moving averge 滑动平均

moving averge 即滑动平均,时间序列处理中常见的方法,简单来说,就是对于一个给定数列,设定一个窗口值N,依次取第1项~第N项,第2项~第N+1项,第3项~第N+2项的平均值,以此类推。

数据来自铁路客运量.csv(2005-2016月度数据)

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import matplotlib.pyplot as plt
import pandas as pd
import requests
import io
import numpy as np
import pylab
pylab.style.use('bmh')
from pylab import rcParams
rcParams['figure.figsize'] = 10, 8
def moving_average(l, N):
sum = 0
result = list( 0 for x in l)
for i in range( 0, N ):
# 从左到右逐渐添加index在N之内的数字
sum = sum + l[i]
result[i] = sum / (i+1)
for i in range( N, len(l) ):
# 加入最右边数字减去最左边数字
sum = sum - l[i-N] + l[i]
result[i] = sum / N
return result
# 使用效率更高的numpy
# http://stackoverflow.com/questions/13728392/moving-average-or-running-mean
def fast_moving_average(x, N):
return np.convolve(x, np.ones((N,))/N)[(N-1):]
url = '铁路客运量.csv'
df = pd.read_csv(url) # python2使用StringIO.StringIO
data = np.array(df['铁路客运量_当期值(万人)'])
dic = {}
for i in [3,5,10,20]:
ma_data = moving_average(data, i)
dic[i] = ma_data
ma_data_df = pd.DataFrame(dic)
ma_data_df.plot()

可以看到,趋势逐渐变得平滑,即对局部震荡不敏感。

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使用numpy.convolve是一种更方便的方法,值得注意的是其有三种mode,分别是’full’(单个重叠也计算), ‘same’(强制等长), ‘valid’(完全重叠),

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def fast_moving_average(x, N, mode):
# return np.convolve(x, np.ones((N,))/N, mode='valid')[(N-1):]
return np.convolve(x, np.ones((N,))/N, mode=mode)
dic = {}
modes = ['full', 'same', 'valid']
i = 10
for mode in modes:
ma_data = fast_moving_average(data, i, mode)
pylab.plot(ma_data)
pylab.legend(modes)

download -1-

参考自斗大熊的博客MovingAverage-滑动平均 – WTF Daily Blog