A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model

Statistics and Probability Letters

Volumn 30, Issue 4, 1996, Pages 305-311

  Lu, Zudi ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Arch model; Conditional heteroscedasticity; Geometric ergodicity; Markov process; Nonlinear time series

Indexed keywords

EID: 0030588766     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(95)00233-2     Document Type: Article

References (17)

1. An, H.Z. and F.C. Huang (1994), The geometric ergodicity of nonlinear autoregressive model, Technical Report, Institute of Applied Mathematics, Academia Sinica, Beijing.
2. Bera, A.K. and M.L. Higgins, (1992), A test for conditional heteroskedasticity in time series models, J. Time Series Anal. 13, 501-519.
3. Bera, A.K. and M.L. Higgins, (1993), A survey of ARCH models: properties of estimation and testing, J. Econom. Surveys 7, 305-366.
4. Chan, K.S. (1990), Deterministic stability, stochastic stability, and ergodicity, in: H. Tong, ed., Nonlinear Time Series: A Dynamical System Approach, pp. 448-466 (Oxford Univ. Press, Oxford).
5. Domowitz, I. and C.S. Hakkio, (1985), Conditional variance and the risk premium in the foreign exchange market, J. Internat. Econom. 19, 47-66.
6. Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of United Kingdom inflation, Econometrica 50, 987-1007.
7. Engle, R.F. (1983), Estimation of the variance of US inflation based on the ARCH model, J. Money Credit Banking 15, 296-301.
8. Engle, R.F. and T. Bollerslev (1986), Modelling the persistence of conditional variances, Economet. Rev. 5, 1-50.
9. Guegan, D. and J. Diebolt (1994), Probabilistic properties of the β-ARCH model, Statistica Sinica 4, 71-87.
10. Nelson, D.B. (1991), Conditional heteroskedasticity in asset returns: a new approach, Econometrica 59, 347-370.
11. Nummelin, E. (1984), General Irreducible Markov Chains and Non-negative Operations (Cambridge Univ. Press, Cambridge).
12. Pantula, S.G. (1984), Autoregressive conditionally heteroscedastic models, Institute of Statistics Mimeograph Series No. 1648, North Carolina State University, Raleigh, NC.
13. Pantula, S.G. (1988), Estimation of autoregresive models with ARCH errors, Sankhya Ser. B 50, 119-138.
14. Tjøstheim, D. (1990), Nonlinear time series and Markov chains, Adv. Appl. Probab. 22, 587-611.
15. Tong, H. (1990), Non-linear Time Series: A Dynamical System Approach (Oxford Univ. Press, Oxford).
16. Weiss, A.A. (1984), ARMA model with ARCH errors, J. Time Series Anal. 5, 129-143.
17. Weiss, A.A. (1986), ARCH and bilinear time series models: comparison and combination, J. Bus. Econom. Statist. 4, 59-70.