Stock Prices Across International Markets: The CCF Approach

Part of the Research Monographs in Japan-U.S. Business & Economics book series (JUSB, volume 8)


The last chapter analyzed stock prices in Germany, Japan, the UK, and the USA using the traditional time-series model of stock price returns. However, there is a growing literature on the linkages between conditional variances across financial markets and their implications for information transmission mechanisms. This chapter extends the previous analysis and examines the transmission mechanisms for the conditional first and second moments in stock prices across international stock markets, and uses the ARCH (autoregressive conditional heteroskedasticity)-type model to analyze the volatility of international stock prices.


Stock Market Stock Return Stock Prex Conditional Variance Standardize Residual 
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  1. 1.
    Some other examples are Hamao, Masulis and Ng (1990), Baillie and Bollerslev (1991), Theodossiou and Lee (1993), Susmel and Engle (1994).Google Scholar
  2. 2.
    See Bollerslev, Chou and Kroner (1992), Campbell, Lo and MacKinlay (1997, Chapter 12), and Watanabe (2000) for examples.Google Scholar
  3. 3.
    Note that i.i.d. means independent and identical distribution.Google Scholar
  4. 4.
    Let X be a random variable with mean E(X), and letg() be a convex function. Then Jensen’s inequality implies E[g(X)] ≥ g(E[X). For the example, note that g(X) = X2 is convex. Hence E[X2] ≥ (E[X])2.Google Scholar
  5. 6.
    The parameter subscripts are not necessary for the GARCH(1,1), GJR(1,1), and EGARCH(1,1) models and are suppressed for the remainder of this section.Google Scholar
  6. 7.
    Nakagawa and Osawa (2000) is a good example of the application of this model.Google Scholar
  7. 8.
    Also see Zakoian (1994).Google Scholar
  8. 9.
    Some other examples are the NGARCH (nonlinear GARCH) model by Engle and Bollerslev (1986) and Higgins and Bera (1992), and the QGARCH (quadratic ARCH) model by Sentana (1995).Google Scholar
  9. 10.
    If the model is correctly specified, standardized residuals should be independent and identically distributed with mean zero and variance one. If standardized residuals are normally distributed, then maximum likelihood estimates are asymptotically efficient. However, even if the residuals are not normally distributed, the estimates are still consistent under quasi-maximum likelihood.Google Scholar
  10. 12.
    If the series is not based on the empirical results of ARMA estimation, then under the null hypothesis Q(s) is approximately distributed as X2 with degrees of freedom equal to the number of autocorrelations. If the series is the residuals of the ARMA estimation, however, the appropriate degrees of freedom are equal to the number of autocorrelations less the number of AR and MA terms.Google Scholar
  11. 13.
    Q(24) also shows that there is no autocorrelation in residuals.Google Scholar
  12. 14.
    Q2(24) also shows that there is no autocorrelation in squared residuals.Google Scholar
  13. 15.
    Note that cross-correlations are not necessarily symmetric around zero.Google Scholar
  14. 16.
    See Hamao, Masulis and Ng (1990) and Theodossiou and Lee (1993) as an example of the multivariate approach.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  1. 1.Kobe UniversityJapan

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