ARIMA model with 1 and 25 lag in R

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Please, when applying the ARIMA(p,d,q) modeling in a series, in the partial autocorrelation function a peak appears in lag 1 and another in 25 and no other statistically significant. There is some command in the R to deal with these two lags only, not including 25 regressive coefficients?

r

  • Henrique, did you ever see if it is not a seasonal behavior? If lag 50 is also not significant?

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Yes there is.

Considering the series lh of R:

> lh
Time Series:
Start = 1 
End = 48 
Frequency = 1 
 [1] 2.4 2.4 2.4 2.2 2.1 1.5 2.3 2.3 2.5 2.0 1.9 1.7 2.2 1.8 3.2 3.2 2.7 2.2 2.2 1.9 1.9
[22] 1.8 2.7 3.0 2.3 2.0 2.0 2.9 2.9 2.7 2.7 2.3 2.6 2.4 1.8 1.7 1.5 1.4 2.1 3.3 3.5 3.5
[43] 3.1 2.6 2.1 3.4 3.0 2.9

Adjust the model like this:

> arima(lh, order = c(1,1,1), fixed = c(NA, 0))

Call:
arima(x = lh, order = c(1, 1, 1), fixed = c(NA, 0))

Coefficients:
          ar1  ma1
      -0.0404    0
s.e.   0.1443    0

sigma^2 estimated as 0.2525:  log likelihood = -34.35,  aic = 72.7

In this case, I am saying that the parameter AR1 is free (estimated by the model) and that the MA1 is equal to zero by means of the argument fixed.

In your case, if you wanted to adjust a arima(25,1,0) with only the coefficients 1 and 25 of the AR, could do so:

> arima(lh, order = c(25,1,0), fixed = c(NA, rep(0,23), NA))

Call:
arima(x = lh, order = c(25, 1, 0), fixed = c(NA, rep(0, 23), NA))

Coefficients:
          ar1  ar2  ar3  ar4  ar5  ar6  ar7  ar8  ar9  ar10  ar11  ar12  ar13  ar14
      -0.0539    0    0    0    0    0    0    0    0     0     0     0     0     0
s.e.   0.1343    0    0    0    0    0    0    0    0     0     0     0     0     0
      ar15  ar16  ar17  ar18  ar19  ar20  ar21  ar22  ar23  ar24    ar25
         0     0     0     0     0     0     0     0     0     0  0.2994
s.e.     0     0     0     0     0     0     0     0     0     0  0.1918

sigma^2 estimated as 0.2297:  log likelihood = -33.3,  aic = 72.6

The argument fixed is always a vector with the number of elements equal to the number of parameters your model has. You can pre-specify any value for the parameters, but normally we only use 0 (when we don’t want that term) and NA (when we want the parameters to be estimated by the model).

  • See if this works: arima(lh, order = c(25,1,1), fixed = c(rep(0,24), NA, NA))

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