What is recommendation of choosing the value of p & q in ARIMA? what are suggested limiting value for p & q? if ARIMA (p=5, q=5) gives lower RMSE than an arima (p=2, q=2 as taken by the ACF & PACF graph) then could it be preferable to go with the earlier one?
Also is it possible that an ARIMA(2,1,3) model having least RMSE than ARIMA(1,1,0), can have greater value of normalised BIC than other one?
what if ARIMA (2,1,3) gives lesser RMSE out of all parametric combination but all three MA lags are nonsignificant?
In ARIMA modelling (as in all modelling) parametric parsimony is required because of the comparative ease of interpretation and application. This does not mean that adequacy has to be always sacrificed on the altar of parsimony. The beauty of automatic information criteria like AIC, BIC, SIC, HQ, etc. is that they balance the need for parsimony and adequacy. As much as possible they should used.
Ette Etuk
Thank a lot
Could you please tell me is it possible to get model having lesser RMSE than the other, can have greater AIC or BIC?
I agree completely with Dr Etuk that combination of some criteria such as AIC, BIC, HQ, RMSE, ... should be used for model selection in modeling a time series.
Prity,
It is not possible to give an absolute answer to your question but in trying to answer I would first make a general observation. The number of lags you allow/test for will be to some extent a function (a) of the frequency of your data and (b) the number of observations you have.
- On the frequency of data, if you have quarterly data it would suggest a maximum of 3 normal (non-seasonal) lags. If you think there is a seasonal element, in addition I would test a seasonal ARIMA model (in effect the seasonal AR MA term is the fourth lag). I would not test any more than this. If you have monthly data, I would consider testing up to six normal lags plus a seasonal lag (in effect the 12th lag). For annual data, there would be no seasonal lag and I would probably not go more than 3 lags. Daily, hourly, minute, etc. would potentially allow more lags.
- On the number of observations, if you do not have so many then be parsimonious. The number of observations is taken into account in the various penalty function statistics, such as Akaike Information Criterion [AIC] or Final Prediction Error [FPE] Criterion (Akaike, 1974), Schwarz Criterion [SC] or Bayesian Information Criterion [BIC] (Schwarz, 1978) and Hannan Quinn Criterion [HQC] (Hannan, 1980). These statistics all take the form minimising the sum of the residual sum of squares plus a ‘penalty’ term which incorporates the number of estimated parameter coefficients to factor in model parsimony. They differ in terms of how additional parameter estimates (and the number of parameter estimates relative to observations) are penalised. The BIC and HQC have the best theoretical properties. The BIC is strongly consistent whereas AIC will usually result in an over-parameterised model; that is a model with too many AR or MA terms. It can be shown that for n greater than seven the BIC imposes a greater penalty for additional parameters than does the AIC.
I hope this is of some help.
Regards
Aidan
Aidan Meyler,
I am very much thankful for your cooperation. This is definitely helpful for me and same time I got all the answers related this question.
Once again thank you very much.
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