[0][0], lags=lags)\n",
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"sm.graphics.tsa.plot_pacf(y_cs, ax=axes[1][0], lags=lags)\n",
"axes[1][0].set_title('Cyclostationary')\n",
"sm.graphics.tsa.plot_pacf(y_ds, ax=axes[1][1], lags=lags)\n",
"axes[1][1].set_title('Difference Stationarity')\n",
"fig.tight_layout()"
]
}
],
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