Abstract
The modelling of multivariate financial time series has attracted an enormous interest recently, both from a theoretical and practical perspective. Focusing on factor type models that reduce the dimensionality and other models that are tractable in high dimensions, we review models for volatility, correlation and dependence, and show their application to quantities of interest such as value-at-risk or minimum-variance portfolio. In an application to a 69-dimensional asset price time series, we compare the performance of factor-based multivariate GARCH, stochastic volatility and dynamic copula models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alexander, C. (2001). Orthogonal GARCH. In Mastering risk, financial times (Vol 2, pp. 21–38). London: Prentice Hall.
Anderson, H. M., & Vahid, F. (2007). Forecasting the volatility of australian stock returns: do common factors help? Journal of Business and Economic Statistics, 25(1), 76–90.
Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39, 885–905.
Andersen, T.G., Shephard, N. (2009): Stochastic volatility: origins and overview. In: T.G. Andersen, R.A. Davis, J.-P. Kreiss, T. Mikosch (Eds.) Handbook of Financial Time Series, p. 233–254, Springer Verlag: Berlin, Heidelberg New York.
Andersen, T. G., Bollerslev, T., & Lange, S. (1999). Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon. Journal of Financial Economics, 61, 43–76.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Ebends, H. (2001). The distribution of realized stock volatility. Journal of Financial Economics, 61, 43–76.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association, 96, 42–55.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579–625.
Andersen, T. G., Bollerslev, T., Diebold, F. X., & Wu, J. (2006). Realized beta: Persistence and predictability. In T. Fomby & D. Terrell (Eds.), Advances in Econometrics: Econometric analysis of economic and financial time series in honor of R. F. Engle and C. W. J. Granger (Vol. B, pp. 1–40).
Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica, 61, 821–856.
Asai, M., & McAleer, M. (2009). The structure of dynamic correlations in multivariate stochastic volatility models. Journal of Econometrics, 150, 182–192.
Asai, M., McAleer, M., & Yu, J. (2006). Multivariate stochastic volatility: A review. Econometric Reviews, 25(2–3), 145–175.
Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71, 135–171.
Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221.
Barndorff-Nielsen, O. E., & Shephard, N. (2002a). Econometric analysis of realized volatility and its use in estimating stochastic volatilty models. Journal of the Royal Statistical Society, Ser. B, 64, 253–280.
Barndorff-Nielsen, O. E., & Shephard, N. (2002b). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17, 457–477.
Barndorff-Nielsen, O. E., & Shephard, N. (2004a). Econometric analyis of realized covariation: high frequency based covariance, regression, and correlation in financial economics. Econometrica, 72, 885–925.
Barndorff-Nielsen, O. E., & Shephard, N. (2004b). Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics, 2, 1–37.
Bauwens, L., Laurent, S., & Rombouts, J. (2006). Multivariate garch models: A survey. Journal of Applied Econometrics, 7, 79–109.
Bera, A., & Higgings, M. (1993). A survey of ARCH models: Properties, estimation and testing. Journal of Economic Surveys, 7, 305–366.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.
Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH approach. Review of Economics and Statistics, 72, 498–505.
Bollerslev, T., & Wooldridge, J. M. (1992). Quasi maximum likelihood estimation of dynamic models with time-varying covariances. Econometric Reviews, 11, 143–172.
Breitung, J., & Eickmeier, S. (2006). Dynamic factor models. In O. Hübler & J. Frohn (Eds.), Modern econometric analysis. Berlin: Springer.
Brillinger, D. R. (1981). Time series: Data analysis and theory. New York: Holt, Rinehart and Winston.
Broto, C., & Ruiz, E. (2004). Estimation methods for stochastic volatility models: a survey. Journal of Economic Surveys, 18(5), 613–649.
Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The econometrics of financial markets. Princeton: Princepton University Press.
Chamberlain, G., & Rothschild, M. (1983). Arbitrage, factor structure, and meanvariance analysis on large asset markets. Econometrica, 51, 1281–1304.
Chan, L. K. C., Karceski, J., & Lakonishok, J. (1999). On portfolio optimization: forcasting covariances and choosing the risk model. The Review of Financial Studies, 12(5), 937–974.
Cherubini, G., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. UK: Wiley.
Clark, P. K. (1973). A subordinate stochastic process model with finite variance for speculative prices. Econometrica, 41, 135–155.
Connor, G, & Korajczyk, R. A. (1993). A test for the number of factors in an approximate factor model. Journal of Finance, 48(4), 1263–1291.
Danielsson, J. (1994). Stochastic volatility in asset prices estimation with simulated maximum likelihood. Journal of Econometrics, 64(1–2), 375–400.
Danielsson, J. (1998). Multivariate stochastic volatility models: Estimation and comparison with VGARCH models. Journal of Empirical Finance, 5, 155–173.
Danielsson, J., & Richard, J. F. (1993). Accelerated Gaussian importance sampler with application to dynamic latent variable models. Journal of Applied Econometrics, 8, 153–174.
Dias, A., & Embrechts, P. (2004). Change-point analysis for dependence structures in finance and insurance. In G. Szegoe (Ed.), Risk measures for the 21st century (Chap. 16, pp. 321–335). New York: Wiley.
Diebold, F. X., & Nerlove, M. (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. Journal of Applied Econometrics, 4, 1–21.
Diebold, F. X., Gunther, T. A., & Tay, A. S. (1998). Evaluating density forecasts. International Economic Review, 39, 863–883.
