Spurious inference in the GARCH (1,1) model when it is weakly identified

Studies in Nonlinear Dynamics and Econometrics

Volumn 11, Issue 1, 2007, Pages

  Ma, Jun ^a   Nelson, Charles R ^a   Startz, Richard ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947145235     PISSN: 10811826     EISSN: 15583708     Source Type: Journal    
DOI: 10.2202/1558-3708.1434     Document Type: Review

References (39)

1. Andrews, D. W. K. (2001): "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, 69, 683-734.
2. Baillie, R. T., and T. Bollerslev (1989): "The message in daily exchange rates: a conditional variance tale," Journal of Business & Economic Statistics, 7, 297-305.
3. Bansal, R., and A. Yaron (2000): "Risks for the Long Run: a Potential Resolution of Asset Pricing Puzzles," NBER Working Paper 8059.
4. Beg, R., M. Silvapulle, and P. Silvapulle (2001): "Tests against inequality constraints when some nuisance parameters are present only under the alternative: test of ARCH in ARCH-M models," Journal of Business & Economic Statistics, 19, 245-253.
5. Berkes, I., Horvath, L., and Kokoszka, P. (2003): "GARCH processes: structure and estimation," Bernoulli, 9, 201-227.
6. Box, G. E.P., and G. M. Jenkins (1976): Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
7. Bollerslev, T. (1986): "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, 31, 307-327.
8. Bollerslev, T. (1987): "A conditional heteroskedastic time series model for speculative prices and rates of return," The Review of Economics and Statistics, 69, 542-547.
9. Bollersleve, T. (1988): "On the correlation structure for the generalized autoregressive conditional heteroskedastic process," Journal of Time Series Analysis, 9, 121-131
10. Bollerslev, T., R. F. Engle, and D. B. Nelson (1994): "ARCH models," in: Engle, R. F., and D. L. McFadden, ed., Handbook of Econometrics, North Holland, Amsterdam, 2959-3038.
11. Bollerslev, T., and J. Wooldridge (1992): "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, 11, 143-172.
12. Bollerslev, T., R. Y. Chou, and K. F. Kroner (1992): "ARCH modeling in finance-a review of the theory and empirical evidence," Journal of Econometrics, 52, 5-59.
13. Cai, J. (1994): "A markov model of switching-regime ARCH," Journal of Business & Economic Statistics, 12, 309-316.
14. Davies, R. B. (1977): "Hypothesis testing when a nuisance parameter is present only under the alternative," Biometrika, 64, 247-254.
15. Davies, R. B. (1987): "Hypothesis testing when a nuisance parameter is present only under the alternative", Biometrika, 74, 33-43.
16. Dueker, M. J. (1997): "Markov switching in GARCH processes and mean-reverting stock-market Volatility," Journal of Business & Economic Statistics,15, 26-34.
17. Engle, R. (1982): "Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation," Econometrica, 50, 987-1008.
18. Engle, R., V. K. Ng, and M. Rothschild (1990): "Asset pricing with a factor-ARCH covariance structure-empirical estimates for treasury bills," Journal of Econometrics, 45, 213-237.
19. Figlewski, S. (1997): "Forecasting volatility," Financial Markets, Institutions and Instruments, 6, 1-88.
20. Fiorentini, G., G. Calzolari, and L. Panattoni (1996): "Analytical derivatives and the computation of GARCH estimates," Journal of Applied Econometrics, 11, 399-417.
21. Hamilton, J. (1994): Time Series Analysis. Princeton: Princeton University Press.
22. Hamilton, J., and R. Susmel (1994): "Autoregressive conditional heteroskedasticity and changes in regimes," Journal of Econometrics, 64, 307-333.
23. Hansen, B. (1996): "Inference when a nuisance parameter is not identified under the null hypothesis," Econometrica, 64, 413-430.
24. Hong, C. H. (1988): "The integrated generalized autoregressive conditional heteroskedastic model: the process, estimation and Monte Carlo experiments," Unpublished Manuscript, Department of Economics, University of California, San Diego, CA.
25. Jensen, S. T., and Rahbek, A. (2004): "Asymptotic inference for nonstationary GARCH," Econometric Theory, 20, 1203-1226.
26. Kim, C. J., C. R. Nelson, and R. Startz (1998): "Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization," Journal of Empirical Finance, 5, 131-154.
27. Lee, S. W., and B. Hansen (1994): "Asymptotic theory for The GARCH(1,1) quasi-maximum likelihood estimator," Econometric Theory, 10, 29-52.
28. 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.
29. Lumsdaine, R. L. (1995): "Finite-sample properties of the maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models: a Monte Carlo investigation," Journal of Business & Economic Statistics, 13, No.1, 1-10.
30. Lutkepohl, H. (1991): Introduction to Multiple Time Series Analysis. Berlin: Springer-Verlag.
31. Ma, J. (2006): "A closed-form asymptotic variance-covariance matrix for the maximum likelihood estimator of the GARCH(1,1) model," working paper, Department of Economics, University of Washington.
32. Ma, J., C. R. Nelson (2006): "A general approach to constructing a valid test in weakly identified models where the Zero-Information-Limit Condition holds," working paper, Department of Economics, University of Washington.
33. Nelson, C. R., and R. Startz (2006): "The Zero-Information-Limit Condition and spurious inference in weakly identified models," forthcoming in the Journal of Econometrics.
34. Nelson, D. (1990): "Stationary and persistence in the GARCH(1,1) model," Econometric Theory, 6, 318-334.
35. Starica, C. (2003): "Is GARCH(1,1) as good a model as the Nobel Prize accolades would imply?" working paper, Department of Mathematical Statistics, Chalmers University of Technology.
36. Weiss, A. (1986): "Asymptotic theory for ARCH models: estimation and testing," Econometric Theory, 2, 107-131.
37. Working, H. (1960): "Note on the correlation of first differences of a random chain," Econometrica, 28, 916-918.
38. Zivot, E., R. Startz, and C. R. Nelson (1998): "Valid confidence intervals and inference in the presence of weak instruments," International Economic Review, 39, 1119-1144.
39. Zivot, E. and J. Wang (2002): Modeling Financial Time Series with S-PLUS. Springer-Verlag.