Exact geometry of explosive autoregressive models

Kees Jan van Garderen

No 1997068, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: This paper derives exact expressions for statistical curvature and related geometric quantities in the first order autoregressive models with stable and unit roots, as well as explosive roots larger than unity. We develop a method for deriving exact moments of arbitrary order in general autoregressive models. The covariance of the minimal sufficient statistic is an application of this method. Of particular interest is the Efron curvature which is continuous and bounded in finite samples, but increases rapidly when the autoregressive parameter changes from stable to explosive values, which has important inferential consequences. The initial value effect is also quantified exactly. We also include results for the Efron curvature in the pure stationary case with stochastic initial value for comparison, extending and correcting results from a previous discussion paper.

Keywords: Differential geometry; statistical curvature; exact distribution theory; exact mgf; unit root; explosive time series; conditional inference; curved exponential models (search for similar items in EconPapers)
Date: 1997-09-01
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://sites.uclouvain.be/core/publications/coredp/coredp1997.html (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:1997068

Access Statistics for this paper

More papers in LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Alain GILLIS ().