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NONPARAMETRIC NONSTATIONARITY TESTS

Published online by Cambridge University Press:  20 August 2013

Federico M. Bandi  and
Valentina Corradi
Federico M. Bandi*
Affiliation:
Johns Hopkins University and Edhec-Risk
Valentina Corradi*
Affiliation:
University of Warwick
*
*Address Correspondence to Federico Bandi, Johns Hopkins Carey Business School, 100 International Drive, Baltimore, MD 21202; e-mail: fbandi1@jhu.edu; or to: Valentina Corradi, Department of Economics, University of Warwick, Coventry CV4 7AL, UK; e-mail: v.corradi@warwick.ac.uk
*Address Correspondence to Federico Bandi, Johns Hopkins Carey Business School, 100 International Drive, Baltimore, MD 21202; e-mail: fbandi1@jhu.edu; or to: Valentina Corradi, Department of Economics, University of Warwick, Coventry CV4 7AL, UK; e-mail: v.corradi@warwick.ac.uk
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Abstract

We propose additive functional-based nonstationarity tests that exploit the different divergence rates of the occupation times of a (possibly nonlinear) process under the null of nonstationarity (stationarity) versus the alternative of stationarity (nonstationarity). We consider both discrete-time series and continuous-time processes. The discrete-time case covers Harris recurrent Markov chains and integrated processes. The continuous-time case focuses on Harris recurrent diffusion processes. Notwithstanding finite-sample adjustments discussed in the paper, the proposed tests are simple to implement and rely on tabulated critical values. Simulations show that their size and power properties are satisfactory. Our robustness to nonlinear dynamics provides a solution to the typical inconsistency problem between assumed linearity of a time series for the purpose of nonstationarity testing and subsequent nonlinear inference.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 127 - 149
Copyright
Copyright © Cambridge University Press 2013 

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References

REFERENCES

Aït-Sahalia, Y. (1996) Testing continuous time models of the spot interest rate. Review of Financial Studies 9, 385–426.Google Scholar
Bandi, F.M., Corradi, V., & Moloche, G. (2009) Bandwidth Selection for Continuous Time Markov Processes. Working paper.Google Scholar
Bandi, F.M., Corradi, V., & Wilhelm, D. (2011) Data-Driven Bandwidth Selection for Nonparametric Nonstationary Regressions. Working paper.CrossRefGoogle Scholar
Bandi, F.M. & Phillips, P.C.B. (2003) Fully nonparametric estimation of scalar diffusion models. Econometrica 71, 241–283.Google Scholar
Bandi, F.M. & Phillips, P.C.B. (2010) Nonstationary continuous-time processes. In Ait-Sahalia, Y. & Hansen, L.P. (eds.), Handbook of Financial Econometrics. Elsevier.Google Scholar
Breitung, J. (2002) Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108, 343–363.Google Scholar
Chen, X. (1999) How often does a Harris recurrent markov chain recur? Annals of Probability 27, 1324–1346.Google Scholar
Conley, T.G., Hansen, L.P., Luttmer, E.G.J., & Scheinkman, J.A. (1997) Short-term interest rates as subordinated diffusions. Review of Financial Studies 10, 525–577.Google Scholar
Corradi, V. & Swanson, N. (2006) The effects of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo and a simple test. Journal of Econometrics 132, 195–229.Google Scholar
Davidson, R. & Flachaire, E. (2008) The wild-bootstrap tamed at last. Journal of Econometrics 146, 162–169.Google Scholar
Dolado, J.J., Gonzalo, J., & Mayoral, L. (2002) A fractional Dickey-Fuller test for unit roots. Econometrica 70, 1963–2006.CrossRefGoogle Scholar
Dufour, J.M. & Kiviet, J.F. (1996) Exact tests for structural changes in first-order dynamic models. Journal of Econometrics 70, 39–68.Google Scholar
Eberlein, E (1986) On string invariance principles under dependence assumptions. Annals of Probability 14, 260–270.Google Scholar
Elliott, G., Rothenberg, T.G., & Stock, J.H. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.Google Scholar
Goncalves, S. & Meddahi, N. (2009) Bootstrapping realized volatility. Econometrica 77, 283–306.Google Scholar
Guerre, E. (2004) Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series. Working paper.Google Scholar
Hajek, J. & Sidak, Z. (1967) Theory of Rank Tests. Academic Press.Google Scholar
Hansen, B.E. (1996) Inference when a parameter is not identified under the null hypothesis. Econometrica 64, 413–430.Google Scholar
Karlsen, H.A. & Tjostheim, V. (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372–416.Google Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159–178.Google Scholar
Löcherbach, E. & Loukianova, D. (2009) The law of the iterated logarithm for additive functionals and martingale additive functionals of harris recurrent Markov processes. Stochastic Processes and Their Applications 119, 2312–2335.Google Scholar
Lutkepohl, H. & Burda, M.M. (1997) Modified Wald tests under nonregular conditions. Journal of Econometrics 78, 315–332.Google Scholar
Meyn, S.P. & Tweedie, R.L. (1993) Stability of Markovian processes 2: Continuous time processes and sampled chains. Advances in Applied Probability 25, 487–517.Google Scholar
Müller, U.K. (2008) The impossibility of consistent discrimination between I (0) and I (1) processes. Econometric Theory 24, 616–630.CrossRefGoogle Scholar
Pearson, E.S. (1950) On questions raised by the combination of tests based on discontinuous distributions. Biometrika 37, 383–398.Google Scholar
Phillips, P.C.B. (1987) Time series regressions with a unit root. Econometrica 55, 277–301.CrossRefGoogle Scholar
Phillips, P.C.B. & Xiao, Z. (1998) A primer on unit root testing. Journal of Economic Surveys 12, 423–469.Google Scholar
Pritsker, M. (1998) Nonparametric density estimators and tests of continuous time interest rate models. Review of Financial Studies 11, 449–487.CrossRefGoogle Scholar
Schienle, M. (2008) Nonparametric Nonstationary Regression with Many Covariates. Working paper.Google Scholar
Stevens, W.L. (1950) Fiducial limits of the parameters of a discontinuous distribution. Biometrika 37, 117–129.Google Scholar
Tocher, K.D. (1950) Extension of the Neyman-Pearson theory of tests to discontinuous variates. Biometrika 37, 130–144.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structural nonparametric cointegrating regression. Econometrica 77, 1901–1948.Google Scholar