时间序列数据的平稳性
Stationarity of a time series data
我正在尝试使用 python 中的 ARIMA 建模对时间序列数据进行建模。我在默认数据系列上使用函数 statsmodels.tsa.stattools.arma_order_select_ic
并分别获得 p 和 q 的值 2,2。代码如下,
dates=pd.date_range('2010-11-1','2011-01-30')
dataseries=Series([22,624,634,774,726,752,38,534,722,678,750,690,686,26,708,606,632,632,632,584,28,576,474,536,512,464,436,24,448,408,528,
602,638,640,26,658,548,620,534,422,482,26,616,612,622,598,614,614,24,644,506,522,622,526,26,22,738,582,592,408,466,568,
44,680,652,598,642,714,562,38,778,796,742,460,610,42,38,732,650,670,618,574,42,22,610,456,22,630,408,390,24],index=dates)
df=pd.DataFrame({'Consumption':dataseries})
df
sm.tsa.arma_order_select_ic(df, max_ar=4, max_ma=2, ic='aic')
结果如下,
{'aic': 0 1 2
0 1262.244974 1264.052640 1264.601342
1 1264.098325 1261.705513 1265.604662
2 1264.743786 1265.015529 1246.347400
3 1265.427440 1266.378709 1266.430373
4 1266.358895 1267.674168 NaN, 'aic_min_order': (2, 2)}
但是当我使用Augumented Dickey Fuller检验时,检验结果显示序列不是平稳的。
d_order0=sm.tsa.adfuller(dataseries)
print 'adf: ', d_order0[0]
print 'p-value: ', d_order0[1]
print'Critical values: ', d_order0[4]
if d_order0[0]> d_order0[4]['5%']:
print 'Time Series is nonstationary'
print d
else:
print 'Time Series is stationary'
print d
输出如下,
adf: -1.96448506629
p-value: 0.302358888762
Critical values: {'5%': -2.8970475206326833, '1%': -3.5117123057187376, '10%': -2.5857126912469153}
Time Series is nonstationary
1
当我用 R 交叉验证结果时,它表明默认序列是平稳的。那为什么augmented dickey fuller test的结果是非平稳序列呢?
很明显,您的数据有一些季节性。然后arma模型和平稳性测试需要仔细做。
显然,python 和 R 之间 adf 测试差异的原因是每个软件使用的默认滞后数。
> (nobs=length(dataseries))
[1] 91
> 12*(nobs/100)^(1/4) #python default
[1] 11.72038
> trunc((nobs-1)^(1/3)) #R default
[1] 4
> acf(coredata(dataseries),plot = F)
Autocorrelations of series ‘coredata(dataseries)’, by lag
0 1 2 3 4 5 6 7 8 9 10 11
1.000 0.039 -0.116 -0.124 -0.094 -0.148 0.083 0.645 -0.072 -0.135 -0.138 -0.146
12 13 14 15 16 17 18 19
-0.185 0.066 0.502 -0.097 -0.151 -0.165 -0.195 -0.160
> adf.test(dataseries,k=12)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -2.6172, Lag order = 12, p-value = 0.322
alternative hypothesis: stationary
> adf.test(dataseries,k=4)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -6.276, Lag order = 4, p-value = 0.01
alternative hypothesis: stationary
Warning message:
In adf.test(dataseries, k = 4) : p-value smaller than printed p-value
> adf.test(dataseries,k=7)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -2.2571, Lag order = 7, p-value = 0.4703
alternative hypothesis: stationary
我正在尝试使用 python 中的 ARIMA 建模对时间序列数据进行建模。我在默认数据系列上使用函数 statsmodels.tsa.stattools.arma_order_select_ic
并分别获得 p 和 q 的值 2,2。代码如下,
dates=pd.date_range('2010-11-1','2011-01-30')
dataseries=Series([22,624,634,774,726,752,38,534,722,678,750,690,686,26,708,606,632,632,632,584,28,576,474,536,512,464,436,24,448,408,528,
602,638,640,26,658,548,620,534,422,482,26,616,612,622,598,614,614,24,644,506,522,622,526,26,22,738,582,592,408,466,568,
44,680,652,598,642,714,562,38,778,796,742,460,610,42,38,732,650,670,618,574,42,22,610,456,22,630,408,390,24],index=dates)
df=pd.DataFrame({'Consumption':dataseries})
df
sm.tsa.arma_order_select_ic(df, max_ar=4, max_ma=2, ic='aic')
结果如下,
{'aic': 0 1 2
0 1262.244974 1264.052640 1264.601342
1 1264.098325 1261.705513 1265.604662
2 1264.743786 1265.015529 1246.347400
3 1265.427440 1266.378709 1266.430373
4 1266.358895 1267.674168 NaN, 'aic_min_order': (2, 2)}
但是当我使用Augumented Dickey Fuller检验时,检验结果显示序列不是平稳的。
d_order0=sm.tsa.adfuller(dataseries)
print 'adf: ', d_order0[0]
print 'p-value: ', d_order0[1]
print'Critical values: ', d_order0[4]
if d_order0[0]> d_order0[4]['5%']:
print 'Time Series is nonstationary'
print d
else:
print 'Time Series is stationary'
print d
输出如下,
adf: -1.96448506629
p-value: 0.302358888762
Critical values: {'5%': -2.8970475206326833, '1%': -3.5117123057187376, '10%': -2.5857126912469153}
Time Series is nonstationary
1
当我用 R 交叉验证结果时,它表明默认序列是平稳的。那为什么augmented dickey fuller test的结果是非平稳序列呢?
很明显,您的数据有一些季节性。然后arma模型和平稳性测试需要仔细做。
显然,python 和 R 之间 adf 测试差异的原因是每个软件使用的默认滞后数。
> (nobs=length(dataseries))
[1] 91
> 12*(nobs/100)^(1/4) #python default
[1] 11.72038
> trunc((nobs-1)^(1/3)) #R default
[1] 4
> acf(coredata(dataseries),plot = F)
Autocorrelations of series ‘coredata(dataseries)’, by lag
0 1 2 3 4 5 6 7 8 9 10 11
1.000 0.039 -0.116 -0.124 -0.094 -0.148 0.083 0.645 -0.072 -0.135 -0.138 -0.146
12 13 14 15 16 17 18 19
-0.185 0.066 0.502 -0.097 -0.151 -0.165 -0.195 -0.160
> adf.test(dataseries,k=12)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -2.6172, Lag order = 12, p-value = 0.322
alternative hypothesis: stationary
> adf.test(dataseries,k=4)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -6.276, Lag order = 4, p-value = 0.01
alternative hypothesis: stationary
Warning message:
In adf.test(dataseries, k = 4) : p-value smaller than printed p-value
> adf.test(dataseries,k=7)
Augmented Dickey-Fuller Test
data: dataseries
Dickey-Fuller = -2.2571, Lag order = 7, p-value = 0.4703
alternative hypothesis: stationary