Abstract
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 \(\chi ^2\) distributed. If this sufficient condition is not satisfied, we suggest a likelihood ratio test based on the Whittle likelihood and derive an asymptotic \(\chi ^2\) 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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Acknowledgements
We deeply thank two reviewers for their comments, which led to a great improvement in our results. This research was supported by the JSPS KAKENHI Grant Numbers 15H02061 and 26540015. The first author is also grateful to Fumiya Akashi for his helpful comments on earlier versions of this paper.
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Nagahata, H., Taniguchi, M. Analysis of variance for multivariate time series. METRON 76, 69–82 (2018). https://doi.org/10.1007/s40300-017-0122-2
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DOI: https://doi.org/10.1007/s40300-017-0122-2