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SPECIFICATION TESTING IN NONLINEAR TIMESERIES WITH LONG-RANGE DEPENDENCE

Published online by Cambridge University Press:  27 August 2010

Jiti Gao ,
Qiying Wang  and
Jiying Yin
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Abstract

This paper proposes a model specification testingprocedure for parametric specification of theconditional mean function in a nonlinear time seriesmodel with long-range dependent. An asymptoticallynormal test is established even when long-rangedependent is involved. To implement the proposedtest in practice using a simulated example, abootstrap simulation procedure is established tofind a simulated critical value to compute both thesize and power values of the proposed test.

Information

Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 2 , April 2011 , pp. 260 - 284
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

The authors thank the co-editor and two refereesfor helpful comments on earlier versions. Theauthors also acknowledge financial support fromthe Australian Research Council Discovery GrantsProgram under grants DP0558602 and DP0879088.

References

REFERENCES

Arapis, M. & Gao, J. (2006) Empirical comparisons in short-term interest rate models using nonparametric methods. Journal of Financial Econometrics 4, 310–345.CrossRefGoogle Scholar
Avram, F. (1988) On bilinear forms in Gaussian random variables and Toeplitz matrices. Probability Theory and Related Fields 79, 37–45.CrossRefGoogle Scholar
Beran, J. (1994) Statistics for Long-Memory Processes. Chapman and Hall.Google Scholar
Beran, J. & Ghosh, S. (1998) Root- n-consistent estimation in partial linear models with long-memory errors. Scandinavian Journal of Statistics 25, 345–357.CrossRefGoogle Scholar
Biedermann, S. & Dette, H. (2000). Testing linearity of regression models with dependent errors by kernel based methods. Test 9, 417–438.CrossRefGoogle Scholar
Cheng, B. & Robinson, P.M. (1994). Semiparametric estimation from time series with long-range dependence. Journal of Econometrics 64, 335–353.CrossRefGoogle Scholar
Csörgö, S. & Mielniczuk, J. (1999). Random-design regression under long-range dependence. Bernoulli 5, 209–224.CrossRefGoogle Scholar
Fan, J. & Yao, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag.CrossRefGoogle Scholar
Fan, Y. & Li, Q. (2000). Consistent model specification tests: Kernel-based tests versus Bierens’ ICM tests. Econometric Theory 16, 1016–1041.CrossRefGoogle Scholar
Fan, Y. & Linton, O. (2003). Some higher-order theory for a consistent nonparametric model specification test. Journal of Statistical Planning and Inference 109, 125–154.CrossRefGoogle Scholar
Fox, R. & Taqqu, M.S. (1987). Central limit theorems for quadratic forms in random variables having long-range dependence. Probability Theory and Related Fields 74, 213–240.CrossRefGoogle Scholar
Gao, J. (2007). Nonlinear Time Series: Semiparametric methods. Chapman and Hall/CRC.CrossRefGoogle Scholar
Gao, J. & Anh, V. (1999). Semiparametric regression with long-range dependent error processes. Journal of Statistical Planning and Inference 80, 37–57.CrossRefGoogle Scholar
Gao, J. & Gijbels, I. (2008). Bandwidth parameter selection in nonparametric kernel testing. Journal of the American Statistical Association 484, 1584–1594.CrossRefGoogle Scholar
Gao, J. & King, M.L. (2004). Adaptive testing in continuous-time diffusion models. Econometric Theory 20, 844–882.CrossRefGoogle Scholar
Gao, J. & Wang, Q. (2006). Long-Range Dependent Time Series Specification. Working paper, University of Adelaide; available at http://www.adelaide.edu.au/directory/jiti.gao.Google Scholar
Giraitis, L. & Surgailis, D. (1990) A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle’s estimate. Probability Theory and Related Fields 86, 87–104.CrossRefGoogle Scholar
Giraitis, L. & Taqqu, M.S. (1997) Limit theorems for bivariate Appell polynomials. I. Central limit theorems. Probability Theory and Related Fields 107, 359–381.CrossRefGoogle Scholar
Hall, P. & Heyde, C. (1980). Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Hidalgo, F.J. (1997). Nonparametric estimation with strongly dependent multivariate time series. Journal of Time Series Analysis 8, 95–122.CrossRefGoogle Scholar
Ho, H.C. & Hsing, T. (1996). On the asymptotic expansion of the empirical processes of long-memory moving averages. Annals of Statistics 24, 992–1024.CrossRefGoogle Scholar
Ho, H.C. & Hsing, T. (1997). Limit theorems for functional of moving averages. Annals of Probability 25, 1636–1669.CrossRefGoogle Scholar
Ho, H.C. & Hsing, T. (2003). A decomposition for generalized U-statistics of long-memory linear processes. In Theory and Applications of Long-Range Dependence, pp. 143–155. Birkhauser.Google Scholar
Horowitz, J. & Spokoiny, V. (2001). An adaptive rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.CrossRefGoogle Scholar
Hsing, T. & Wu, W.B. (2004). On weighted U-statistics for stationary processes. Annals of Probability 32, 1600–1631.CrossRefGoogle Scholar
Li, Q. (1999). Consistent model specification tests for time series econometric models. Journal of Econometrics 92, 101–147.CrossRefGoogle Scholar
Li, Q. & Racine, J. (2007). Nonparametric Econometrics. Princeton University Press.Google Scholar
Li, Q. & Wang, S. (1998). A simple consistent bootstrap test for a parametric regression functional form. Journal of Econometrics 87, 145–165.CrossRefGoogle Scholar
Mielniczuk, J. & Wu, W.B. (2004). On random-design model with dependent errors. Statistica Sinica 14, 1105–1126.Google Scholar
Robinson, P.M. (1995). Gaussian semiparametric estimation of long-range dependence. Annals of Statistics 23, 1630–1661.CrossRefGoogle Scholar
Robinson, P.M. (1997). Large-sample inference for nonparametric regression with dependence errors. Annals of Statistics 25, 2054–2083.CrossRefGoogle Scholar
Zhao, Z. & Wu, W.B. (2008) Confidence bands in nonparametric time series regression. Annals of Statistics 36, 1854–1878.CrossRefGoogle Scholar
Zheng, J.X. (1996). A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics 75, 263–289.CrossRefGoogle Scholar