How to find the optimal p for AR model

Hi everyone,

I now have a nitrate time series and I have decomposed it with an additive model, which is Y=T+S+R. I hope to find the best-fit AR(p) model for my residuals. I read from some papers that Mann-Wald process could be used. It would be really great if someone could provide a code on how to find the p. Below is my nitrate residuals. Thanks!

0.160157983184890 2.17307720054057 1.52955989565626 1.45006890417194 2.45078566444762 1.82790551974331 2.69034445775899 4.42816184597468 2.34540928553036 2.68279049780604 1.62871903928173 0.508296837837410 -1.62288362596995 1.00584965715162 -0.543055573966803 0.444003915314771 1.52210606035635 2.59531316141792 2.23891089519949 3.05301642518107 3.10129331550264 0.429833321544216 -0.483079342214210 0.722657253107364 -2.30055733593411 -1.25196701104664 -1.31637009539918 -0.531355848351714 0.193111664455751 1.34662635028322 1.17338288183068 1.38414720557814 0.521082891665609 -0.939218305526926 0.469027827480539 3.37592322056800 2.33001561329242 3.25061121894578 1.20307030535913 1.16590066017249 1.22124884474584 0.251845091339198 1.67106041465255 1.28918353716591 1.18477801701926 0.0406356165926184 -0.0849594546340268 -1.09190526778067 -2.24995407529036 -2.44871656287112 -1.47128179369187 -0.438992641112626 0.582514336226620 1.16346937958587 1.01304349966511 0.941625416944357 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Answer 1

[Roger Wohlwend]

You could use the Akaike or the Bayesian Information criterion (Matlab function aicbic). Also consult the page "Choosing ARMA lags using BIC" in the Matlab documentation.

A less sophisticated way is to try different values for p, estimate the model in each case and choose the p where the model's residual are free of autocorrelation.

The Matlab function parcorr suggests that the optimal value for p is 1 in your case. Indeed, for p = 1 the model seem to be quite good. The residuals are free of autocorrelation, the R-square is 0.35 and the coefficient is significant.

[xiaoli su]

Thanks Roger, I have tried the BIC before and it showed the best model ARMA model. However, when I was using autocorr, I got a ACF graph which has a quite significant value at lag 12. I wonder if this is related to the p of AR model or what it indicates.