How to find the optimal p for AR model
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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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0.774783777917767 3.60581389697948 2.61549207606119 2.76878934386290 -0.744105601135384 0.0338708192063266 1.60881035226804 1.63889721452975 1.09333333887146 1.23066646885013 0.306902806757731 0.514602623425335 0.356773715492936 -1.77063737567946 -1.12520039783186 -2.26704433826426 -2.17208048749665 -0.219945266389052 0.984453062438551 4.21439872146615 10.6309936395738 9.58348556531831 4.84058069899181 3.25023931042530 2.76976919525879 1.30981690685228 1.62141267746578 1.80372752879927 1.38985018133276 2.03514418820625 1.38900131579975 -0.0668942244067584 0.495559489466734 -0.124789789022819 0.229564143416563 0.229581547615947 0.273870225215330 1.82887673657471 1.85863130295410 1.18370495705348 0.587686401352863 1.44833920699225 0.397255127351630 0.528218379911014 3.31003088855040 3.85584040582673 3.65225313103201 2.73822933399728 1.88907681036256 1.00744211748783 2.54305547663310 1.16348792049838 0.774428165563654 -0.157960233031073 -0.634385520905799 -0.874163468580525 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采纳的回答
Roger Wohlwend
2015-7-24
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.
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