STATIONARITY AND β-MIXING PROPERTY OF A MIXTURE AR-ARCH MODELS

Title & Authors
STATIONARITY AND β-MIXING PROPERTY OF A MIXTURE AR-ARCH MODELS
Lee, Oe-Sook;

Abstract
We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, $\small{{\beta}-mixing}$ property and existence of moments of the model are given via Markovian representation technique.
Keywords
mixture AR-ARCH model;Markov chain;stationarity;geometric ergodicity;$\small{{\beta}-mixing}$;
Language
English
Cited by
1.
Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach, Journal of Applied Statistics, 2014, 41, 2, 275
References
1.
D. B. H. Cline and H. H. Pu, Stability and the Lyapounov exponent of threshold AR-ARCH models, Ann. Appl. Probab. 14 (2004), no. 4, 1920-1949

2.
D. Dijk, T. TerÄasvirta, and P. Franses, Smooth transition autoregressive models: a survey of recent developments, Econometric Rev. 21 (2002), no. 1, 1-47

3.
R. F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of the United Kingdom inflation, Econometrica 50 (1982), no. 4, 987-1007

4.
M. Lanne and P. Saikkonen, Modeling the U.S. Short-term interest rate by mixture autoregressive processes, Journal of Financial Econometrics 1 (2003), no. 1, 96-125

5.
M. Lanne and P. Saikkonen, On mixture autoregressive models, 2004, preprint

6.
N. D. Le, R. D. Martin, and A. E. Raftery, Modeling Flat Stretches, bursts and outliers in time series using mixture transition distribution models, J. Amer. Statist. Assoc. 91 (1996), no. 436, 1504-1515

7.
O. Lee, Geometric ergodicity and existence of higher-order moments for DTARCH (p, q) process, J. Korean Statist. Society 32 (2003), no. 2, 193-202

8.
S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability, Springer-Verlag, 1993

9.
H. Tong, Nonlinear Time Series: A Dynamical System Approach, Oxford: Oxford University Press, 1990

10.
C. S. Wong and W. K. Li, On a mixture autoregressive model, J. Royal Stat. Soc. Ser. B Stat. Methodl. 62 (2000), no. 1, 95-115

11.
C. S. Wong and W. K. Li, On a mixture autogressive conditional heteroscedastic model, J. Amer. Statist. Assoc. 96 (2001), no. 455, 982-995

12.
C. S. Wong and W. K. Li, On a logistic mixture autoregressive model, Biometrika 88 (2001), no. 3, 833-846

13.
A. J. Zeevi, R. Meir, and R. J. Adler, Nonlinear models for time series using mixtures of autoregressive models, 2000