Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Suy diễn biến ngẫu nhiên cho các mô hình GARCH
Tóm tắt
Các thuật toán suy diễn biến ngẫu nhiên biến thể được phát triển để phù hợp với nhiều mô hình chuỗi thời gian không đồng nhất. Chúng tôi xem xét các mô hình GARCH ứng đáp Gaussian, t và t lệch và phù hợp với chúng bằng cách sử dụng mật độ xấp xỉ biến thể Gaussian. Chúng tôi thực hiện các quy trình tăng gradient ngẫu nhiên hiệu quả dựa trên việc sử dụng biến kiểm soát hoặc thủ thuật tái tham số hóa và chứng minh rằng các triển khai được đề xuất cung cấp một sự thay thế nhanh chóng và chính xác cho việc lấy mẫu chuỗi Markov Monte Carlo. Thêm vào đó, chúng tôi trình bày các phiên bản cập nhật tuần tự của các thuật toán biến thể của chúng tôi, thích hợp cho việc xây dựng danh mục đầu tư hiệu quả và phân bổ tài sản động.
Từ khóa
#Suy diễn biến ngẫu nhiên #mô hình GARCH #chuỗi thời gian không đồng nhất #xấp xỉ biến thể Gaussian #tăng gradient ngẫu nhiên.Tài liệu tham khảo
Alonso, A.M., Maharaj, E.A.: Comparison of time series using subsampling. Comput. Stat. Data Anal. 50(10), 2589–2599 (2006)
Ardia, D., Hoogerheide, L.F.: Bayesian estimation of the GARCH (1, 1) model with student-t innovations. R J. 2(2), 41–47 (2010)
Ardia, D., et al.: Financial Risk Management with Bayesian Estimation of GARCH Models, vol. 612. Springer, berlin (2008)
Baillie, R.T., Bollerslev, T.: Common stochastic trends in a system of exchange rates. J. Finance 44(1), 167–181 (1989)
Beine, M., Bénassy-Quéré, A., Lecourt, C.: Central bank intervention and foreign exchange rates: new evidence from FIGARCH estimations. J. Int. Money Finance 21(1), 115–144 (2002)
Bishop, C.M., Nasrabadi, N.M.: Pattern Recognition and Machine Learning, vol. 4. Springer, Berlin (2006)
Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J. Econom. 31(3), 307–327 (1986)
Bollerslev, T.: A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev. Econ. Stat. 69, 542–547 (1987)
Broderick, T., Boyd, N., Wibisono, A., et al.: Streaming variational Bayes. In: Burges, C.J., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol. 26. Curran Associates, Red Hook (2013)
Brooks, S.P., Gelman, A.: General methods for monitoring convergence of iterative simulations. J. Comput. Graph. Stat. 7(4), 434–455 (1998)
Chan, J.C., Grant, A.L.: Modeling energy price dynamics: GARCH versus stochastic volatility. Energy Econ. 54, 182–189 (2016)
Contino, C., Gerlach, R.H.: Bayesian tail-risk forecasting using realized GARCH. Appl. Stoch. Models Bus. Ind. 33(2), 213–236 (2017)
Degiannakis, S.: Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model. Appl. Financ. Econ. 14(18), 1333–1342 (2004)
Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12(7), 2121–2159 (2011)
Engle, R.F.: Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econom. J. Econom. Soc. 50, 987–1007 (1982)
Engle, R.: GARCH 101: the use of ARCH/GARCH models in applied econometrics. J. Econ. Perspect. 15(4), 157–168 (2001)
Fernández, C., Steel, M.F.: On Bayesian modeling of fat tails and skewness. J. Am. Stat. Assoc. 93(441), 359–371 (1998)
Fiorentini, G., Calzolari, G., Panattoni, L.: Analytic derivatives and the computation of GARCH estimates. J. Appl. Econom. 11(4), 399–417 (1996)
Foti, N., Xu, J., Laird, D., et al.: Stochastic variational inference for hidden Markov models. In: Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol. 27. Curran Associates, Red Hook (2014)
