How to automate ARIMA model 'order' selection based on ACF and PACF plots?

While modeling in MATLAB, we have to provide values of p, d and q in arima(p,d,q) implementation, by observing ACF - PACF plots and may be differencing the data afterwards. Is there a way so that these values can be assigned automatically from ACF - PACF plots and AIC test? I know, there are some other factors affecting these input argument values. But, for beginning I would be focusing on ACF - PACF plot, AIC test and need of differentiating the data only. The aim of this procedure is to get best fit possible.

Answer 1

[Asad (Mehrzad) Khoddam]

I am not sure that it is your answer or not. But I have used this function to find the best values for p and q for a given time series y

function ar=checkArima(y,pp,qq)
% pp is the maximum for p
% qq is the maximum for q
LOGL = zeros(pp+1,qq+1); %Initialize
PQ = zeros(pp+1,qq+1);
for p = 1:pp+1
    for q = 1:qq+1
        mod = arima(p-1,0,q-1)
        [fit,~,logL] = estimate(mod,y,'print',false);
        LOGL(p,q) = logL;
        PQ(p,q) = p+q;
     end
end

LOGL = reshape(LOGL,(pp+1)*(qq+1),1);
PQ = reshape(PQ,(pp+1)*(qq+1),1);
[~,bic] = aicbic(LOGL,PQ+1,100);
ar=reshape(bic,pp+1,qq+1);
% the rows correspond to the AR degree (p) and the
% columns correspond to the MA degree (q). The smallest value is best

[na ja]

Thanks Asad,what if I consider AIC test instead of BIC? What pros and cons each have compared to other? And, I am more interested in implementing some numerical analysis on values of ACF and PACF,so that I can know whether they are tailing off or cutting off.

[Hamed Majidiyan]

Hi Asad,

Thanks for the code in advance. I ran the code and I got the following results, even though I don't know how to intrepret the outcomes, so any help would be highly appreciated

ARMA=checkarma(datac_chunk,2,1,2)

ARMA(:,:,1) =

1.0e+05 *

-0.9306 -1.7988 -0.9305

-1.7988 -2.5917 -1.6927

-2.6918 -3.0212 -0.0683

ARMA(:,:,2) =

1.0e+05 *

-1.7987 -0.9305 -1.7987

-2.5914 -1.6966 -2.5907

-1.7986 -1.5608 -3.1177

[Hamed Majidiyan]

Hi Asad,

Thanks for the code in advance. I ran the code and I got the following results, even though I don't know how to intrepret the outcomes, so any help would be highly appreciated

ARMA=checkarma(datac_chunk,2,1,2)

ARMA(:,:,1) =

1.0e+05 *

-0.9306 -1.7988 -0.9305

-1.7988 -2.5917 -1.6927

-2.6918 -3.0212 -0.0683

ARMA(:,:,2) =

1.0e+05 *

-1.7987 -0.9305 -1.7987

-2.5914 -1.6966 -2.5907

-1.7986 -1.5608 -3.1177