zbMATH — the first resource for mathematics

Testing for volatility interactions in the constant conditional correlation GARCH model. (English) Zbl 1190.62160
Summary: We propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation generalized autoregressive conditional heteroskedasticity (GARCH) model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that model in which volatility is modelled as a linear combination not only of its own lagged squared innovations and volatilities but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatilities transmissions among variables in the model. Monte Carlo experiments show that the proposed test has satisfactory finite-sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M07 Non-Markovian processes: hypothesis testing
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G70 Statistical methods; risk measures
65C05 Monte Carlo methods
Full Text: DOI
[1] Baillie, Intra-day and inter-market volatility in foreign exchange rates, Review of Economic Studies 58 pp 565– (1990)
[2] Bera, Testing constancy of correlation and other specifications of the BGARCH model with an application to international equity returns, Journal of Empirical Finance 9 pp 171– (2002)
[3] Berben, Comovement in international equity markets: A sectoral view, Journal of International Money and Finance 24 pp 832– (2005)
[4] Bollerslev, Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH approach, Review of Economics and Statistics 72 pp 498– (1990)
[5] Cecchetti, Estimation of the optimal futures hedge, Review of Economic Studies 70 pp 623– (1988)
[6] Cheung, A causality-in-variance test and its application to financial market prices, Journal of Econometrics 72 pp 33– (1996) · Zbl 0842.62095
[7] Cifarelli, Volatility linkages across three major equity markets: A financial arbitrage approach, Journal of International Money and Finance 24 pp 413– (2005)
[8] Engle, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 pp 339– (2002)
[9] Hamao, Correlations in price changes and volatility across international stock markets, The Review of Financial Studies 3 pp 281– (1990)
[10] He, An extended constant conditional correlation GARCH model and its fourth-moment structure, Econometric Theory 20 pp 904– (2004) · Zbl 1071.62077
[11] Hong, A test for volatility spillover with application to exchange rates, Journal of Econometrics 103 pp 183– (2001) · Zbl 1053.62118
[12] Jarque, Efficient tests for normality, homoscedasticity and serial independence of regression residuals, Economics Letters 6 pp 255– (1980)
[13] Jeantheau, Strong consistency of estimators for multivariate ARCH models, Econometric Theory 14 pp 70– (1998)
[14] Kawakatsu, Matrix exponential GARCH, Journal of Econometrics 134 pp 95– (2006)
[15] Kim, On more robust estimation of skewness and kurtosis, Finance Research Letters 1 pp 56– (2004)
[16] Ling, Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory 19 pp 280– (2003)
[17] Lomnicki, Tests for departure from normality in the case of linear stochastic processes, Metrika 4 pp 37– (1961) · Zbl 0107.36503
[18] McLeod, Diagnostic checking ARMA time series models using squared residual autocorrelations, Journal of Time Series Analysis 4 pp 269– (1983) · Zbl 0536.62067
[19] Nakatani, Appendix to Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model (2008)
[20] Nakatani, Positivity constraints on the conditional variances in the family of conditional correlation GARCH models, Finance Research Letters 5 pp 88– (2008)
[21] R Development Core Team, R: A Language and Environment for Statistical Computing (2008)
[22] Silvennoinen, SSE/EFI (2005)
[23] Tse, A test for constant correlations in a multivariate GARCH model, Journal of Econometrics 98 pp 107– (2000) · Zbl 0968.62066
[24] Wong, On a multivariate conditional heteroscedastic model, Biometrika 84 pp 111– (1997) · Zbl 0883.62106
[25] Wong, H. , W. K. Li , and S. Ling (2000). A cointegrated conditional heteroscedastic model with financial applications. Preprint No. 2000-5, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.