Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
@Glen_b Can I say that for $Cov[X_1, X_{1000}]$ I am actually not sure about the null hypothesis? The estimation accuracy might be ideal as I speed up my code and run for thousands iterations.
@Glen_b May I know more details about "test the correlation"? Or I could state in this way: I am interested in an indicator which guides me to some meaningful cross-covariance matrices.
@Glen_b It could be longer, the reason is half efficiency half "good-enough". The current result is useful enough so I would rather consider how to include the cross-covariance than speeding up my code.
@Glen_b Oh, I am not trying to figure out a skip interval, my purpose remains to estimate the variance reasonably. In my scenario the after-burn-in period might between 50~100, and a reasonable maximum lag to consider might be less than 20. I just feel estimating a covariance matrix needs more data so I don't want to look into long lags.
@Glen_b I totally agree with you. Besides in my case, the longer the lag, the fewer data I could use to make the estimation, thus I have to restrict the number of $(i,j)$ pairs to consider.
@Glen_b I observed similar behaviour in my simulation. However in my limited experiences in time series analysis, the "autocorrelation" could happen, say, at lag 1 and 4 ( but jump over lag 2 and 3). I feel it is kind of similar to the autocorrelation scenario.
