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NEAR-INTEGRATED RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES

Published online by Cambridge University Press:  23 June 2008

Alexander Aue
Alexander Aue*
Affiliation:
University of California, Davis
*
Address correspondence to Alexander Aue, Department of Sciences, University of California, One Shields Avenue, Davis, CA 95616, USA; e-mail: [email protected]
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Abstract

We determine the limiting behavior of near-integrated first-order random coefficient autoregressive RCA(1) time series. It is shown that the asymptotics of the finite-dimensional distributions crucially depends on how the critical value 1 is approached, which determines whether the process is near-stationary, has a unit root, or is mildly explosive. %In a second part, we derive the limit distribution of the serial correlation coefficient in the near stationary and the mildly explosive settings under very general conditions on the parameters. The results obtained are in accordance with those available for first-order autoregressive time series and can hence serve as an addition to existing literature in the area.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 5 , October 2008 , pp. 1343 - 1372
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Anderson, T.W. (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676–687.Google Scholar
Aue, A. & Horváth, L. (2007) A limit theorem for mildly explosive autoregression with stable errors. Econometric Theory 23, 201–220.Google Scholar
Aue, A., Horváth, L., & Steinebach, J. (2006) Estimation in random coefficient autoregressive models. Journal of Time Series Analysis 27, 61–76.Google Scholar
Berkes, I., Horváth, L., & Kokoszka, P. (2005) Near-integrated GARCH sequences. Annals of Applied Probability 15, 890–913.Google Scholar
Billingsley, P. (1995) Probability and Measure, 3rd ed. Wiley.Google Scholar
Brockwell, P.J. & Davis, R.A. (1991) Time Series: Theory and Methods, 2nd ed. Springer-Verlag.Google Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050–1063.Google Scholar
Chan, N.H. & Wei, C.Z. (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.Google Scholar
Chow, Y.S. & Teicher, H. (1988) Probability Theory: Independence, Interchangeability, Martingales, 2nd ed. Springer-Verlag.CrossRefGoogle Scholar
Ling, S. & Li, W.K. (1998) Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors. Annals of Statistics 26, 84–125.Google Scholar
Nelson, C.R. & Plosser, C. (1982) Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics 10, 139–162.Google Scholar
Nicholls, D.F. & Quinn, B.G. (1982) Random Coefficient Autoregressive Models: An Introduction. Springer-Verlag.Google Scholar
Phillips, P.C.B. (1988) Regression theory for near-integrated time series. Econometrica 56, 1021–1043.CrossRefGoogle Scholar
Phillips, P.C.B. & Magdalinos, T. (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics 136, 115–130.CrossRefGoogle Scholar
Tong, H. (1990) Non-Linear Time Series: A Dynamical System Approach. Clarendon.Google Scholar