Abstract
We propose a new monitoring procedure based on moving sums (MOSUM) for detecting single or multiple structural breaks in factor copula models. The test compares parameter estimates from a rolling window to those from a historical data set and analyzes the behavior under the null hypothesis of no parameter change. The case of multiple breaks is also treated. In the model, the joint copula is given by the copula of random variables which arise from a factor model. This is particularly useful for analyzing high dimensional data. Parameters are estimated with the simulated method of moments (SMM). We analyze the behavior of the monitoring procedure in Monte Carlo simulations and a real data application. We consider an online procedure for predicting the day-ahead Value-at-risk based on the suggested monitoring procedure.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: “Strukturbrüche und Zeitvariation in hochdimensionalen Abhängigkeitsstrukturen”
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The project is funded by the Deutsche Forschungsgemeinschaft (DFG grant “Strukturbrüche und Zeitvariation in hochdimensionalen Abhängigkeitsstrukturen”).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Bedford, T., and R. Cooke. 2002. “Vines - A New Graphical Model for Dependent Random Variables.” Annals of Statistics 30: 1031–068, https://doi.org/10.1214/aos/1031689016.Search in Google Scholar
Berens, T., D. Wied, G. Weiß, and D. Ziggel. 2014. “A New Set of Improved Value-at-Risk Backtests.” Journal of Banking and Finance 48: 29–41, https://doi.org/10.1016/j.jbankfin.2014.07.005.Search in Google Scholar
Bücher, A., I. Kojadinovic, T. Rohmer, and J. Segers. 2014. “Detecting Changes in Cross-sectional Dependence in Multivariate Time Series.” Journal of Multivariate Analysis 132: 111–28, https://doi.org/10.1016/j.jmva.2014.07.012.Search in Google Scholar
Chu, C.-S. J., K. Hornik, and C.-M. Kuan. 1995. “MOSUM Tests for Parameter Constancy.” Biometrika 82: 603–17, https://doi.org/10.1093/biomet/82.3.603.Search in Google Scholar
Chu, C., M. Stinchcombe, and H. White. 1996. “Monitoring structural change.” Econometrica 64 (5): 1045–65, https://doi.org/10.2307/2171955.Search in Google Scholar
Dette, H., and J. Goesmann. 2019. “A Likelihood Ratio Approach to Sequential Change Point Detection”. Journal of the American Statistical Association 115: 1–17. https://doi.org/10.1080/01621459.2019.1630562.Search in Google Scholar
Dowd, K. and D. Blake. 2006. “After VaR: The Theory, Estimation and Insurance Applications of Quantile-based Risk Measures.” The Journal of Risk and Insurance 73: 193–229, https://doi.org/10.1111/j.1539-6975.2006.00171.x.Search in Google Scholar
Francq, C., and J. Zakoian. 2004. “Maximum Likelihood Estimation of Pure GARCH and ARMA-GARCH Processes.” Bernoulli 10 (4): 605–37, https://doi.org/10.3150/bj/1093265632.Search in Google Scholar
Galeano, P., and D. Wied. 2014. “Multiple Break Detection in the Correlation Structure of Random Variables.” Computational Statistics and Data Analysis 76: 262–82, https://doi.org/10.1016/j.csda.2013.02.031.Search in Google Scholar
Garthoff, R. 2014. “Sequential Analysis of Financial Time Series using Residual Charts.” Advances in Statistical Analysis 8: 91–113, https://doi.org/10.1007/s11943-014-0145-6.Search in Google Scholar
Genest, C., and B. Rémillard. 2008. “Validity of the Parametric Bootstrap for Goodness-of-Fit Testing in Semiparametric Models.” Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 44: 1096–127, https://doi.org/10.1214/07-aihp148.Search in Google Scholar
Gray, S. 1996. “Modeling the Conditional Distribution of Interest Rates as a Regime-switching Process.” Journal of Financial Economics 42: 27–62, https://doi.org/10.1016/0304-405x(96)00875-6.Search in Google Scholar
Hoga, Y., and D. Wied. 2017. “Sequential Monitoring of the Tail Behavior of Dependent Data.” Journal of Statistical Planning and Inference 182: 29–49, https://doi.org/10.1016/j.jspi.2016.08.010.Search in Google Scholar
Klaassen, F. 2002. “Improving GARCH Volatility Forecasts with Regime- Switching GARCH.” Empirical Economics 27: 363–94, https://doi.org/10.1007/s001810100100.Search in Google Scholar
Krupskii, P., and H. Joe. 2013. “Factor Copula Models for Multivariate Data.” Journal of Multivariate Analysis 120: 85–101, https://doi.org/10.1016/j.jmva.2013.05.001.Search in Google Scholar
Kurozumi, E. 2017. “Monitoring Parameter Constancy with Endogenous Regressors.” Journal of Time Series Analysis 38: 791–805, https://doi.org/10.1111/jtsa.12236.Search in Google Scholar
Manganelli, S., and R. Engle. 2004. “CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles.” Journal of Business and Economic Statistics 22: 4, https://doi.org/10.1198/073500104000000370.Search in Google Scholar
Manner, H., F. Stark, and D. Wied. 2019. “Testing for Structural Breaks in Factor Copula Models.” Journal of Econometrics 208: 324–45, https://doi.org/10.1016/j.jeconom.2018.10.001.Search in Google Scholar
McNeil, A., and R. Frey. 2000. “Estimation of Tail-related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach.” Journal of Empirical Finance 7: 270–300, https://doi.org/10.1016/s0927-5398(00)00012-8.Search in Google Scholar
Na, O., and J. Lee. 2014. “Monitoring Test for Stability of Copula Parameter in Time Series.” Journal of the Korean Statistical Society 43: 483–501, https://doi.org/10.1016/j.jkss.2014.08.002.Search in Google Scholar
Oh, D., and A. Patton. 2013. “Simulated Method of Moments Estimation for Copula-Based Multivariate Models.” Journal of the American Statistical Association 108, https://doi.org/10.1080/01621459.2013.785952.Search in Google Scholar
Oh, D. H., and A. J. Patton. 2017. “Modelling Dependence in High Dimensions with Factor Copulas.” Journal of Business and Economic Statistics 35: 139–54, https://doi.org/10.1080/07350015.2015.1062384.Search in Google Scholar
Pape, K., D. Wied, and P. Galeano. 2017. “Monitoring Multivariate Variance Changes.” Journal of Empirical Finance 39 (A): 54–68, https://doi.org/10.1016/j.jempfin.2016.08.007.Search in Google Scholar
Rémillard, B. 2017. “Goodness-of-Fit Tests for Copulas of Multivariate Time Series.” Econometrics 35: 139–54. https://doi.org/10.3390/econometrics5010013.Search in Google Scholar
Savu, C., and M. Trede. 2010. “Hierarchies of Archimedean Copulas.” Quantitative Finance 10: 295–304, https://doi.org/10.1080/14697680902821733.Search in Google Scholar
Wied, D., and P. Galeano. 2013. “Monitoring Correlation Change in a Sequence of Random Variables.” Journal of Statistical Planning and Inference 143: 186–96. https://doi.org/10.1016/j.jspi.2012.06.007.Search in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2019-0081).
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