Gerlach, R., Tuyl, F.: MCMC methods for comparing stochastic volatility and GARCH models. Int. J. Forecast. 22(1), 91–107 (2006)
González-Rivera, G., Drost, F.C.: Efficiency comparisons of maximum-likelihood-based estimators in GARCH models. J. Econom. 93(1), 93–111 (1999)
Gunawan, D., Kohn, R., Nott, D.: Variational Bayes approximation of factor stochastic volatility models. Int. J. Forecast. 37(4), 1355–1375 (2021)
Hansen, B.E.: Autoregressive conditional density estimation. Int. Econ. Rev. 35, 705–730 (1994)
Henneke, J.S., Rachev, S.T., Fabozzi, F.J., et al.: MCMC-based estimation of Markov switching ARMA-GARCH models. Appl. Econ. 43(3), 259–271 (2011)
Hoffman, M.D., Blei, D.M., Wang, C., et al.: Stochastic variational inference. J. Mach. Learn. Res. 14, 1303–1347 (2013)
Iqbal, F., Triantafyllopoulos, K.: Bayesian inference of multivariate rotated GARCH models with skew returns. Commun. Stat. Simul. Comput. 50(10), 3105–3123 (2021)
Jondeau, E., Zhang, Q., Zhu, X.: Average skewness matters. J. Financ. Econ. 134(1), 29–47 (2019)
Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., et al.: An introduction to variational methods for graphical models. Learn. Graph. Models 37, 105–161 (1998)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization (2014). arXiv preprint arXiv:1412.6980
Kingma, D.P., Welling, M.: Auto-encoding variational Bayes (2013). arXiv preprint arXiv:1312.6114
Lambert, P., Laurent, S.: Modelling financial time series using GARCH-type models with a skewed student distribution for the innovations. Technical report (2001)
Lambert, M., Bonnabel, S., Bach, F.: The recursive variational Gaussian approximation (R-VGA). Stat. Comput. 32(1), 10 (2022)
Levy, G.F.: Analytic derivatives of asymmetric Garch models. J. Comput. Finance 6(3), 21–64 (2003)
Li, D., Clements, A., Drovandi, C.: Efficient Bayesian estimation for GARCH-type models via sequential Monte Carlo. Econom. Stat. 19, 22–46 (2021)
Liu, Y., Li, J.S.H., Ng, A.C.Y.: Option pricing under Garch models with Hansen’s skewed-t distributed innovations. N. Am. J. Econ. Finance 31, 108–125 (2015)
Liu, L., Jiang, H., He, P., et al.: On the variance of the adaptive learning rate and beyond (2019). arXiv preprint arXiv:1908.03265
Livingston, G., Jr., Nur, D.: Bayesian inference of multivariate-GARCH-BEKK models. Stat. Pap. 64, 1–26 (2022)
Maestrini, L., Wand, M.P.: Variational message passing for skew t regression. Stat 7(1), e196 (2018)
Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)
Mozumder, S., Choudhry, T., Dempsey, M.: Option pricing model biases: Bayesian and Markov chain Monte Carlo regression analysis. Comput. Econ. 57, 1287–1305 (2021)
Nakatsuma, T.: Bayesian analysis of ARMA-GARCH models: a Markov chain sampling approach. J. Econom. 95(1), 57–69 (2000)
Nott, D.J., Tan, S.L., Villani, M., et al.: Regression density estimation with variational methods and stochastic approximation. J. Comput. Graph. Stat. 21(3), 797–820 (2012)
Ong, V.M., Nott, D.J., Tran, M.N., et al.: Variational Bayes with synthetic likelihood. Stat. Comput. 28, 971–988 (2018a)
Ong, V.M.H., Nott, D.J., Smith, M.S.: Gaussian variational approximation with a factor covariance structure. J. Comput. Graph. Stat. 27(3), 465–478 (2018b)
Opper, M., Archambeau, C.: The variational Gaussian approximation revisited. Neural Comput. 21(3), 786–792 (2009)
Ormerod, J.T., Wand, M.P.: Explaining variational approximations. Am. Stat. 64(2), 140–153 (2010)
