Dear all R users,
   
  I am really struggling to determine the most appropriate lag order of ARIMA model. My understanding is that, as for MA [q] model the auto correlation coeff vanishes after q lag, it says the MA order of a ARIMA model, and for a AR[p] model partial autocorrelation vanishes after p lags it helps to determine the AR lag. And most appropriate model choosed by this argument gives min AIC.
   
  Now I considered following data :
   
  2.1948 2.2275 2.2669 2.2839 1.9481 2.1319 2.0238 2.3109 2.5727 2.5176
2.5728 2.6828 2.8221 2.879 2.8828 2.9955 2.9906 2.9861 3.0452 3.068
2.9569 3.0256 3.0977 2.985 2.9572 3.0877 3.1009 3.1149 2.8886 2.9631
3.0325 2.9175 2.7231 2.7905 2.8493 2.8208 2.8156 2.9115 2.701 2.6928
2.7881 2.723 2.7266 2.9494 3.113 3.0566 3.0358 3.05 3.0724 3.1365
3.1083 3.0257 3.2211 3.4269 3.327 3.1205 2.9997 3.0201 3.0803 3.2059
3.1997 3.038 3.1613 3.2802 3.2194     
   
  ACF for 1st diff series:
  Autocorrelations of series 'diff(data1)', by lag
       0      1      2      3      4      5      6      7      8      9     10 
 1.000 -0.022 -0.258 -0.016  0.066  0.034  0.035 -0.001 -0.089  0.028  0.222 
    11     12     13     14     15     16     17     18 
-0.132 -0.184 -0.038  0.048 -0.026 -0.041 -0.067  0.059 
   
    PACF for 1st diff series:
  Partial autocorrelations of series 'diff(data1)', by lag
       1      2      3      4      5      6      7      8      9     10     11 
-0.022 -0.258 -0.031 -0.002  0.026  0.057  0.021 -0.069  0.029  0.194 -0.124 
    12     13     14     15     16     17     18 
-0.100 -0.111 -0.043 -0.078 -0.056 -0.085  0.086 

  On basis of that I choose ARIMA[2,1,2] for the original data
   
  But I got error while doing that :
   
  > arima(data1, c(2,1,2))
Error in arima(data1, c(2, 1, 2)) : non-stationary AR part from CSS
   
  And AIC for other combination of lags are:
  > arima(data1, c(2,1,1))$aic
[1] -84.83648
> arima(data1, c(1,1,2))$aic
[1] -84.35737
> arima(data1, c(1,1,1))$aic
[1] -83.79392

  Hence on basis of AIC criteria if I choose ARIMA[2,1,1] model, then the first rule that I said earlier does not support.
   
  Am I making anything wrong? Can anyone give me any suggestion on what is the "universal" rule for choosing the best lag?
   
  Regards,


  
 
   
   

       
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