Inference in Heavy-Tailed Nonstationary Multivariate Time Series

• 成果类型: Article
• 署名作者: Barigozzi, Matteo; Cavaliere, Giuseppe; Trapani, Lorenzo
• 署名单位: University of Bologna; University of Nottingham
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2128807
• 发表日期: 2024
• 页码: 565-581
• 关键词: common stochastic trends; error-correction; limit theory; AUTOREGRESSIVE PROCESSES; cointegration tests; sample covariance; rank; models; number; LAW

摘要

We study inference on the common stochastic trends in a nonstationary, N-variate time series y(t), in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail index, or even knowledge as to whether certain moments (such as the variance) exist or not, and develop an estimator of the number of stochastic trends m based on the eigenvalues of the sample second moment matrix of y(t). We study the rates of such eigenvalues, showing that the first m ones diverge, as the sample size T passes to infinity, at a rate faster by O (T) than the remaining N - m ones, irrespective of the tail index. We thus exploit this eigen-gap by constructing, for each eigenvalue, a test statistic which diverges to positive infinity or drifts to zero according to whether the relevant eigenvalue belongs to the set of the first m eigenvalues or not. We then construct a randomized statistic based on this, using it as part of a sequential testing procedure, ensuring consistency of the resulting estimator of m. We also discuss an estimator of the common trends based on principal components and show that, up to a an invertible linear transformation, such estimator is consistent in the sense that the estimation error is of smaller order than the trend itself. Importantly, we present the case in which we relax the standard assumption of iid innovations, by allowing for heterogeneity of a very general form in the scale of the innovations. Finally, we develop an extension to the large dimensional case. A Monte Carlo study shows that the proposed estimator for m performs particularly well, even in samples of small size. We complete the article by presenting two illustrative applications covering commodity prices and interest rates data. Supplementary materials for this article are available online.