# Problem with ARMA modeling with high order (p,q)

Hello,
So I'm trying to fit a model for the evolution of financial indexes to observe the exogenous fluctuations of COVID-19. I determined that for the S&P 500, I have to estimate a ARMA(21,15) by looking at the autocorrelation of the series. But when I try to fit the model with the tseries function arma(), I get an error with the optim function that I believe is suppose to optimize the likelihood. I don't know what to do. Please help.
I am working on the returns series that are stationary. (sorry for my poor English writing skills)
Here the preview :

``````library(quantmod)
library(tseries)

tickers<-c("^GSPC","^DJI","^IXIC","^FTSE","^FCHI","^N100","^N225","^GDAXI","000001.SS","^HSI","^BVSP")
indices<-c("S&P500","Dow Jones","NASDAQ","FTSE 100","CAC 40","EURONEXT 100","NIKKEI 225","DAX ","SSE Composite","HANG SENG","IBOVESPA")

valeurs<-NULL
for(ticker in tickers)
valeurs<-cbind(valeurs,
getSymbols(ticker,src = "yahoo",from = "2017-01-04",auto.assign = FALSE)[,4])

colnames(valeurs)<-indices
rm(ticker,tickers)
valeurs<-valeurs["20170104/20210329"]
valeurs<-na.locf(valeurs)
rendements<-na.omit(ROC(valeurs))
armasp<-arma(rendements\$`S&P500`,order = c(21,15))
#> Error in optim(coef, err, gr = NULL, hessian = TRUE, ...): valeur non-finie fournie par optim
``````

S&P500 returns are very close to white noise. You are almost certainly estimating too many parameters and the likelihood function is flat. This is what's known as the "root cancellation" problem.

I understand then I just have to select my orders with informative criterion or to take the previous autocorrelation cancel, right ? I'm glad to know the name of my problem. Thank you so much Mr Startz !

I believe that information criteria don't work too well either. You might want to estimate on a training sample and see how a given model does in "out of sample" prediction.

That's doesn't seem very rigorous...

Depends on your objective. If all you're trying to get is the residuals, then it probably doesn't matter a huge amount what ARMA model you use. (Though I'm not sure why you would call these residuals "exogenous.")

The fundamental problem is that an ARMA(0,0) is the same as an ARMA(1,1) with equal AR and MA coefficients. Standard statistical tests don't work very well in distinguishing the two.

Got it. Though I am not sure about what I am trying to do. I am thinking of estimating the model for the whole period and then use a chow test to look if the covid caused a structural break, thus I might need the coefficients to be as good as possible . It is also a work for school so I want to be as academic as I can.

That's quite sensible. While it's a good idea to use as low an order ARMA specification as you can, my memory is that the estimated log-likelihoods aren't too bad so a Chow test ought to work.

I think I'll go towards that, I'll explain that I can't estimate ARMA with higher orders because of the series being almost white noises. I hope my professor likes it.
Huge thank again

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