Hi aboltabol,
If we put autocorr(y), it will assume the true process is a white noise, under which the autocorrelations rho(j) have the asymptotics: sqrt(T) * rho(j) converge in distribution to N(0,1), hence the approximate 95% bounds [-2/sqrt(T), 2/sqrt(T)].
If we put something like autocorr(y,[],2), it will assume the true process is a MA(2) process, and approximate the 95% bounds for autocorrelations beyond 2 lags by [-2*SE, 2*SE], where SE = sqrt( (1+rho(-2)+rho(-1)+rho(1)+rho(2)) / T), where rho(j) is the estimated autocorrelation at lag j.
By Anderson correleogram test, I am not sure if you mean the bounds like [(-1-1.64*sqrt(T-j-1))/(T-j), (-1+1.64*sqrt(T-j-1))/(T-j)]? The formula appears not identical.
Thank you,
Hang Qian
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