Time-varying parameters vector autoregressions with multivariatestochastic volatility

向量自回归(VARs)被广泛应用于提供一种系统的方法来捕捉多个时间序列中的丰富动态，因此已成为宏观经济学和Nance中广泛使用的建模和预测工具。近年来，具有时变参数和随机波动性的VAR(TVP-VAR)受到了越来越多的关注，因为越来越多的证据质疑通常的参数稳定假设，特别是在数据包含几十年的时间序列中，增加了潜在随机过程动态结构变化的概率。像标准VAR一样，TVP-VAR是一种数据描述、预测、结构推断和政策分析的方法，因此可以用于分析大量的经济问题。然而，用于TVP-VAR创新的时变协方差矩阵的标准多变量随机波动率(MSV)分布并不是不变的。对VAR系统中的时间序列变量进行排序，从而不希望这种排序影响推断结果。在这个项目中，我们考虑基于Wishart过程的排序不变但可扩展的MSV模型。它们在金融应用中已经变得流行起来，但它们在实证应用中所需的统计推断仍然是一项具有挑战性的任务。我们的目标是开发基于蒙特卡洛的推理程序，用于Wishart MSV模型的最大似然分析，然后将扩展推理程序，用于分析具有Wishart MSV规范的创新协方差矩阵的TVPVAR。开发的方法将被广泛应用于金融和宏观经济领域。

Vector autoregressions (VARs) are widely used to provide a systematic way to capture richdynamics in multiple time series, and thus have become a widely used tool for modelingand forecasting in macroeconomics and nance. In recent years, VARs with time-varyingparameters and stochastic volatility (TVP-VARs) have received increasing attention becauseof an ever-growing body of evidence questioning the usual assumption of stable parameters,especially, in time series where data encompass several decades, increasing the probabilityof changes in the dynamic structure of the underlying stochastic process. Like standardVARs, TVP-VARs oer an approach to data description, forecasting, structural inferenceand policy analysis, and as such can be used to analyze a large number of economic problems.However, standard multivariate stochastic volatility (MSV) specications used for the timevaryingcovariance matrix of the TVP-VAR innovations are not invariant w.r.t. the orderingof the time series variables in the VAR system so that this ordering undesirably aects theinference results.In this project we consider ordering-invariant yet exible MSV models based on Wishartprocesses. They have become popular in nancial applications but the statistical inferencerequired for their empirical application remains to be a challenging task. We aim at developingMonte-Carlo based inference procedures for a maximum likelihood analysis of thoseWishart MSV models and then will extend the inference procedures for the analysis of TVPVARswith Wishart MSV specications for the covariance matrix of the innovations. Thedeveloped methods will be implemented for thorough nancial and marcoeconomic applications.