what does 'bounds' signify in the autocorr function

Sir, I am using the 'autocorr' function of the econometrics toolbox and one of the example shows the following:

[ACF,lags,bounds] = autocorr(y,[],2); bounds bounds =

    0.0843
   -0.0843

 bounds displays (-0.0843, 0.0843), which are the upper and lower confidence bounds.

I would like to know which confidence intervals are being shown by this? In general we use the Anderson correleogram test to determine the significance of the correlation values, are these bounds linked to this test in anyway?

Answer 1

[Hang Qian]

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