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I tried to find p and q by using auto.arima function in RStudio. It gave ARIMA(1,1,0). However, after applying p=1 and q=0 to the GARCH model, ar1 became insignificant and AIC became higher. p=0 and q=0 gave the best results according to the Information Criteria. I want to know whether I am doing something wrong.

library(quantmod)
library(forecast)
library(rugarch)

getSymbols("BNTX", to="2022-12-31")
returns_BNTX=CalculateReturns(BNTX$BNTX.Adjusted)[-1]
auto.arima(returns_BNTX)
mod_specify=ugarchspec(mean.model=list(armaOrder=c(0,0)), variance.model=list(model="sGARCH", garchOrder=c(1,1)), distribution.model='sstd')
mod_fitting_ssstd_BNTX=ugarchfit(data=returns_BNTX, spec=mod_specify, out.sample=20)
mod_fitting_ssstd_BNTX

The AIC with ARMA(0,0)= -3,0605 The AIC with ARMA(1,0)= -3.0595 (insignificant ar1) +not sure how to apply drift in ARFIMA(1,1,0) to the GARCH model.

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    $\begingroup$ It is not clear whether the AIC and BIC values are comparable across the models, as (1) different software may use different conventions (adding or dropping a constant, calculating AIC/BIC for the entire sample vs. per observation and the like) and (2) applying differencing in some but not all models makes AIC/BIC comparisons harder. You would need to supply much more detailed information about your models and the packages and functions used to fit them to facilitate a more definite analysis. $\endgroup$ Dec 30, 2022 at 20:50
  • $\begingroup$ @RichardHardy I added some code. Hope it will be helpful $\endgroup$
    – Rashid
    Dec 30, 2022 at 21:13

1 Answer 1

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The AIC and BIC values are incomparable across the models, as

  1. forecast and rugarch packages use different conventions, i.e. forecast reports "proper" AIC/BIC values while rugarch divide them by the number of observations; there may or may not be differences in adding or dropping a constant, too;
  2. applying differencing on some but not all models prohibits direct AIC/BIC comparisons.

It is not exactly clear which models you are comparing, but it would not surprise me very much if the AIC/BIC rankings of pure ARIMA models (no GARCH) with different AR and MA orders and ARMA-GARCH models with the corresponding AR and MA orders would not coincide exactly. This can happen if the data generating process is approximated roughly equally well (or equally poorly) by several different AR-MA combinations.

Also, do not worry about the statistical significance of the coefficient estimates; significance is a poor guide for model selection.

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  • $\begingroup$ (I could not replicate the code, as getSymbols throws the following error message: Error in new.session() : Could not establish session after 5 attempts.) $\endgroup$ Dec 31, 2022 at 10:48
  • $\begingroup$ I used "quantmod" package for the function. I want to find the mean order of the GARCH model using auto.arima() function. But applying the output does not give proper results. $\endgroup$
    – Rashid
    Dec 31, 2022 at 10:53
  • $\begingroup$ @Rashid, if you want to find it using auto.arima, then just do it. $\endgroup$ Dec 31, 2022 at 11:33
  • $\begingroup$ I guess there is a misunderstanding. I use the function. I get ARIMA(1,1,0). But when I apply to the GARCH the ar1 becomes insignificant and AIC becomes bigger. ARMA(0,0) fits better. So what should I use all in all? $\endgroup$
    – Rashid
    Dec 31, 2022 at 13:00
  • $\begingroup$ @Rashid, as I write in my answer, significance is a non-issue. Can you update the post with an exact list of models and their corresponding AICs? Your verbal descriptions are not detailed enough for a sound analysis. $\endgroup$ Dec 31, 2022 at 14:37

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