"Frontmatter". In: Analysis of Financial Time Series

442 MCMC METHODS4. Consider the monthly log returns of General Motors stock from 1950 to 1999 with600 observations: (a) build a GARCH model for the series, (b) build a stochasticvolatility model for the series, and (c) compare and discuss the two volatilitymodels.5. Build a stochastic volatility model for the daily log return of Cisco Systems stockfrom January 1991 to December 1999. You may download the data from CRSPdatabase or the file “d-csco9199.dat.” Use the model to obtain a predictive distributionfor 1-step ahead volatility forecast at the forecast origin December 1999.Finally, use the predictive distribution to compute the Value at Risk of a longposition worth $1 million with probability 0.01 for the next trading day.6. Build a bivariate stochastic volatility model for the monthly log returns of GeneralMotors stock and the S&P 500 index for the sample period from January 1950 toDecember 1999. Discuss the relationship between the two volatility processes andcompute the time-varying beta for GM stock.REFERENCESBox, G. E. P., and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis. Addison-Wesley: Reading, MA.Chang, I., Tiao, G. C., and Chen, C. (1988), “Estimation of time series parameters in thepresence of outliers,” Technometrics, 30, 193–204.Carlin, B. P., and Louis, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis,2nd ed., Chapman and Hall: London.DeGroot, M. H. (1970), Optimal Statistical Decisions, McGraw-Hill: New York.Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum likelihood from incompletedata via the EM algorithm” (with discussion), Journal of the Royal Statistical Society,Series B, 39, 1–38.Elerian, O., Chib, S., and Shephard, N. (2001), “Likelihood inference for discretely observednonlinear diffusions,” Econometrica, 69, 959–993.Eraker, B. (2001), “Markov Chain Monte Carlo analysis of diffusion models with applicationto finance,” Journal of Business & Economic Statistics 19, 177–191.Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-based approaches to calculatingmarginal densities,” Journal of the American Statistical Association, 85, 398–409.Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995), Bayesian Data Analysis, CRCPress: London.Geman, S., and Geman, D. (1984), “Stochastic relaxation, Gibbs distributions, and theBayesian restoration of images,” IEEE transactions on Pattern Analysis and MachineIntelligence, 6, 721–741.Hasting, W. K. (1970), “Monte Carlo sampling methods using Markov chains and their applications,”Biometrika, 57,97–109.Jacquier, E., Polson, N. G., and Rossi, P. E. (1994), “Bayesian analysis of stochastic volatilitymodels” (with discussion), Journal of Business & Economic Statistics, 12, 371–417.Jones, R. H.(1980), “Maximum likelihood fitting of ARMA models to time series with missingobservations,” Technometrics, 22, 389–395.