Python 时间序列数据的平稳性

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\u order\u select\u ic

，得到p和q的值分别为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)}

adf:  -1.96448506629
p-value:  0.302358888762
Critical values:  {'5%': -2.8970475206326833, '1%': -3.5117123057187376, '10%': -2.5857126912469153}
Time Series is  nonstationary
1

但当我使用Augumented Dickey-Fuller测试时，测试结果表明序列不是平稳的

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：

{'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)}

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。那么为什么预兆的dickey fuller检验结果是非平稳序列呢？

很明显，你的数据中有一些季节性。然后，需要仔细进行arma模型和平稳性测试

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延迟数

> (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

---

adfuller并不否认存在单位根。这也可能意味着，即使过程是静止的，也没有足够的力量来拒绝单位根假设。你在R中使用了什么？你“显示”了序列是平稳的？我在R中使用了auto.arima（y），它给了我结果（1,0,1），但在python中adfuller测试将序列y描述为非平稳的。但即使指定滞后顺序=12。序列保持非平稳，测试结果为adf=-1.96448506629，p=0.3023588762，这与您的答案中的滞后12结果显著不同。还有一组数据，R和Python都将其显示为非平稳的。对于python中的本系列，If-lag被取为4。它变得静止不动。如何考虑实际滞后？这是上面提到的系列[ 9560,4010,3790,3840,9150,10230,9570,8230,4640,3730,5820,10410,10220,10040,6720,4290,3820,8700,10040,10820,10080,4160,4320,4140, 9360,10000,10410,7830,9640,3950,5130,9420,9590,9070,10950,10320,3640,4260,10270,10380,9230,10750,10410,5160,5540,11160,11000,11110, 9850,867,4830,5100,10680,11290,10930,10410,10380,4300,4270,10550,9170,13158,12407,10111，599750831057710464105921190811150586755711226211099858489801391613556811030908010124541089910706525957311139299201164011401401401401]见自相关函数acf，plot=TRUE，第七个滞后是有固定滞后和常数的显著滞后，趋势

sm.tsa.adfuller（a，maxlag=12，autolag=None，regression='ct'））

报告的测试统计数据与Robert的答案相同，但p值不同，基于外推，不精确。