ABSTRACT
Simulation results for the autocorrelations. In 5 out of 1000 replications Sa was less than 1.645.
Means S.D. Lag True z Z.UB OPT OPT.UB z Z.UB OPT OPT.UB
I 0.87 0.81 0.82 0.81 0.82 0.21 0.19 0.21 0.19 2 0.75 0.68 0.70 0.68 0.69 0.22 0.21 0.22 0.20 3 0.66 0.57 0.59 0.56 0.58 0.26 0.25 0.24 0.23 4 0.58 0.48 0.50 0.46 0.48 0.30 0.29 0.27 0.27 5 0.51 0.41 0.44 0.39 0.42 0.31 0.31 0.28 0.28 6 0.45 0.34 0.37 0.32 0.35 0.31 0.31 0.28 0.28
Note that the bias improved versions of the estimates of the autocovariances do indeed have better bias properties but at the expense of higher variance. The bias adjusted estimates for the autocovariances have the same magnitude of bias, but the optimal ones have smaller variances. The estimates of autocorrelations also have better bias properties, although the unadjusted estimates perform reasonably well, and have comparable variances. This means that for correlation estimation and identification purposes, the bias adjusted estimates are preferable to the unadjusted
2.8 Estimation Zeger's treatment of the estimation of the latent process model is based on a quasi-likelihood approach used to correct for serial correlation in the latent process { c1}. Assumptions on the distributional properties of this process are not explicitly stated but for much of his treatment these are not required. However for the alternative specification in terms of the { 61} process the requirement that these be normally distributed is made quite explicitly in the treatment given in Chan and Ledolter (1995). Indeed as we will demonstrate later, it is difficult to obtain the exact and large sample statistical properties required for inference in this log-normal specification without the assumption of normality.
