Autoregressive Time Series Analysis of Variance with Skew Normal Innovations

Independence and normality of observations for each level of the classification variables are two fundamental assumptions in traditional analysis of variance (ANOVA), whereas in many real applications the data violate seriously from these assumptions. Accordingly, in these situations using this traditional theory leads to unappealing results. We consider time series ANOVA by assuming a skew normal distribution for innovations. We provide iterative closed forms for the maximum likelihood estimators and construct asymptotic confidence intervals for them. A simulation study and a real data example are used to evaluate the efficiency and applicability of the proposed model for analyzing skew-symmetric time series data.