Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors
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.
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Volume (Year): 83 (2013)
Issue (Month): 1 ()
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References listed on IDEAS
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- Hwang, S.Y. & Kim, S. & Lee, S.D. & Basawa, I.V., 2007. "Generalized least squares estimation for explosive AR(1) processes with conditionally heteroscedastic errors," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1439-1448, July.
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- Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
- Monsour, Michael J. & Mikulski, Piotr W., 1998. "On limiting distributions in explosive autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 141-147, February.
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