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Analysis of variance for multivariate time series

Author

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  • Hideaki Nagahata

    (Waseda University)

  • Masanobu Taniguchi

    (Waseda University)

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 $$\chi ^2$$ χ 2 distributed. If this sufficient condition is not satisfied, we suggest a likelihood ratio test based on the Whittle likelihood and derive an asymptotic $$\chi ^2$$ χ 2 distribution of our test. Finally, we provide some numerical examples using simulated and real financial data as applications of these results.

Suggested Citation

  • Hideaki Nagahata & Masanobu Taniguchi, 2018. "Analysis of variance for multivariate time series," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 69-82, April.
    • Handle: RePEc:spr:metron:v:76:y:2018:i:1:d:10.1007_s40300-017-0122-2
    DOI: 10.1007/s40300-017-0122-2
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    References listed on IDEAS

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    1. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
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    Cited by:

    1. Yuichi Goto & Koichi Arakaki & Yan Liu & Masanobu Taniguchi, 2023. "Homogeneity tests for one-way models with dependent errors under correlated groups," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 163-183, March.
    2. Yuichi Goto & Kotone Suzuki & Xiaofei Xu & Masanobu Taniguchi, 2023. "Tests for the existence of group effects and interactions for two-way models with dependent errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 511-532, June.

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