Deviance Critical Values for Finite Sample Size When Testing the Reduction of Gaussian AR(1)-(G)ARCH(1,1) to Random Walk : Results from MATLAB vs. R-Project

Finite point percentile estimates of Demos and Sentana (1998), Andrews (2001) and Kluppelberg et al. (2002) deviance statistics are determined for the case of tting a null of a Gaussian random walk and the parameters lie on the boundary against the alternate univariate AR(1)-(G)ARCH(1; 1) and the likelihood maximising parameter set 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 R. The results demonstrate the comparative power of these software packages ability to the deviance statistic under small sample asymptotic conditions as sample length T \rightarrow \infty. Results presented by employing the graphical methods of Davidson and MacKinnon (1998) for power and size. 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. The results have implications when calculating confi dence intervals (for avoiding type I,II errors) and selecting suitable software in numerical studies when investigating conditional heteroskedasticity in the case of solutions for the size parameter possibly lie on the boundary