JOURNAL BROWSE
Search
Advanced SearchSearch Tips
PARAMETER CHANGE TEST FOR NONLINEAR TIME SERIES MODELS WITH GARCH TYPE ERRORS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
PARAMETER CHANGE TEST FOR NONLINEAR TIME SERIES MODELS WITH GARCH TYPE ERRORS
Lee, Jiyeon; Lee, Sangyeol;
  PDF(new window)
 Abstract
In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.
 Keywords
nonlinear time series models with GARCH type errors;parameter change;CUSUM test;weak convergence to a Brownian bridge;
 Language
English
 Cited by
1.
Parameter change test for zero-inflated generalized Poisson autoregressive models, Statistics, 2016, 50, 3, 540  crossref(new windwow)
 References
1.
F. Chan and M. McAleer, Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence, J. Appl. Econometrics 17 (2002), 509-534. crossref(new window)

2.
F. Chan, M. McAleer, and M. C. Medeiros, Structure and asymptotic theory for nonlinear models with GARCH errors, KIER Working Papers 754, Kyoto University, Institute of Economic Research, 2010.

3.
K. S. Chan and H. Tong, On estimating thresholds in autoregressive models, J. Time Ser. Anal. 7 (1986), no. 3, 179-190. crossref(new window)

4.
D. B. H. Cline, Stability of nonlinear stochastic recursions with application to nonlinear AR-GARCH models, Adv. Appl. Probab. 39 (2007), 462-491. crossref(new window)

5.
M. D. de Poorter and D. van Dijk, Testing for changes in volatility in heteroscadastic time series - a further examination, (No. EI 2004-38), Report / Econometric Institute, Erasmus University Rotterdam, 2004.

6.
P. Gaenssler and E. Haeusler, On martingale central limit theory, In E. Eberlein and M. S. Taqqu, (Eds.), Dependence in probability and statistics: A survey of recent results, pp. 303-334, Boston: Birkhauser, 1986.

7.
D. Kristensen and A. Rahbek, Asymptotics of the QMLE for a class of ARCH(q) models, Econometric Theory 21 (2005), no. 5, 946-961.

8.
S. Lee, J. Ha, O. Na, and S. Na, The cusum test for parameter change in time series models, Scand. J. Statist. 30 (2003), no. 4, 781-796. crossref(new window)

9.
S. Lee and J. Lee, Residual based cusum test for parameter change in AR-GARCH models, In Modeling Dependence in Econometrics, Advances in Intelligent Systems and Computing 251 (2014), 101-111. crossref(new window)

10.
S. Lee and J. Song, Test for parameter change in ARMA models with GARCH innovations, Statist. Probab. Lett. 78 (2008), no. 13, 1990-1998. crossref(new window)

11.
S. Lee, Y. Tokutsu, and K. Maekawa, The cusum test for parameter change in regression models with ARCH errors, J. Japan Statist. Soc. 34 (2004), 173-188. crossref(new window)

12.
S. Ling, On probability properties of a double threshold ARMA conditional heteroskedasticity model, J. Appl. Probab. 36 (1999), 688-705. crossref(new window)

13.
J. Liu, W. K. Li, and C. W. Li, On a threshold autoregression with conditional heteroscedastic variances, J. Statist. Plann. Inference 62 (1997), no. 2, 279-300. crossref(new window)

14.
S. Lundbergh and T. Terasvirta, Modeling economic high frequency time series with STAR-STGARCH models, SSE/EFI Working Paper Series in Economics and Finnce 291, 1999.

15.
R. Luukkonen, P. Saikkonen, and T. Terasvirta, Testing linearity in univariate time series models, Scand. J. Statist. 15 (1988), no. 3, 161-175.

16.
M. Meitz and P. Saikkonen, Stability of nonlinear AR-GARCH models, J. Time Ser. Anal. 29 (2008), no. 3, 453-475. crossref(new window)

17.
M. Meitz and P. Saikkonen, Parameter estimation in nonlinear AR-GARCH models, Econometric Theory 27 (2011), no. 6, 1236-1278. crossref(new window)

18.
O. Na, J. Lee, and S. Lee, Change point detection in copula ARMA-GARCH Models, J. Time Ser. Anal. 33 (2012), no. 4, 554-569. crossref(new window)

19.
J. Z. Pan, H. Wang, and H. Tong, Estimation and tests for power-transformed and threshold GARCH models, J. Econometrics 142 (2008), no. 1, 352-378. crossref(new window)

20.
D. Straumann and T. Mikosch, Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach, Ann. Statist. 34 (2006), no. 5, 2449-2495. crossref(new window)

21.
H. Tong, Nonlinear Time Series: A Dynamical System Approach, Oxford University Press, Oxford, 1990.