Residual-Based Bootstrap Tests for Normality in Autoregressions.

- It is well known that the asymptotic distribution of residual-based test statistics for normality may provide a poor approximation in finite samples. We propose the use of bootstrap critical values to improve small-sample performance and compare the accuracy of the asymptotic and bootstrap versions of the Bera-Jarque test for normality in autoregressions. The proposed bootstrap test is shown to be considerably more accurate than the asymptotic test for a wide range of univariate and multivariate finite order AR models. It effectively eliminates size distortions. The bootstrap test also has high power against a variety of non-Gaussian alternatives including GARCH innovations. Our results are useful in many areas of forecasting and econometric inference, including maximum likelihood estimation and inference for cointegrated systems, the construction of forecast intervals and multivariate forecast regions for autoregressions, backcasting techniques in conditional bootstrap prediction, tests for structural instability in autoregressions, and resampling techniques based on second-moment approximations.