A local dynamic conditional correlation model

Feng, Yuanhua (2006): A local dynamic conditional correlation model.

Abstract

This paper introduces the idea that the variances or correlations in financial returns may all change conditionally and slowly over time. A multi-step local dynamic conditional correlation model is proposed for simultaneously modelling these components. In particular, the local and conditional correlations are jointly estimated by multivariate kernel regression. A multivariate k-NN method with variable bandwidths is developed to solve the curse of dimension problem. Asymptotic properties of the estimators are discussed in detail. Practical performance of the model is illustrated by applications to foreign exchange rates.

• Item Type: MPRA Paper
• Institution: Maxwell Institute for Mathematical Sciences, Heriot-Watt University
• Language: English
• Keywords: Local and conditional correlations; multivariate nonparametric ARCH; multivariate kernel regression; multivariate k-NN method
• Subjects: G - Financial Economics > G0 - General; G - Financial Economics > G1 - General Financial Markets; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

References

Bauwens, L., S. Laurent and J. Rombouts, 2005, Multivariate GARCH models: A survey. CORE discussion paper, 2003/31 (revised 2005).

Beran, J. and Y. Feng, 2002, SEMIFAR models - A semiparametric framework for modelling trends, long-range dependence and nonstationarity. Computational Statistics and Data Analysis, 27, 393-419.

Bollerslev, T, 1986, Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 31, 307-327.

Bollerslev, T., 1990, Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Review of Economics and Statistics, 72, 498-505.

Bollerslev, T., R. Chou and K. Kroner, 1992, ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52, 5-59.

Bollerslev, T., R.F. Engle and J.M. Wooldridge, 1988, A Capital Asset Pricing Model with Time-Varying Covariances. Journal of Political Economy, 96, 116-131.

Brooks, C. and O. Henry, 2002, The impact of news on measures of undiversifiable risk: Evidence from the UK stock markets. Oxford Bulletin of Econonics and Statistics, 64, 487-507.

Bühlmann, P. and A.J. McNeil, 2002, An algorithm for nonparametric GARCH modelling. Computational Statistics and Data Analysis, 40, 665-683.

Cappiello, L., R.F. Engle and K. Sheppard, 2003, Evidence of Asymmetric Effects in the Dynamics of International Equity and Bond Return Covariance. Preprint, European Central Bank.

Dahlhaus, R., 1997, Fitting time series models to nonstationary processes. Annals of Statistics, 25, 1-37.

Engle, R.F., 1982, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation. Econometrica, 50, 987-1008.

Engle, R.F., 2001, Financial econometrics - A new discipline with new methods. Journal of Econometrics, 100, 53-56.

Engle, R.F., 2002, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics, 20, 339-350.

Engle, R.F. and K.F. Kroner, 1995, Multivariate simultaneous GARCH. Econometric Theory, 11, 122-150.

Engle, R.F. and K. Sheppard, 2001, Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. Preprint, National Bureau of Economic Research.

Fan, J. Q. and Yao, 1998, Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645-60.

Feng, Y., 2004, Simultaneously modelling conditional heteroskedasticity and scale change. Econometric Theory, 20, 563-596.

Feng, Y. and S. Heiler, 1998, Locally weighted autoregression, in: R. Galata and H. Küchenhoff (Eds.) Econometrics in theory and practice, Physica-Verlag, Heidelberg, pp. 101-117.

Feng, Y. and K. Yu, 2005, A Slowly Changing Vector Random Walk Model. Preprint, Heriot-Watt University and Brunel University.

Härdle, W., A.B. Tsybakov and L. Yang, 1998, Nonparametric vector autoregression. Journal of Statistical Planning and Inference, 68, 221-245.

Hafner, C.M., D. van Dijk and P.H. Franses, 2005, Semi-parametric modelling of correlation dynamics. Research Report, Erasmus University Rotterdam.

Hafner, C.M. and P.H. Franses, 2003, A generalized dynamic conditional correlation model for many asset returns. Research Report, Erasmus University Rotterdam.

Herzel, S. C. Starica and R. Tutungu, 2006, A non-stationary paradigm for the dynamics of multivariate model for financial returns. Preprints, University of Perugia.

Ling, S. and M. McAleer, 2002, Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models. Econometric Theory, 18, 722-729.

Pelletier, D., 2006, Regime Switching for Dynamic Correlations. Journal of Econometrics, 131, 445-473.

Ruppert, D. and M.P. Wand, 1994, Multivariate locally weighted least squares regression. Annals of Statistics, 22, 1346-1370.

Silvennoinen, A. and T. Teräsvirta, 2005, Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations. Preprint, Stockholm School of Economics.

Tse, Y. and A. Tsui, 2002, A multivariate GARCH model with time varying correlations. Journal of Business and Economic Statistics, 20, 352-362.