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I am fitting an AR(p) model to the daily time series of S&P500 returns. I have examined AIC/BIC up to 5 lags and both show that model with 2 lags is optimal. However, when I examine the residuals of regression, autocorrelation appears at 20+ lags, as shown below.

What can be explanation for this? VOlatillity clustering/need for GARCH? MA? AR(30) solves it, but I don't know how to interpret all of this.... I hope that someone would like to help! enter image description here

enter image description here

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  • $\begingroup$ I wonder what is unclear for those who voted for closing this as unclear. $\endgroup$ – Richard Hardy Feb 3 '18 at 18:35
  • $\begingroup$ Cross-posted at Quantitative Finance SE here. Be aware that cross-posting at SE sites is discouraged. $\endgroup$ – Richard Hardy Feb 3 '18 at 20:01

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