Local explosion modelling by non-causal process

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...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series B, Statistical methodology Jg. 79; H. 3; S. 737 - 756
Hauptverfasser: Gourieroux, Christian, Zakoian, Jean-Michel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford John Wiley & Sons Ltd 01.06.2017
Oxford University Press
Schlagworte:
Asymmetry
Asymptotic properties
Autocorrelation
Autoregressive processes
Behavior
Cauchy problems
Causal innovation
Causality
Correlation analysis
Diagnostic systems
diagnostic techniques
Diagnostic tests
Economic models
Economics
equations
Errors
Explosions
Explosive bubble
Global local relationship
Heavy‐tailed errors
Mathematical models
NASDAQ trading
Nonlinear dynamics
Non‐causal process
Price indexes
prices
Regression analysis
Samples
Stable process
Statistical methods
Statistics
Stock market indexes
Studies
Time series
time series analysis
ISSN:1369-7412, 1467-9868
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Beschreibung
Zusammenfassung: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.
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12193