Nonparametric estimation of time varying parameters under shape restrictions
In this paper we propose a new method to estimate nonparametrically a time varying parameter model when some qualitative information from outside data (e.g. seasonality) is available. In this framework we make two main contributions. First, the resulting estimator is shown to belong to the class of generalized ridge estimators and under some conditions its rate of convergence is optimal within its smoothness class. Furthermore, if the outside data information is fullfilled by the underlying model, the estimator shows efficiency gains in small sample sizes. Second, for the implementation process, since the estimation procedure envolves the computation of the inverse of a high order matrix we provide an algorithm that avoids this computation and, also, a data-driven method is derived to select the control parameters. The practical performance of the method is demonstrated in a simulation study and in an application to the demand of soft drinks in Canada.
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- Ferreira, Eva & Nunez-Anton, Vicente & Rodriguez-Poo, Juan, 2000. "Semiparametric approaches to signal extraction problems in economic time series," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 315-333, May.
- repec:cup:cbooks:9780521405737 is not listed on IDEAS
- Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2003. "An algorithm to estimate time-varying parameter SURE models under different types of restriction," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 363-383, March.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
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- Cooley, Thomas F & Prescott, Edward C, 1973. "An Adaptive Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 364-71, June.
- Mark Gersovitz & James G. MacKinnon, 1977. "Seasonality in Regression: An Application of Smoothness Priors," Working Papers 257, Queen's University, Department of Economics.
- Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
- Lutkepohl, Helmut & Herwartz, Helmut, 1996. "Specification of varying coefficient time series models via generalized flexible least squares," Journal of Econometrics, Elsevier, vol. 70(1), pages 261-290, January.
- P o, Juan M. Rodriguez, 1999. "Constrained Smoothing Splines," Econometric Theory, Cambridge University Press, vol. 15(01), pages 114-138, February.
- Cooley, Thomas F & Prescott, Edward C, 1976. "Estimation in the Presence of Stochastic Parameter Variation," Econometrica, Econometric Society, vol. 44(1), pages 167-84, January.
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