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http://dx.doi.org/10.5351/CSAM.2013.20.3.207

An Empirical Study on Explosive Volatility Test with Possibly Nonstationary GARCH(1, 1) Models  

Lee, Sangyeol (Department of Statistics, Seoul National University)
Noh, Jungsik (Department of Statistics, Seoul National University)
Publication Information
Communications for Statistical Applications and Methods / v.20, no.3, 2013 , pp. 207-215 More about this Journal
Abstract
In this paper, we implement an empirical study to test whether the time series of daily returns in stock and Won/USD exchange markets is strictly stationary or explosive. The results indicate that only a few series show nonstationary volatility when dramatic events erupted; in addition, this nonstationary behavior occurs more often in the Won/USD exchange market than in the stock market.
Keywords
GARCH model; Lyapunov exponent; strict stationarity testing;
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1 Kingman, J. F. C. (1973). Subadditive ergodic theory, The Annals of Probability, 1, 883-899.   DOI   ScienceOn
2 Lee, S.-W. and Hansen, B. E. (1994). Asymptotic theory for the GARCH(1, 1) quasi-maximum likelihood estimator, Econometric Theory, 10, 29-52.   DOI   ScienceOn
3 Lee, S. and Lee, T. (2012). Inference for Box-Cox transformed threshold garch models with nuisance parameters, Scandinavian Journal of Statistics, 39, 568-589.   DOI   ScienceOn
4 Li, W. K., Ling, S. and McAleer, M. (2002). Recent theoretical results for time series models with GARCH errors, Journal of Economic Surveys, 16, 245-269.   DOI   ScienceOn
5 Lumsdaine, R. L. (1996). Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1, 1) and covariance stationary GARCH(1, 1) models, Econometrica, 64, 575-596.   DOI   ScienceOn
6 Medeiros, M. C. and Veiga, A. (2009). Modeling multiple regimes in financial volatility with a flexible coefficient GARCH(1,1) model, Econometric Theory, 25, 117-161.   DOI   ScienceOn
7 Nelson, D. B. (1990). Stationarity and persistence in the GARCH(1, 1) model, Econometric Theory, 6, 318-334.   DOI
8 Pantula, S. G. (1988). Estimation of autoregressive models with ARCH errors, Sankhya B, 50, 119-138.
9 Straumann, D. and Mikosch, T. (2006). Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach, The Annals of Statistics, 34, 2449-2495.   DOI
10 Weiss, A. A. (1986). Asymptotic theory for ARCH models: Estimation and testing, Econometric Theory, 2, 107-131.   DOI
11 Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007.   DOI   ScienceOn
12 Billingsley, P. (1995). Probability and Measure, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 3rd edn, A Wiley-Interscience Publication.
13 Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327.   DOI   ScienceOn
14 Bougerol, P. and Picard, N. (1992). Stationarity of GARCH processes and of some nonnegative time series, Journal of Econometrics, 52, 115-127.   DOI   ScienceOn
15 Francq, C. and Zakoian, J.-M. (2004). Maximum likelihood estimation of pure GARCH and ARMAGARCH processes, Bernoulli, 10, 605-637.   DOI   ScienceOn
16 Francq, C. and Zakoian, J.-M. (2012). Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity models, Econometrica, 80, 821-861.   DOI   ScienceOn
17 Jensen, S. T. and Rahbek, A. (2004). Asymptotic inference for nonstationary GARCH, Econometric Theory, 20, 1203-1226.
18 Berkes, I., Horvath, L. and Kokoszka, P. (2003). GARCH processes: Structure and estimation, Bernoulli, 9, 201-227.   DOI   ScienceOn