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LATENT VARIABLE NONPARAMETRIC COINTEGRATING REGRESSION

Published online by Cambridge University Press:  23 March 2020

Qiying Wang ,
Peter C.B. Phillips  and
Ioannis Kasparis
Qiying Wang*
Affiliation:
The University of Sydney
Peter C.B. Phillips
Affiliation:
University of Auckland, Yale University, University of Southampton, Singapore Management University
Ioannis Kasparis
Affiliation:
University of Cyprus
*
Address correspondence to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail: qiying@maths.usyd.edu.au
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Abstract

This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such models occur in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent or filtered variable as in mixed-data-sampling. The treatment allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable, including correctly specified as well as misspecified systems, and is therefore intermediate between nonlinear nonparametric cointegrating regression and completely spurious nonparametric nonstationary regression. The results relate to recent work on dynamic misspecification in nonparametric nonstationary systems and the limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. Some implications for forecasting under misspecification are also examined.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 1 , February 2021 , pp. 138 - 168
Copyright
© Cambridge University Press 2020

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Footnotes

The authors thank the Co-Editor, Rob Taylor, and two referees for helpful comments on the original manuscript, which have led to many improvements. Qiying Wang acknowledges research support from the Australian Research Council and Peter C.B. Phillips acknowledges research support from the Kelly Fund, University of Auckland.

References

REFERENCES

Adusumilli, K. & Otsu, T. (2018) Nonparametric instrumental regression with errors in variables. Econometric Theory 34, 1256–1280.CrossRefGoogle Scholar
Baxter, M. & King, R.G. (1999) Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics 81, 575–593.CrossRefGoogle Scholar
Bollerslev, T., Osterrieder, D., Sizova, N. & Tauchen, G. (2013) Risk and return: Long-run relations, fractional cointegration and return predictability. Journal of Financial Economics 108, 409–424.CrossRefGoogle Scholar
Chen, X. & Reiss, M. (2011) On rate optimality for ill-posed inverse problems in econometrics. Econometric Theory 27, 497–521.CrossRefGoogle Scholar
Duffy, J.A. (2014) Three Essays on the Nonparametric Estimation of Nonlinear Cointegrating Regression. Doctoral Dissertation, Yale University.Google Scholar
Duffy, J.A. & Hendry, D.F. (2017) The impact of integrated measurement errors on modelling long-run macroeconomic time series. Econometric Reviews 36, 568–587.CrossRefGoogle Scholar
Gao, J. & Dong, C. (2018) Specification testing driven by orthogonal series for nonlinear cointegration with endogeneity. Econometric Theory 34, 754–789.Google Scholar
Ghysels, E., Santa-Clara, P. & Valkanov, R. (2004) The MIDAS touch: MIxed DAta Sampling Regression Models. Mimeo, Chapel Hill, NC.Google Scholar
Ghysels, E., Santa-Clara, P. & Valkanov, R. (2006) Predicting volatility: Getting the most out of return data sampled at different frequencies. Journal of Econometrics 131, 59–95.CrossRefGoogle Scholar
Giraitis, L., Houl, H.L. & Surgailis, D. (2012) Large Sample Inference for Long Memory Processes. Imperial College Press.CrossRefGoogle Scholar
Granger, C.W.J. & Newbold, P. (1974) Spurious regressions in econometrics. Journal of Econometrics 74, 111–120.CrossRefGoogle Scholar
Hall, P. & Horowitz, J.L. (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 2904–2929.CrossRefGoogle Scholar
Hodrick, R.J. & Prescott, E.C. (1997) Postwar US business cycles: An empirical investigation. Journal of Money, Credit, and Banking 29, 1–16.CrossRefGoogle Scholar
Horowitz, J.L. (2011) Applied nonparametric instrumental variables estimation. Econometrica 79, 347–394.Google Scholar
Jeganathan, P. (2008) Limit Theorems for Functional Sums that Converge to Fractional Brownian and Stable Motions. Cowles Foundation Discussion Paper No. 1649, Cowles Foundation for Research in Economics, Yale University.Google Scholar
Kasparis, I. & Phillips, P.C.B. (2012) Dynamic misspecification in nonparametric cointegrating regression. Journal of Econometrics 168, 270–284.CrossRefGoogle Scholar
Leser, C.E.V. (1961) A simple method of trend construction. Journal of the Royal Statistical Society, B 23, 91–107.Google Scholar
Phillips, P.C.B. (1986) Understanding spurious regressions in econometrics. Journal of Econometrics 33, 311–340.CrossRefGoogle Scholar
Phillips, P.C.B. (2009) Local limit theory and spurious nonparametric regression. Econometric Theory 25, 1466–1497.CrossRefGoogle Scholar
Phillips, P.C.B. (2010) Two New Zealand pioneer econometricians. New Zealand Economic Papers 44, 1–26.CrossRefGoogle Scholar
Phillips, P.C.B. & Jin, S. (2015) Business Cycles, Trend Elimination, and the HP Filter, Cowles Foundation Discussion Paper No. 2005, Yale University.CrossRefGoogle Scholar
Schennach, S.M. (2004) Nonparametric regression in the presence of measurement error. Econometric Theory 20, 1046–1093.CrossRefGoogle Scholar
Wang, Q. (2014) Martingale limit theorem revisited and nonlinear cointegrating regression. Econometric Theory 30, 509–535.CrossRefGoogle Scholar
Wang, Q. (2015) Limit Theorems for Nonlinear Cointegrating Regression. World Scientific.CrossRefGoogle Scholar
Wang, Q., Lin, Y.X. & Gulati, C.M. (2003) Asymptotics for general fractionally integrated processes with applications to unit root tests. Econometric Theory 19, 143–164.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structural nonparametric cointegrating regression. Econometrica 77, 1901–1948.Google Scholar
Wang, Q. & Phillips, P.C.B. (2011) Asymptotic theory for zero energy functionals with nonparametric regression applications. Econometric Theory 27, 235–259.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2016) Nonparametric cointegrating regression with endogeneity and long memory. Econometric Theory 32, 359–401.CrossRefGoogle Scholar
White, H. (1981) Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association 76, 419–433.CrossRefGoogle Scholar
Whittaker, E.T. (1923) On a new method of graduation. Proceedings of the Edinburgh Mathematical Association 78, 81–89.Google Scholar