Suy diễn Bayes cho Mô hình GARCH Kiểu Hỗn hợp Gauss bằng Thuật toán Monte Carlo Hamilton

Alexander, C., & Lazar, E. (2006). Normal mixture garch(1,1): Applications to exchange rate modelling. Journal of Applied Econometrics, 21(3), 307–336. Ausín, M. C., & Galeano, P. (2007). Bayesian estimation of the gaussian mixture garch model. Computational Statistics & Data Analysis, 51(5), 2636–2652. Bai, X., Russell, J. R., & Tiao, G. C. (2003). Kurtosis of garch and stochastic volatility models with non-normal innovations. Journal of Econometrics, 114, 349–360. Bauwens, L., Bos, C. S. & Van Dijk, H. K. (1999) . Adaptive polar sampling with an application to a bayes measure of value-at-risk, Working paper, CORE, Universite Catholique de Louvain . Bauwens, L., & Lubrano, M. (1998). Bayesian inference on garch models using gibbs sampler. Econometrics Journal, 1(1), 23–46. Beskos, A., Pillai, N., Roberts, G., Sanz-Serna, J. M., & Stuart, A. (2013). Optimal tuning of the hybrid monte carlo algorithm. Bernoulli, 19(5A), 1501–1534. Betancourt, M. (2011) . Nested sampling with constrained hamiltonian monte carlo, AIP Conference Proceedings, Vol. 1305, American Institute of Physics, pp. 165–172. Betancourt, M. (2017) . A conceptual introduction to hamiltonian monte carlo, arXiv preprint arXiv:1701.02434 . Bollerslev, T. (1986). Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3), 307–327. Bollerslev, T. (1987). A conditionally heteroscedastic time series model for speculative prices and rates of return. The Review of Economics and Statistics, 69(3), 524–547. Bollerslev, T., & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric reviews, 11(2), 143–172. Burda, M., & Bélisle, L. (2019). Copula multivariate garch model with constrained hamiltonian monte carlo. Dependence Modeling, 7(1), 133–149. Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., et al. (2016). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1), 1–32. Diebolt, J., & Robert, C. P. (1994). Estimation of finite mixture distributions through bayesian sampling. Journal of the Royal Statistical Society: Series B, 56(2), 363–375. Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid monte carlo. Physics Letters B, 195, 216–222. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica, 50, 987–1008. Engle, R. F., & Bollerslev, T. (1986). Modelling the persistence of conditional variances. Econometric Reviews, 5(1), 1–50. Fama, E. F. (1965). The behaviour of stock market prices. Journal of Business, 38(1), 34–105. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Bayesian Statistics, 4, 641–649. Geweke, J. (1994) . Bayesian comparison of econometric models, Working Paper, Federal Reserve Bank of Minneapolis (35). Girolami, M., & Calderhead, B. (2011). Riemann manifold langevin and hamiltonian monte carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2), 123–214. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779–1801. Haas, M., Mittnik, S., & Paolella, M. S. (2004). Mixed normal conditional heteroskedasticity. Journal of Financial Econometrics, 2, 211–250. Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1), 97–109. Hoffman, M., & Gelman, A. (2014). The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo. Journal of Machine Learning Research, 15, 1593–1623. Jorion, P. (2000) . Value at Risk: The New Benchmark for Managing Financial Risk(second ed.). Kreuzer, A., & Czado, C. (2021). Bayesian inference for a single factor copula stochastic volatility model using hamiltonian monte carlo. Econometrics and Statistics, 19, 130–150. Leimkuhler, B. & Reich, S. (2004). Simulating hamiltonian Dynamics, Cambridge University Press. Mandelbrot, B. (1963). New method in statistical economics. Journal of Political Economy, 71(5), 421–440. McFarland, J. W., Pettit, R. R., & Sung, S. K. (1982). The distribution of foreign exchange price changes: Trading day effects and risk measurement. Journal of Finance, 37(3), 693–715. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), 1087–1092. Neal, R. M. (2011) . MCMC Using Hamiltonian Dynamics, Handbook of Markov Chain Monte Carlo(S. Brooks, A. Gelman, G. L. Jones and X.-L. Meng, eds.) CRC Press, New York. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica: Journal of the Econometric Society pp. 347–370. Paixão, R. S. & Ehlers, R. S. (2017) . Zero variance and hamiltonian monte carlo methods in garch models, arXiv preprint arXiv: 1710.07693 . Pan, J., Wang, H., & Tong, H. (2008). Estimation and tests for power-pransformed and threshold garch models. Journal of Econometrics, 142, 352–378. Plummer, M., Best, N., Cowles, K. & Vines, K. (2008). Coda: Output analysis and convergence diagnosis for mcmc. https://CRAN.R-project.org/package=coda Ritter, C., & Tanner, M. A. (1992). Facilitating the gibbs sampler: The gibbs stopper and the griddy-gibbs sampler. Journal of the American Statistical Association, 87, 861–868. Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540. Westerfield, R. (1977). The distribution of common stock price changes: An application of transactions time and subordinated stochastic models, Journal of Financial and Quantitative Analysis pp. 743–765. Wong, C. S., & Li, W. K. (2001). On a mixture autoregressive conditional heteroscedastic model. Journal of the American Statistical Association, 96(455), 982–995. Xia, Q., Wong, H., Liu, J., & Liang, R. (2017). Bayesian analysis of power-transformed and threshold garch models: A griddy-gibbs sampler approach. Computational Economics, 50(3), 353–372. Yu, B., & Mykland, P. (1994). Looking at markov samplers through cumsum path plots: A simple diagnostic idea, Technical Report 413. Department of Statistics: University of California at Berkeley. Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control, 18(5), 931–955. Zhang, Z., Li, W. K., & Yuen, K. C. (2006). On a mixture garch time-series model. Journal of Time Series Analysis, 27(4), 577–597.