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

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  • Hwang, S.Y.
  • Kim, S.
  • Lee, S.D.
  • Basawa, I.V.

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(1) 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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:13:p:1439-1448
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    References listed on IDEAS

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    1. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    2. Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    3. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Hwang, S.Y., 2013. "Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 127-134.
    2. Christoph P. Kustosz & Anne Leucht & Christine H. MÜller, 2016. "Tests Based on Simplicial Depth for AR(1) Models With Explosion," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 763-784, November.

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