时间序列中的异常

参考资料：时间序列中的异常

例子：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.signal import lfilter, unit_impulse
def arma_process(ar, ma, size=200, scale=1., e=None):
    if e is None:
        e = np.random.normal(size=size)
    return lfilter(ma, ar, scale*e)
# 考虑一个 ARMA(1, 1) 模型
ar = [1, 0.85]
ma = [1, 0.65]
sample = arma_process(ar, ma)
io = arma_process(ar, ma, e=10*unit_impulse(200, 100))
ao = 10*unit_impulse(200, 100)
tc = arma_process([1, -0.9], [1], e=10*unit_impulse(200, 100))
ls = arma_process([1, -1], [1], e=10*unit_impulse(200, 100))
x = range(200)
plt.figure(figsize=(12, 12))
plt.subplot(511)
plt.plot(x, sample)
plt.title('original signal')
plt.subplot(523)
plt.plot(x, io)
plt.title('innovational outlier (IO)')
plt.subplot(524)
plt.plot(x, sample+io, label='with IO')
plt.plot(x, sample, label='without IO')
plt.title('signal with IO')
plt.legend()
plt.subplot(525)
plt.plot(x, ao)
plt.title('additive outlier (AO)')
plt.subplot(526)
plt.plot(x, sample+ao, label='with AO')
plt.plot(x, sample, label='without AO')
plt.title('signal with AO')
plt.legend()
plt.subplot(527)
plt.plot(x, tc)
plt.title('temporary change (TC)')
plt.subplot(528)
plt.plot(x, sample+tc, label='with TC')
plt.plot(x, sample, label='without TC')
plt.title('signal with TC')
plt.legend()
plt.subplot(529)
plt.plot(x, ls)
plt.title('level shift (LS)')
plt.subplot(5,2,10)
plt.plot(x, sample+ls, label='with LS')
plt.plot(x, sample, label='without LS')
plt.title('signal with LS')
plt.legend()
plt.tight_layout()
plt.show()