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Variance changes detection in multivariate time series

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  • Galeano, Pedro
  • Peña, Daniel

Abstract

This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures are considered. The first is based on the likelihood ratio test and the second on cusum statistics. These two procedures are compared in a simulation study and we conclude that the cusum procedure is more powerful. The procedures are illustrated in two examples.R

Suggested Citation

  • Galeano, Pedro & Peña, Daniel, 2004. "Variance changes detection in multivariate time series," DES - Working Papers. Statistics and Econometrics. WS ws041305, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws041305
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    1. Sangyeol Lee & Siyun Park, 2001. "The Cusum of Squares Test for Scale Changes in Infinite Order Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 625-644, December.
    2. Ulrich Menzefricke, 1981. "A Bayesian Analysis of a Change in the Precision of a Sequence of Independent Normal Random Variables at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 141-146, June.
    3. D. A. Hsu, 1977. "Tests for Variance Shift at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 279-284, November.
    4. B. Abraham & W. Wei, 1984. "Inferences about the parameters of a time series model with changing variance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 183-194, December.
    5. Booth, N.B. & Smith, A.F.M., 1982. "A Bayesian approach to retrospective identification of change-points," Journal of Econometrics, Elsevier, vol. 19(1), pages 7-22, May.
    6. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    7. Howard Grubb, 1992. "A Multivariate Time Series Analysis of Some Flour Price Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 95-107, March.
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    Cited by:

    1. Josua Gösmann & Daniel Ziggel, 2018. "An innovative risk management methodology for trading equity indices based on change points," Journal of Asset Management, Palgrave Macmillan, vol. 19(2), pages 99-109, March.
    2. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    3. Pedro Galeano & Dominik Wied, 2017. "Dating multiple change points in the correlation matrix," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 331-352, June.
    4. Herwartz, Helmut & Morales-Arias, Leonardo, 2010. "An empirical analysis of the relationship between US monetary policy and international asset prices," Kiel Working Papers 1581, Kiel Institute for the World Economy (IfW Kiel).
    5. Dominik Wied & Matthias Arnold & Nicolai Bissantz & Daniel Ziggel, 2012. "A new fluctuation test for constant variances with applications to finance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1111-1127, November.
    6. Dominik Wied, 2017. "A nonparametric test for a constant correlation matrix," Econometric Reviews, Taylor & Francis Journals, vol. 36(10), pages 1157-1172, November.

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