Estimation and Inference in Autoregressive Models with Trending Innovation Variance

35 Pages Posted: 26 Jan 2009

See all articles by Nikolaos Kourogenis

Nikolaos Kourogenis

University of Piraeus, Department of Banking and Financial Management

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management

Date Written: September 22, 2008

Abstract

This paper develops the asymptotic theory for stable autoregressive models in which the noise variance grows in a polynomial-like fashion. It is shown that the asymptotic distribution of the OLS estimator of the coefficient vector is multivariate normal with a covariance matrix that depends on the order, k, of the variance growth. A consistent estimator of k is proposed, which delivers heteroscedasticity-robust test statistics. The opposite case of "variance decline" is studied as well. It is demonstrated that by means of a simple data transformation producing the time reversed image of the original series, the problem of "variance decrease" can be reformulated in terms of that of polynomial-like variance growth. Simulation evidence suggests that the new procedures work quite well in small samples.

Keywords: polynomial-like noise variance, limiting distribution, order of variance growth, modified t-statistic, heteroscedasticity-robust t-statistic, variance decline

JEL Classification: C22

Suggested Citation

Kourogenis, Nikolaos and Pittis, Nikitas, Estimation and Inference in Autoregressive Models with Trending Innovation Variance (September 22, 2008). Available at SSRN: https://ssrn.com/abstract=1333125 or http://dx.doi.org/10.2139/ssrn.1333125

Nikolaos Kourogenis (Contact Author)

University of Piraeus, Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

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