"Frontmatter". In: Analysis of Financial Time Series

366 MULTIVARIATE VOLATILITY MODELSwhich hit the Hong Kong Market on October 17, 1997. The data are obtained fromDatastream. Figure 9.1 shows the time plots of the two index returns. Let r 1t be theindex return for the Hong Kong stock market and r 2t for the Japanese stock market.If univariate GARCH models are entertained, we obtain the modelsr 1t = 0.137r 1,t−1 + a 1t , a 1t = σ 1t ɛ 1t ,σ1t 2 = 0.164 + 0.142a2 1,t−1 + 0.765σ 1,t−1 2 (9.18)r 2t = a 2t , a 2t = σ 2t ɛ 2t ,σ2t 2 = 0.085 + 0.128a2 2,t−1 + 0.807σ 2,t−1 2 , (9.19)(a) Hong Kongvolatility2 4 6 8 10 12where all of the parameter estimates are highly significant except for the AR(1) coefficientof the r 1t series, which has a p value of 0.029. The Ljung–Box statistics of thestandardized residuals and their squared series of the prior two models fail to indicateany model inadequacy. Figure 9.2 shows the estimated volatilities of the previous twounivariate GARCH(1, 1) models. The Hong Kong stock market appears to be morevolatile than the Japanese stock market, but the Japanese market exhibits an increas-0 100 200 300 400days(b) Japanvolatility1 2 3 40 100 200 300 400daysFigure 9.2. Estimated volatilities for daily log returns in percentages of stock market indexesfor Hong Kong and Japan from January 1, 1996 to October 16, 1997: (a) the Hong Kongmarket, and (b) the Japanese market. Univariate models are used.