MCMC Algorithm For SV-ARMA (p,q) With Fat Fails And Correlated Errors

As the Econometric literature is becoming more and more popular, many math-ematic models were advanced to explain the phenomena appeared in eonomic and financial fields. Engle(1982) originally presented ARCH models and later Boller-lev(1986) expanded to the more popular GARCH models. From that time, GARCH models are offen applied in financial research, because GARCH models embody the characteristics of the fat tails and volatility clustering which are usually taken on in financial datas. However, GARCH models have the limitations, such as the strong request for the parameters and unsuitability for the conditional variance only decided by former conditional variance and volatility. Recently, pepole apply stochastic volatility models on financial time series, because stochastic volatility models not only embody the characteristics of the fat tails and volatility clustering but also overcome the limitations of GARCH models in a certain extent. However, stochastic volatility models are much less applied in financial fields for its difficulty in estimate. Markov Chain Monte Marlo(MCMC) is a simple and effective method in Bayes calculation, which can make many difficultly calculation ease. Jacquier(2004) completed estimate for stochastic volatility(SV) models(AR(1)) with fat tails and correlated errors by MCMC algorithm. Meanwhile, we naturally expanded SV-ARMA(p, q) with fat tails and correlated errors:ε_t and v_t are correlated, (ε_t, v_t) iid, t = 1,...., T. and presented its MCMC algorithm. Finally we maked simulation and demonstration for the new models by our MCMC algorithm, and proved its feasibility.