Detecting Serially Correlated Errors in an Autoregressive Model

CFA Level II Quant
#1

CFA Program Curriculum; Volume 1; pp 422-425; Reading 13; Section 4.2 Detecting Serially Correlated Errors in an Autoregressive Model.

Hey guys, I’m just looking for some clarification on this topic error basically - I’m assuming that error autocorrelations are always calculated and analysed individually, i.e. error (t) * error (t-k) / Std Error --> i.e. all of the error autocorrelations for a particular lag are NOT summed together and divided by the Std Error and analysed, but are worked individually?

E.g. in ‘Example 4’ on page 424, ‘Table 4’ has figures for Autocorrelations of the Residual, with different autocorrelations for different lags - these presumably are individual error autocorrelations as described above, and not ALL of the error autocorrelation calculations for a particular lag summed together?

Sorry if this isn’t clear but if someone could put my mind to rest!!

Cheers.

#2

Remember that correlation is a calculation done on long lists of paired values; you don’t calculate the correlation of a single X value and a single Y value.

So, you calculate the autocorrelation of the Xs and the 1-period lagged Xs: (X1, X2), (X2, X3), . . ., (Xn, Xn+1). That’s one autocorrelation calculation.

Then you calculate the autocorrelation of the Xs and the 2-period lagged Xs: (X1, X3), (X2, X4), . . ., (Xn, Xn+2). That’s your second autocorrelation calculation.

And so on.

I hope that that helps.

#3

Perfect - thanks very much for your help - this just was not made clear at all in any of the books!!

Though of course now you’ve spelt it out, it’s pretty obvious … I blame just getting lost in hours of study!

Thanks again.

#4

My pleasure.