Duffie, D., & Singleton, K. J. (1993). Simulated moments estimation of markov models of asset prices. Econometrica, 61, 929–952.
Eichler, M., Motta, G., & von Sachs, R. Fitting dynamic factor models to non-stationary time series. Journal of Econometrics163(1), 51–70.
Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.
Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics, 20(3), 339–350.
Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11, 122–150.
Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22(4), 367–381.
Engle, R. F., & Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. NBER working paper 8554, National Bureau of Economic Research.
Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica, 55, 391–407.
Engle, R. F., Ng, V. K., & Rothschild, M. (1990). Asset pricing with a factor ARCH covariance structure: Empirical estimates for treasury bills. Journal of Econometrics, 45, 213–238.
Engle, R. F., Shephard, N., & Sheppard, K. (2007). Fitting and testing vast dimensional time-varying covariance models. NYU Working Paper No. FIN-07-046.
Fama, E. F. (1965). The behavior of stock market prices. Journal of Business, 38, 34–105.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56.
Fleming, J., Kirby, C., & Ostdiek, B. (2001). The economic value of volatility timing. The Journal of Finance, 56(1), 329–352.
Forni, M., Hallin, M., Lippi, M., & Reichlin, L. (2000). The generalized dynamic factor model: Identification and estimation. The Review of Economics and Statistics, 82, 540–554.
Franke, J., Härdle, W., & Hafner, C. M. (2008). Statistics of financial markets an introduction. Berlin: Springer.
Gallant, A. R., & Tauchen, G. (1996). Which moments to match. Econometric Theory, 12, 657–681.
Ghysels, E., Harvey, A. C., & Renault, E. (1996). Stochastic volatility. In G. Maddala & C. R. Rao (Eds.), Handbook of statistics (Vol. 14). Amsterdam: Elsevier.
Giacomini, E., Härdle, W., & Spokoiny, V. (2009). Inhomogeneous dependency modelling with time varying copulae. Journal of Business and Economic Statistics, 27, 224–234.
Gourieroux, C., Monfort, A., & Renault, E. (1993). Indirect inference. Journal of Applied Econometrics, 8, 85–118.
Hafner, C. M., & Franses, P. H. (2009). A generalized dynamic conditional correlation model: Simulation and application to many assets. Econometric Reviews, 28, 612–631.
Hafner, C. M., & Herwartz, H. (2000). Testing linear autoregressive dynamics under heteroskedasticity. The Econometrics Journal, 3, 177–197.
Hafner, C. M., & Manner, H. (2011). Dynamic stochastic copula models: Estimation, inference and applications. Journal of Applied Econometrics. doi: 10.1002/jae.1197.
Hafner, C. M., & Reznikova, O. (2010). Efficient estimation of a semiparametric dynamic copula model. Computational Statistics and Data Analysis, 54, 2609–2627.
Harvey, A. C., Ruiz, E., & Shephard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247–264.
Hentschel, L. (1995). All in the family: Nesting symmetric and asymmetric garch models. Journal of Financial Economics, 39, 71–104.
Hull, J., & White, A. (1987). The pricing of options with stochastic volatilities. Journal of Finance, 42, 281–300.
Jacquier, E., Polson, N. G., & Rossi, P. E. (1994). Bayesian analysis of stochastic volatitliy models (with discussion). Journal of Business and Economic Statistics, 12, 371–389.
Joe, H. (1997). Multivariate models and dependence concepts. London: Chapman & Hall.
Kim, S., Shephard, N., & Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies, 65, 361–393.
Ledoit, O, Santa-Clara, P, & Wolf, M. (2003). Flexible multivariate GARCH modeling with an application to international stock markets. Review of Economics and Statistics, 85, 735–747.
Liesenfeld, R., & Richard, J. F. (2003). Univariate and multivariate volatility models: Estimation and diagnostics. Journal of Empirical Finance, 10, 505–531.
Lintner, J. (1965). Security prices, risk and maximal gains from diversification. Journal of Finance, 20, 587–615.
Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36, 394–419.
Manner, H. & Candelon, B. (2010). Testing for asset market linkages: A new approach based on time-varying copulas. Pacific Economic Review 15, 364–384. doi: 10.1111/j.1468- 0106.2010.00508.x
Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. New York: Wiley.
Motta, G., Hafner, C., & von Sachs, R. (2011). Locally stationary factor models: Identification and nonparametric estimation. Econometric Theory, 27(6).
Nelsen, R. B. (2006). An introduction to copulas. New York: Springer.
Patton, A. (2006a). Modelling asymmetric exchange rate dependence. International Economic Review, 47(2), 527–556.
Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341–360.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442.
Stock, J. H., & Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97, 1167–1179.
Taylor, S. J. (1986). Modelling financial time series. Chichester: Wiley.
Taylor, S. J. (1994). Modelling stochastic volatility: A review and comparative study. Mathematical finance, 4, 183–204,.
Tse, Y. K., & Tsui, A. K. C. (2002). A multivariate GARCH model with time-varying correlations. Journal of Business and Economic Statistics, 20(3), 351–362.
van der Weide, R. (2002). Go-garch: A multivariate generalized orthogonal GARCH model. Journal of Applied Econometrics, 17, 549–564.
Yu, J., & Meyer, R. (2006). Multivariate stochastic volatility models: Bayesian estimation and model comparison. Econometric Reviews, 25(2–3), 361–384.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hafner, C.M., Manner, H. (2012). Multivariate Time Series Models for Asset Prices. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-17254-0_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17253-3
Online ISBN: 978-3-642-17254-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)