Asymmetric conditional correlations in stock returns. (English) Zbl 1400.62236

Jiang, Hui; Saart, Patrick W.; Xia, Yingcun

Ann. Appl. Stat. 10, No. 2, 989-1018 (2016).

Summary: Modeling and estimation of correlation coefficients is a fundamental step in risk management, especially with the aftermath of the financial crisis in 2008, which challenged the traditional measuring of dependence in the financial market. Because of the serial dependence and small signal-to-noise ratio, patterns of the dependence in the data cannot be easily detected and modeled. This paper introduces a common factor analysis into the conditional correlation coefficients to extract the features of dependence. While statistical properties are thoroughly derived, extensive empirical analysis provides us with common patterns for the conditional correlation coefficients that give new insight into a number of important questions in financial data, especially the asymmetry of cross-correlations and the factors that drive the cross-correlations.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H25	Factor analysis and principal components; correspondence analysis

Keywords:

conditional cross-correlation coefficient; kernel smoothing; reduced rank model; semiparametric models

References:

[1]	Aielli, G. P. (2013). Dynamic conditional correlation: On properties and estimation. J. Bus. Econom. Statist. 31 282-299.
[2]	Amira, K., Taamouti, A. and Tsafack, G. (2011). What drives international equity correlations? Volatility or market direction? J. Int. Money Financ. 30 1234-1263.
[3]	Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2001). The distribution of realized exchange rate volatility. J. Amer. Statist. Assoc. 96 42-55. · Zbl 1015.62107 · doi:10.1198/016214501750332965
[4]	Ang, A. and Bekaert, G. (2002). International asset allocation with regime shifts. Rev. Financ. Stud. 15 1137-1187.
[5]	Ang, A. and Chen, J. (2002). Asymmetric correlations of equity portfolios. J. Financ. Econ. 63 443-494.
[6]	Aslanidis, N. and Casas, I. (2013). Noparametric correlation models for portfolio allocation. J. Bank. Financ. 37 2268-2283.
[7]	Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica 70 191-221. · Zbl 1103.91399 · doi:10.1111/1468-0262.00273
[8]	Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Rev. Econ. Stat. 72 498-505.
[9]	Boneva, L., Linton, O. and Vogt, M. (2015). A semiparametric model for heterogeneous panel data with fixed effects. J. Econometrics 188 327-345. · Zbl 1337.62242 · doi:10.1016/j.jeconom.2015.03.003
[10]	Chesnay, F. and Jondeau, E. (2001). Does correlation between stock returns really increase during turbulent periods? Economic Notes by Banca Monte dei Paschi di Siena SpA 30 53-80.
[11]	Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Bus. Econom. Statist. 20 339-350.
[12]	Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. J. Finance 48 1779-1801.
[13]	Engle, R. F., Ng, V. K. and Rothschild, M. (1990). Asset pricing with a factor-ARCH covariance structure: Empirical estimates for treasury bills. J. Econometrics 45 213-237.
[14]	Erb, C. B., Harvey, C. R. and Viskanta, T. E. (1994). Forecasting international equity correlations. Financ. Anal. J. 50 32-45.
[15]	Fan, J. and Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85 645-660. · Zbl 0918.62065 · doi:10.1093/biomet/85.3.645
[16]	Härdle, W. and Marron, J. S. (1990). Semiparametric comparison of regression curves. Ann. Statist. 18 63-89. · Zbl 0703.62053 · doi:10.1214/aos/1176347493
[17]	James, G. M., Hastie, T. J. and Sugar, C. A. (2000). Principal component models for sparse functional data. Biometrika 87 587-602. · Zbl 0962.62056 · doi:10.1093/biomet/87.3.587
[18]	Jiang, H., Saart, P. W. and Xia Y. (2016). Supplement to “Asymmetric conditional correlations in stock returns.” . · Zbl 1400.62236 · doi:10.1214/16-AOAS924
[19]	Kaplanis, E. (1988). Stability and forecasting of the comovement measures of international stock market returns. J. Int. Money Financ. 7 63-75.
[20]	Kring, S., Rachev, S. T., Hochstotter, M. and Fabozzi, F. J. (2007). Composed and factor composed multivariate GARCH models. Technical report, University of Karlsruhe.
[21]	Lanne, M. and Saikkonen, P. (2007). A multivariate generalized orthogonal factor GARCH model. J. Bus. Econom. Statist. 25 61-75.
[22]	Li, Y., Wang, N. and Carroll, R. J. (2013). Selecting the number of principal components in functional data. J. Amer. Statist. Assoc. 108 1284-1294. · Zbl 1288.62102 · doi:10.1080/01621459.2013.788980
[23]	Longin, F. and Solnik, B. (1995). Is the correlation in international equity returns constant: 1960-1990? J. Int. Money Financ. 14 3-26.
[24]	Longin, F. and Solnik, B. (2001). Extreme correlations in international equity markets. J. Finance 56 649-676.
[25]	Munk, A. and Dette, H. (1998). Nonparametric comparison of several regression functions: Exact and asymptotic theory. Ann. Statist. 26 2339-2368. · Zbl 0927.62040 · doi:10.1214/aos/1024691474
[26]	Pelletier, D. (2006). Regime switching for dynamic correlations. J. Econometrics 131 445-473. · Zbl 1337.62277 · doi:10.1016/j.jeconom.2005.01.013
[27]	Ramchand, L. and Susmel, R. (1998). Volatility and cross correlation across major stock markets. J. Empir. Finance 5 397-416.
[28]	Santos, A. A. P. and Moura, G. V. (2014). Dynamic factor multivariate GARCH model. Comput. Statist. Data Anal. 76 606-617. · Zbl 1506.62160
[29]	Sheppard, K. and Xu, W. (2014). Factor high-frequency based volatility (heavy) models. Working paper, Univ. Oxford.
[30]	Silvennoinen, A. and Teräsvirta, T. (2015). Modeling conditional correlations of asset returns: A smooth transition approach. Econometric Rev. 34 174-197. · doi:10.1080/07474938.2014.945336
[31]	Tse, Y. K. and Tsui, A. K. C. (2002). A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. J. Bus. Econom. Statist. 20 351-362.
[32]	Vrontos, I. D., Dellaportas, P. and Politis, D. N. (2003). A full-factor multivariate GARCH model. Econom. J. 6 312-334. · Zbl 1065.91553 · doi:10.1111/1368-423X.t01-1-00111