Local explosion modelling by non-causal process

• 成果类型: Article
• 署名作者: Gourieroux, Christian; Zakoian, Jean-Michel
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; University of Toronto; Universite de Lille
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12193
• 发表日期: 2017
• 页码: 737-756
• 关键词: limit theory; bubbles; exuberance; tests

摘要

The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto-correlations is studied in a semiparametric non-causal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided.