Bayesian Inference for Autoregressive Models with Skewed Exponential Power Errors Ryu, Hyunnam; Kim, Dal Ho;
An autoregressive model with normal errors is a natural model that attempts to fit time series data. More flexible models that include normal distribution as a special case are necessary because they can cover normality to non-normality models. The skewed exponential power distribution is a possible candidate for autoregressive models errors that may have tails lighter(platykurtic) or heavier(leptokurtic) than normal and skewness; in addition, the use of skewed exponential power distribution can reduce the influence of outliers and consequently increases the robustness of the analysis. We use SIR algorithm and grid method for an efficient Bayesian estimation.
Autoregressive model;Bayesian p-value;skewed exponential power distribution;Gibbs sampler;robust;
Azzalini, A. (1985). A Class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178.
Azzalini, A. (1986). A further results on a class of distributions which includes the normal ones, Statistica, 46, 199-208.
Box, G. E. P. and Tiao, G. C. (1992). Bayesian Inference in Statistical Analysis, New York : Wiley.
DiCiccio, T. J. and Monti, A. C. (2004). Inferential aspects of the skew exponential power distribution, Journal of the American Statistical Association, 99, 439-450.
Meng, X. L. (1994). Posterior predictive p-values, The Annals of Statistics, 22, 1142-1160.
Rubin, D. B. (1987). The calculation of posterior distributions by data augmentation: Comment: A noniterative sampling/importance resampling alternative to the data augmentation algorithm for creating a Few imputations when fractions of missing information are modest: The SIR algorithm, Journal of the American Statistical Association, 82, 543-546.