This study establishes a new approach for the analysis of variance (ANOVA) of time series. ANOVA has been sufficiently tailored for cases with independent observations, but there has recently been substantial demand across many fields for ANOVA in cases with dependent observations. For example, ANOVA for dependent observations is important to analyze differences among industry averages within financial data. Despite this demand, the study of ANOVA for dependent observations is more nascent than that of ANOVA for independent observations, and, thus, in this analysis, we study ANOVA for dependent observations. Specifically, we show the asymptotics of classical tests proposed for independent observations and give a sufficient condition for the observations to be asymptotically χ2 distributed. If this sufficient condition is not satisfied, we suggest a likelihood ratio test based on the Whittle likelihood and derive an asymptotic χ2 distribution of our test. Finally, we provide some numerical examples using simulated and real financial data as applications of these results.
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