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Local explosion modelling by non‐causal process
Author(s) -
Gouriéroux Christian,
Zakoïan JeanMichel
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12193
Subject(s) - econometrics , unit root , cauchy distribution , mathematics , generalized pareto distribution , economics , statistical physics , statistics , extreme value theory , physics
Summary 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.