Ormerod, J.T., Wand, M.P.: Gaussian variational approximate inference for generalized linear mixed models. J. Comput. Graph. Stat. 21(1), 2–17 (2012)
Paisley, J., Blei, D., Jordan, M.: Variational Bayesian inference with stochastic search (2012). arXiv preprint arXiv:1206.6430
Politis, D.N.: The impact of bootstrap methods on time series analysis. Stat. Sci. 18, 219–230 (2003)
Polyak, B.T.: Some methods of speeding up the convergence of iteration methods. USSR Comput. Math. Math. Phys. 4(5), 1–17 (1964)
Quiroz, M., Nott, D.J., Kohn, R.: Gaussian variational approximations for high-dimensional state space models. Bayesian Anal. 1(1), 1–28 (2022)
R Core Team R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2023). https://www.R-project.org/
Ranganath, R., Gerrish, S., Blei, D.: Black box variational inference. In: Artificial Intelligence and Statistics, PMLR, pp. 814–822 (2014)
Rezende, D.J., Mohamed, S., Wierstra, D.: Stochastic backpropagation and approximate inference in deep generative models. In: International Conference on Machine Learning, PMLR, pp. 1278–1286 (2014)
Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22, 400–407 (1951)
Robert, C.P., Casella, G., Casella, G.: Monte Carlo Statistical Methods, vol. 2. Springer, Berlin (1999)
Shiferaw, Y.A.: Time-varying correlation between agricultural commodity and energy price dynamics with Bayesian multivariate DCC-GARCH models. Physica A Stat. Mech. Appl. 526(120), 807 (2019)
Shirvani, A., et al.: Stock returns and roughness extreme variations: a new model for monitoring 2008 market crash and 2015 flash crash. Appl. Econ. Finance 7(3), 78–95 (2020)
Silvennoinen, A., Teräsvirta, T.: Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model. Econom. Stat. (2021). https://doi.org/10.1016/j.ecosta.2021.07.008
Tan, L.S., Nott, D.J.: Gaussian variational approximation with sparse precision matrices. Stat. Comput. 28, 259–275 (2018)
Tieleman, T., Hinton, G., et al.: Lecture 6.5-rmsprop: divide the gradient by a running average of its recent magnitude. COURSERA Neural Netw. Mach. Learn. 4(2), 26–31 (2012)
Titsias, M., Lázaro-Gredilla, M.: Doubly stochastic variational Bayes for non-conjugate inference. In: International Conference on Machine Learning, PMLR, pp. 1971–1979 (2014)
Tomasetti, N., Forbes, C., Panagiotelis, A.: Updating variational Bayes: fast sequential posterior inference. Stat. Comput. 32(1), 4 (2022)
Tran, M.N., Nguyen, D.H., Nguyen, D.: Variational Bayes on manifolds. Stat. Comput. 31, 1–17 (2021a)
Tran, M.N., Nguyen, T.N., Dao, V.H.: A practical tutorial on variational Bayes (2021b). arXiv preprint arXiv:2103.01327
Virbickaite, A., Ausín, M.C., Galeano, P.: Bayesian inference methods for univariate and multivariate GARCH models: a survey. J. Econ. Surv. 29(1), 76–96 (2015)
Wand, M.P.: Fully simplified multivariate normal updates in non-conjugate variational message passing. J. Mach. Learn. Res. 15, 1351–1369 (2014)
Wuertz, D., RUnit, S., Chalabi, M.Y.: Package ‘fGarch’. Tech. rep., working paper/manual, 09.11. 2009 (2022). http://cran.r-project.org/web
Xaba, L.D., Moroke, N.D., Metsileng, L.D.: Performance of MS-GARCH models: Bayesian MCMC-based estimation. In: Handbook of Research on Emerging Theories, Models, and Applications of Financial Econometrics, pp. 323–356 (2021)
Zeiler, M.D.: Adadelta: an adaptive learning rate method (2012). arXiv preprint arXiv:1212.5701