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Generalized least squares estimation for explosive AR(1) processes with conditionally heteroscedastic errors

Authors
Hwang, S. Y.Kim, S.Lee, S. D.Basawa, I. V.
Issue Date
15-Jul-2007
Publisher
ELSEVIER SCIENCE BV
Keywords
ARCH errors; explosive AR(1); generalized least squares; Martingale
Citation
STATISTICS & PROBABILITY LETTERS, v.77, no.13, pp.1439 - 1448
Journal Title
STATISTICS & PROBABILITY LETTERS
Volume
77
Number
13
Start Page
1439
End Page
1448
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/14663
DOI
10.1016/j.spl.2007.02.010
ISSN
0167-7152
Abstract
This article is concerned with explosive AR(1) processes generated by conditionally heteroscedastic errors. Conditional least squares as well as generalized least squares estimation for autoregressive parameter are discussed and relevant limiting distributions are expressed as products of certain random variables. These results can be viewed as generalizations of classical results obtained for the standard explosive AR(l) model with i.i.d. errors (cf. [Fuller, W.A., 1996. Introduction to Statistical Time Series, second ed. Wiley, New York (Chapter 10)]). The model under consideration accommodates diverse conditionally heteroscedastic processes including Engle [1982. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987-1008]'s ARCH, threshold-ARCH and beta-ARCH processes. Based on residuals, least squares estimation for parameters appearing in the conditional variance is also discussed and is illustrated for various ARCH type processes. (C) 2007 Elsevier B.V. All rights reserved.
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