Deviance critical values for finite sample size when testing the reduction of (G)ARCH(1,1) to a Gaussian random walk: Results from MATLAB

Finite point percentile estimates of Demos and Sentana (1998) and Andrews (2001) deviance statistics are determined for the case of fitting a null of a random walk and the parameters lie on the boundary against the alternate univariate (G)ARCH(1, 1) and the likelihood maximising parameter set Ω possibly lie in the adjacent neighbourhood. We present a way to adjust the asymptotic critical value for sample size when using default settings of the relevant estimation routines in MATLAB and RProject. The results demonstrate the comparative power of these software packages ability to fit the deviance statistic under small sample asymptotic conditions as sample length N →∞. Results presented by employing the graphical methods of Davidson and MacKinnon (1998). These equations are applied to Deutsche mark/British pound FX data from Bollerslev and Ghysels (1996) which has become the generally accepted data set for benchmarking GARCH(1,1) software using the approach of Calzolari and Panattoni (1988). The results have implications when calculating confidence intervals (for avoiding type I,II errors) and selecting suitable software in numerical studies and investigating conditional heteroskedasticity when solutions for the size parameter possibly lie on the boundary.