Bayesian estimation of a multivariate TAR model when the noise process follows a <i>Student-t</i> distribution

In this paper, we introduce a Bayesian methodology for the estimation of non-structural parameters (autoregressive matrices, covariance matrices and degrees of freedom) of a multivariate TAR model (MTAR) when noise process follows a multivariate <i>Student-t</i> distribution. For this, the use of non-informative prior distributions is proposed to obtain the full conditional distributions. MCMC methods are used to obtain samples of such distributions. The performance of the estimation is evaluated by means simulations. Finally, the model is applied to the returns data from the Bovespa, Colcap and Standard and Poor indexes.

本文提出一种贝叶斯方法（Bayesian methodology），用于在噪声过程服从多元学生t分布（multivariate Student-t distribution）时，估计多元TAR模型（multivariate TAR model, MTAR）的非结构参数——包括自回归矩阵、协方差矩阵与自由度。为此，本文提出采用无信息先验分布（non-informative prior distributions）以获取全条件分布（full conditional distributions），并采用马尔可夫链蒙特卡洛方法（Markov Chain Monte Carlo, MCMC）获取此类分布的采样样本。本文通过模拟实验评估该估计方法的性能，最后将所提模型应用于博维斯帕（Bovespa）、科尔卡普（Colcap）以及标准普尔（Standard and Poor）指数的收益率数据。