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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