New Directions in Econometric Practice: General to Specific Modelling, Cointegration, and Vector Autoregression

By Wojciech W. Charemza; Derek F. Deadman | Go to book overview

Appendix: Statistical Tables

Technical Notes

Tables of critical values of particular test statistics have been prepared through simulation repeated n times (where n is sufficiently large) of a data generating process (DGP) which represents the process under the null hypothesis, computing the statistics n times and then analysing the percentiles of simulated distributions of particular test statistics. For each test the procedure (that is, the simulation of distributions of statistics formed using n computed test statistics) has been repeated for different sample sizes (that is, lengths of individual data series chosen for the DGP in each replication). This length of data series is denoted by T. Let the percentile computed for a distribution obtained from a DGP using samples of size T be denoted as πT. Since T varies, it is possible to smooth the percentiles through a regression approximation. It was found out that the most satisfactory approximation was given by a quadratic regression:

where α, β and γ are the regression coefficients and eT denotes residuals of the regression. Let the standard error of this regression be denoted as s(eT) and the fitted values as ϖT. Hence, upper and lower limits for the smoothed percentiles of distributions of particular statistics, regarded as the upper and lower limits for the critical values of test statistics and denoted as and respectively are given by: and where ST) is the David and Johnson ( 1954) estimate of the standard error of a particular percentile.

The computations have been programmed using the GAUSS 4.2 language and conducted on the CRAY CS6400 computer at the University of Manchester under the UNIX operating system.

Particular DGPs, sample sizes and numbers of replications used for the computations are described below:

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