# Analysis of variance for multivariate time series

Analysis of variance for multivariate time series 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png METRON Springer Journals

# Analysis of variance for multivariate time series

, Volume 76 (1) – Sep 20, 2017
14 pages

/lp/springer_journal/analysis-of-variance-for-multivariate-time-series-UhEkUvIjX6
Publisher
Springer Journals
Subject
Statistics; Statistics, general; Statistical Theory and Methods
ISSN
0026-1424
eISSN
2281-695X
D.O.I.
10.1007/s40300-017-0122-2
Publisher site
See Article on Publisher Site

### 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.

### Journal

METRONSpringer Journals

Published: Sep 20, 2017

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