Functional cointegration: definition and nonparametric estimation

Pitarakis, Jean-Yves (2012): Functional cointegration: definition and nonparametric estimation.

Abstract

We formally define a concept of functional cointegration linking the dynamics of two time series via a functional coefficient. This is achieved through the use of a concept of summability as an alternative to I(1)'ness which is no longer suitable under nonlinear dynamics. We subsequently introduce a nonparametric approach for estimating the unknown functional coefficients. Our method is based on a piecewise local least squares principle and is computationally simple to implement. We establish its consistency properties and evaluate its performance in finite samples.

• Item Type: MPRA Paper
• Language: English
• Keywords: Functional Coefficients, Unit Roots, Cointegration, Piecewise Local Linear Estimation
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Banerjee, A. N., 1994. A method of estimating the average derivative. CORE Discussion Paper: 9403, Universite Catholique de Louvain.

Banerjee, A. N., 2007. A method of estimating the average derivative. Journal of Econometrics, 136, 65-88.

Berenguer-Rico, V., 2010. Summability of Stochastic Processes: A Generalization of Integration and Co-integration valid for Non-linear Processes, Universidad Carlos III de Madrid Working Paper.

Berenguer-Rico, V. and Gonzalo, J., 2011. Co-Summability: From Linear to Non-Linear Co-Integration, Universidad Carlos III de Madrid Working Paper.

Breitung, J., 2001. Rank tests for nonlinear cointegration, Journal of Business and Economic Statistics, 19, 331-340.

Cai, Z., Li, Q. and Park, J. Y., 2009. Functional Coecient Models for Nonstationary Time Series Data, Journal of Econometrics, 148, 101-113.

Cleveland, W.S., Grosse, E., and Shyu, W.M., 1991. Local Regression Models. In Statistical Models in S (J.M. Chambers and T.J. Hastie, ed.). Wadsworth & Brooks, Pacic Grove. CA. pp. 309-376.

Chen, R. and Tsay, R.S., 1993. Functional Coefficient Autoregressive Models, Journal of the American Statistical Association, 88, 298-308.

Fan, J. and Zhang, W., 1999. Statistical Estimation in Varying Coefficient Models, The Annals of Statistics, 27, 1491-1518.

Fan, J. and Yao, Q., 2003. Nonlinear Time Series. Springer-Verlag, New-York.

Gonzalo, J. and Pitarakis, J., 2006. Threshold Effects in Cointegrating Relationships, Oxford Bulletin of Economics and Statistics, 68, 813-833.

Granger, C.W.J. and Hallman, J., 1991. Nonlinear Transformations of Integrated Time Series, Journal of Time Series Analysis, 12, 207-234.

Hansen, B., 1991. Strong Laws for Dependent Heterogeneous Processes, Econometric Theory, 7, 213-221.

Hansen, B., 2008. Uniform Convergence Rates for Kernel Estimation with Dependent Data, Econometric Theory, 24, 726-748.

Hastie, T. J. and Tibshirani, R. J., 1993. Varying Coefficient Models, Journal of the Royal Statistical Society, Series B, 55, 757-796.

Juhl, T., 2005. Functional-Coefficient Models under Unit Root Behaviour, Econometrics Journal, 8, 197-213.

Karlsen, H. A., Myklebust, T. and Tjostheim, D., 2007. Nonparametric estimation in a nonlinear cointegration type model, Annals of Statistics, 35, 252-299.

Kasparis, I. and Phillips, P. C. B., 2009. Dynamic Misspecification in Nonparametric Cointegrating Regression. Yale University Working Paper

Phillips, P.C.B., 1987. Time series regression with unit roots, Econometrica, 55, 277-302.

Saikkonen, P. and Choi, I., 2004. Testing linearity in cointegrating smooth transition regressions, Econometrics Journal, 7, 341-365.

Senturk, D. and Mueller, H. G., 2005. Covariate-adjusted regression. Biometrika, 92, 75-89.

Senturk, D. and Mueller, H. G., 2006. Inference for covariate adjusted regression via varying coefficient models. Annals of Statistics, 34, 654-679.

Wang, Q. and Phillips, P.C.B., 2009. Structural Nonparametric Cointegrating Regression, Econometrica, 77, 1901-1948.

Xiao, Z., 2009. Functional-Coefficient Cointegration Models, Journal of Econometrics, 152, 81-92.