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on Econometric Time Series |
| By: | Román Mínguez; María Durbán; José María Montero; Dae-Jin Lee |
| Abstract: | In this work we propose the combination of P-splines with traditional spatial econometric models in such a way that it allows for their representation as a mixed model. The advantages of combining these models include: (i) dealing with complex non-linear and non-separable trends, (ii) estimating short-range spatial correlation together with the large-scale spatial trend, (iii) decomposing the systematic spatial variation into those two components and (iv) estimating the smoothing parameters included in the penalized splines together with the other parameters of the model. The performance of the proposed spatial non-parametric models is checked by both simulation and a empirical study. More specifically, we simulate 3,600 datasets generated by those models (with both linear and non-linear-non-separable global spatial trends). As for the empirical case, we use the well-known Lucas county data on housing prices. Our results indicate that the proposed models have a better performance than the traditional spatial strategies, specially in the presence of nonlinear trend |
| Keywords: | Global spatial trend, Mixed models, P-splines, PS-SAR, PS-SEM |
| JEL: | C14 C15 C21 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws132925&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Degui Li (University of York); Jiti Gao (The University of Adelaide and Monash University) |
| Abstract: | This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to re-orient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions (or combinations) of the (functional) parameter space. Both rates are faster than the usual (?nh) rate for nonlinear models with smoothly changing coefficients and local stationarity. Hence two types of super-consistency apply in nonparametric kernel estimation of time-varying coefficient cointegration models. The higher rate of convergence (n?h) lies in the direction of the nonstationary regressor vector at the local coordinate point. The lower rate (nh) lies in the degenerate directions but is still super-consistent for nonparametric estimators. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case. Simulations are conducted to explore the finite sample properties of the methods and a practical application is given to examine time varying empirical relationships involving consumption, disposable income, investment and real interest rates. |
| Keywords: | Cointegration, Endogeneity, Kernel degeneracy, Nonparametric regression, Super-consistency, Time varying coefficients |
| JEL: | C13 C14 C32 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1910&r=ets |
| By: | Jiti Gao (The University of Adelaide and Monash University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960-2009. |
| Keywords: | Aggregate consumption, Asymptotic theory, Cointegration, Density, Local time, Nonlinear functional, Nonparametric estimation, Semiparametric, Time series, Varying coefficient model |
| JEL: | C13 C14 C23 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1911&r=ets |