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Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series

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  • Robert Garthoff
  • Iryna Okhrin
  • Wolfgang Schmid

Abstract

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, 1990 ) or a dynamic conditional correlation model Engle (J Bus Econ Stat 20:339–350, 2002 ). We introduce several EWMA and CUSUM control charts. These control schemes are based on univariate EWMA statistics, multivariate EWMA recursions, and different types of cumulative sums. The recursions are applied to local measures for means and covariances, e.g. the present observations and the conditional covariances. Further, they are applied to means and covariances of residuals. The control statistics are obtained by computing the Mahalanobis distance between the EWMA or CUSUM statistics and their expectations if no change occurs. Via Monte Carlo simulation the performance of the proposed charts is compared. Our empirical study illustrates an application of these control procedures to bivariate logarithmic returns of the European indices FTSE100 and DAX. In order to assess the performance of the introduced schemes we apply the average run length and the maximum conditional expected delay. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:3:p:225-255
    DOI: 10.1007/s10182-013-0220-2
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    References listed on IDEAS

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    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
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    3. Sven Knoth & Marianne Frisén, 2012. "Minimax optimality of CUSUM for an autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 357-379, November.
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    7. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    8. Olha Bodnar & Wolfgang Schmid, 2007. "Surveillance of the mean behavior of multivariate time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 383-406, November.
    9. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
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    11. Zhang, Jiujun & Li, Zhonghua & Wang, Zhaojun, 2010. "A multivariate control chart for simultaneously monitoring process mean and variability," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2244-2252, October.
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    Cited by:

    1. Robert Garthoff, 2014. "Sequentielle Überwachung von Finanzzeitreihen anhand von Residuenkarten," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 8(3), pages 91-113, September.
    2. Robert Garthoff & Philipp Otto, 2017. "Control charts for multivariate spatial autoregressive models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 67-94, January.
    3. Robert Garthoff & Philipp Otto, 2018. "Verfahren zur Überwachung räumlicher autoregressiver Prozesse mit externen Regressoren [Statistical surveillance of spatial autoregressive processes with exogenous regressors]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(2), pages 107-133, September.

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