Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root
This paper derives the limiting distribution of the Lagrange Multiplier (LM) test for threshold nonlinearity in a TAR model with GARCH errors when one of the regimes contains a unit root. It is shown that the asymptotic distribution is nonstandard and depends on nuisance parameters that capture the degree of conditional heteroskedasticity and non-Gaussian nature of the process. We propose a bootstrap procedure for approximating the exact finite-sample distribution of the test for linearity and establish its asymptotic validity.
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- Nikolay Gospodinov, 2005. "Testing For Threshold Nonlinearity in Short-Term Interest Rates," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 344-371.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
- Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
- Jun Yu & Peter Phillips, 2004.
"Jackknifing Bond Option Prices,"
Econometric Society 2004 North American Winter Meetings
115, Econometric Society.
- Yu, Jun & Phillips, Peter, 2002. "Jacknifing Bond Option Prices," Working Papers 187, Department of Economics, The University of Auckland.
- Peter C.B. Phillips & Jun Yu, 2003. "Jackknifing Bond Option Prices," Cowles Foundation Discussion Papers 1392, Cowles Foundation for Research in Economics, Yale University.
- Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(04), pages 541-564, August.
- Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
- Hansen, Bruce E, 1999.
" Testing for Linearity,"
Journal of Economic Surveys,
Wiley Blackwell, vol. 13(5), pages 551-576, December.
- H. Peter Boswijk, 2001.
"Testing for a Unit Root with Near-Integrated Volatility,"
Tinbergen Institute Discussion Papers
01-077/4, Tinbergen Institute.
- H. Peter Boswijk, 2000. "Testing for a Unit Root with Near-Integrated Volatility," Econometric Society World Congress 2000 Contributed Papers 1101, Econometric Society.
- Boswijk, H.P., 2000. "Testing for a Unit Root with Near-Integrated Volatility," CeNDEF Working Papers 00-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Jesús Miguel & Pilar Olave, 1999. "Bootstrapping forecast intervals in ARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 345-364, December.
- Bruce E. Hansen & Mehmet Caner, 1997.
"Threshold Autoregressions with a Unit Root,"
Boston College Working Papers in Economics
381, Boston College Department of Economics.
- Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
- Shiqing Ling & W. K. Li & Michael McAleer, 2003.
"Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence,"
Taylor & Francis Journals, vol. 22(2), pages 179-202.
- Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," CIRJE F-Series CIRJE-F-207, CIRJE, Faculty of Economics, University of Tokyo.
- Shiqing Ling & W. K. Li & Michael McAleer, 2001. "Estimation and Testing for Unit Root Processes with GARCH(1,1) Errors: Theory and Monte Carlo Evidence," ISER Discussion Paper 0544, Institute of Social and Economic Research, Osaka University.
- Donald W.K. Andrews & Werner Ploberger, 1992.
"Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative,"
Cowles Foundation Discussion Papers
1015, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
- Hansen, B.E., 1991.
"Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis,"
RCER Working Papers
296, University of Rochester - Center for Economic Research (RCER).
- Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
- Hansen Bruce E., 1997.
"Inference in TAR Models,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 2(1), pages 1-16, April.
- Tom Doan, "undated". "THRESHTEST: RATS procedure to perform Hansen's Test for Threshold Break," Statistical Software Components RTS00210, Boston College Department of Economics.
- Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(05), pages 815-834, October.
- Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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