来自预测包的auto.arima（）的季节性

Question

my_data <- c(232,294,320,314,336,189,331,185,161,140,49,7,0,3,4,9,38,169,275,316,366,422,328,283,213,238,220,193,250,308,224,190,188,99,41,17,19,9,1,3,10,108,149,189,168,170,155,101,119,89,142,169,192,242,152,141,105,76,39,20,17,13,5,3,8,54,102,102,155,159,164,200,183,144,204,190,219,158,128,142,130,86,58,13,12,0,6,4,20,302,297,312,345,293,233,275,233,199,279,250,208,161,200,181,133,140,17,14,2,0,2,4,36,183,379,371,356,425,320,282,172,214,226,250,196,239,183,194,135,75,28,11,2,3,5,4,29,212,316,343,375,431,225,248,209,258,262,230,218,162,193,178,126,131,37,7,5,3,0,1,20,149,258,408,316,307,352,247,285,236,254,321,233,175,264,114,104,82,37,49,4,16,2,14,22,169,259,355,379,346,261,256,220,238,227,201,242,185,121,160,114,91,33,9,4,2,0,2,22,62,114,156,190,186,140,155,141,135,140,137,179,128,156,124,98,66,63,32,27,0,21,5,4,39,73,162,175,207,183,121,174,107,160,177,258,170,152,165,117,59,35,69,7,0,3,3,28,98,165,194,200,190,162,160,170,200,189,187,141,224,152,115,111,47,20,15,2,0,0,29,10,59,170,212,164,201,193,182,277,283,376,310,194,247,177,164,140,192,95,49,10,10,2,5,38,52,156,331,480,378,231,172,132,199,245,267,192,223,182,168,152,81,20,14,13,6,14,16,6,21,51,113,94,103,113,93,205,98,118,97,138,112,98,99,79,74,71,38,31,30,31,38,41,48,131,159,212,134,150,145,149,105,142,149,122,137,193,105,68,75,35,33,41,38,33,29,44,54,85,109,118,117,113,107,112,92,112,98,111,81,120,113,66,55,10,20,26,25,3,10,15,30,60,91,97,67,100,99,75,92,98,126,116,103,110,87,124,66,55,30,31,28,28,31,29,49,109,144,152,116,106,88,164,127,121,161,186,104,81,79,103,69,47,35,35,30,28,34,42,56,114,110,149,153,112,151,138,151,141,139,206,225,166,173,185,384,221,100,61,51,35,44,38,83,87,182,205,243,191,144,106,112,167,234,147,136,152,107,156,53)

my_data has a clear season of 24 periods as can be seen from acf/pacf correlation plots.

library(forecast)
tsdisplay(my_data)

How can auto.arima be configured in order to capture the seasonality?

Unfortunately

auto.arima(my_data, seasonal = TRUE, approximation = FALSE, stepwise = FALSE)

only accounts for (p,d,q) factor, rather than the expected (p,d,q)(P,D,Q)[24]

Series: my_data 
ARIMA(3,1,2)                    

Coefficients:
         ar1      ar2      ar3      ma1     ma2
      1.8061  -0.8164  -0.0587  -1.9453  0.9672
s.e.  0.0478   0.0896   0.0474   0.0178  0.0171

sigma^2 estimated as 2261:  log likelihood=-2581.68
AIC=5175.36   AICc=5175.54   BIC=5200.52

Answer 1

Convert my_data to a ts object and then try auto.arima . For instance, suppose your data started in Jan 2010 and went through Oct 2030.

> my_data <- c(232,294,320,314,336,189,331,185,161,140,49,7,0,3,4,9,38,169,275,316,366,422,328,283,213,238,220,193,250,308,224,190,188,99,41,17,19,9,1,3,10,108,149,189,168,170,155,101,119,89,142,169,192,242,152,141,105,76,39,20,17,13,5,3,8,54,102,102,155,159,164,200,183,144,204,190,219,158,128,142,130,86,58,13,12,0,6,4,20,302,297,312,345,293,233,275,233,199,279,250,208,161,200,181,133,140,17,14,2,0,2,4,36,183,379,371,356,425,320,282,172,214,226,250,196,239,183,194,135,75,28,11,2,3,5,4,29,212,316,343,375,431,225,248,209,258,262,230,218,162,193,178,126,131,37,7,5,3,0,1,20,149,258,408,316,307,352,247,285,236,254,321,233,175,264,114,104,82,37,49,4,16,2,14,22,169,259,355,379,346,261,256,220,238,227,201,242,185,121,160,114,91,33,9,4,2,0,2,22,62,114,156,190,186,140,155,141,135,140,137,179,128,156,124,98,66,63,32,27,0,21,5,4,39,73,162,175,207,183,121,174,107,160,177,258,170,152,165,117,59,35,69,7,0,3,3,28,98,165,194,200,190,162,160,170,200,189,187,141,224,152,115,111,47,20,15,2,0,0,29,10,59,170,212,164,201,193,182,277,283,376,310,194,247,177,164,140,192,95,49,10,10,2,5,38,52,156,331,480,378,231,172,132,199,245,267,192,223,182,168,152,81,20,14,13,6,14,16,6,21,51,113,94,103,113,93,205,98,118,97,138,112,98,99,79,74,71,38,31,30,31,38,41,48,131,159,212,134,150,145,149,105,142,149,122,137,193,105,68,75,35,33,41,38,33,29,44,54,85,109,118,117,113,107,112,92,112,98,111,81,120,113,66,55,10,20,26,25,3,10,15,30,60,91,97,67,100,99,75,92,98,126,116,103,110,87,124,66,55,30,31,28,28,31,29,49,109,144,152,116,106,88,164,127,121,161,186,104,81,79,103,69,47,35,35,30,28,34,42,56,114,110,149,153,112,151,138,151,141,139,206,225,166,173,185,384,221,100,61,51,35,44,38,83,87,182,205,243,191,144,106,112,167,234,147,136,152,107,156,53)
> myts <- ts(my_data, start=c(2010, 1), end=c(2030, 10), frequency=24)
> auto.arima(myts, seasonal = T)
Series: myts 
ARIMA(1,1,0)(1,0,0)[24]                    

Coefficients:
          ar1   sar1
      -0.1427  0.373
s.e.   0.0532  0.052

sigma^2 estimated as 2502:  log likelihood=-2607.86
AIC=5221.73   AICc=5221.78   BIC=5234.31

Be careful to NOT set approximation and stepwise to False if you want to save time.