Abstract

A new mixture autoregressive model based on Student’s t–distribution is proposed. A key feature of our model is that the conditional t–distributions of the component models are based on autoregressions that have multivariate t–distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component model is a linear function of past observations and the conditional variance is also time-varying. Compared to previous mixture autoregressive models our model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. An empirical example employing a realized kernel series constructed from S&P 500 high-frequency intraday data shows that the proposed model performs well in volatility forecasting. Our methodology is implemented in the freely available StMAR Toolbox for MATLAB.

摘要

提出了一种新的基于学生t分布的混合自回归模型。我们模型的一个关键特征是组件模型的条件t分布基于具有多元t的自回归–分布作为它们的（低维）平稳分布。具有这种平稳分布的自回归并不是立竿见影的。我们的公式意味着每个组件模型的条件均值是过去观察的线性函数，条件方差也是时变的。因此，与以前的混合自回归模型相比，我们的模型可能在数据表现出相当强的条件异方差性的应用中很有用。我们的公式还具有理论上的优势，即始终满足平稳性和遍历性的条件，并且这些属性比非线性自回归模型中常见的属性更容易建立。使用由 S& 构造的已实现内核系列的经验示例 P 500 高频盘中数据表明，所提出的模型在波动率预测方面表现良好。我们的方法在免费提供的 MATLAB StMAR 工具箱中实现。