A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student's t distribution changes over time, we construct a robust filter which is able to overcome several issues that naturally arise when modeling heavy-tailed phenomena and, more in general, vectors of dependent non-Gaussian time series. We derive conditions for stationarity and invertibility and estimate the unknown parameters by maximum likelihood (ML). Strong consistency and asymptotic normality of the estimator are proved and the finite sample properties are illustrated by a Monte-Carlo study. From a computational point of view, analytical formulae are derived, which consent to develop estimation procedures based on the Fisher scoring method. The theory is supported by a novel empirical illustration that shows how the model can be effectively applied to estimate consumer prices from home scanner data.
翻译:通过开发多变量计分驱动过滤器,从噪音矢量过程中提取信号。假设多变量学生 t分布随时间变化而变化的有条件位置矢量,我们将构建一个强大的过滤器,能够克服在模拟重尾现象以及更一般地说,依赖非圭亚那时间序列的矢量时自然产生的若干问题。我们从静止性和可视性中得出条件,并以最大可能性来估计未知参数(ML)。测量仪的强烈一致性和无症状常态得到了证明,而一个蒙特-卡洛研究则展示了有限的样本特性。从计算角度来看,得出了分析公式,同意根据Fisher的评分方法制定估算程序。该理论得到一个新的实验性说明的支持,该说明该模型如何能够有效地用于从家扫描器数据中估算消费价格。