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I would like to smooth some financial time series data under the assumption that the data consists of variable trend and cyclic components plus white noise. I am thinking of applying an AR model to the data, in Octave, for which purpose I have the choice of using the in-built arburg function or code from this github repo.

The model selection criterion available between the two are:

  • AKICc approximate corrected Kullback information criterion
  • KIC Kullback information criterion
  • AICc corrected Akaike information criterion
  • AIC Akaike information criterion
  • FPE final prediction error criterion
  • BIC Bayesian information criterion
  • CIC - combined information criterion
  • FIC finite information criterion
  • FSIC finite sample information criterion
  • GIC generalized information criterion
  • MCC minimally consistent criterion

where only AIC and AICc are common to both, which has implications for my choice of which to use.

My intended use is to automatically fit an AR model using one of the above criterion and then use the coefficients on the data to smooth it such that the residuals are as theoretically close to white noise as possible. This fitting would be carried out in a sliding window of fairly short length ( @ 50 data points max? ).

Given this requirement, which criterion would provide the closest fit to my assumed model? Parsimony in the coefficients or their interpretability are of no concern.

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Since you are using small windows it would be better to use criteria that don't overfit (e.g. I know aic overfits sometimes). However, I would recommend to apply all and choose the model order based on the majority vote. P.s can't you estimate them by yourself? Extract the errors and apply the formulas for each criterion

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