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Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors
- Authors
- Hwang, S. Y.
- Issue Date
- Jan-2013
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Explosive AR(1); Initial value; Random norm; Dependent errors
- Citation
- STATISTICS & PROBABILITY LETTERS, v.83, no.1, pp 127 - 134
- Pages
- 8
- Journal Title
- STATISTICS & PROBABILITY LETTERS
- Volume
- 83
- Number
- 1
- Start Page
- 127
- End Page
- 134
- ISSN
- 0167-7152
1879-2103
- Abstract
- This article is concerned with a broad class of explosive AR(1) models. Allowing stationary dependence on the error process, we do not restrict ourselves to independent and identically distributed errors. The model accommodates, as special cases, GARCH errors, AR(1) errors and Gaussian ARMA errors. The error distribution is permitted to be non-normal. To circumvent the effect of initial values, the limit distribution of the least squares estimate using a random norm (rather than a constant norm) is derived. It is shown that the limit distribution using a random norm is free from the initial value provided the error is symmetrically distributed about zero. (C) 2012 Elsevier B.V. All rights reserved.
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