Semiparametric Cointegrating Rank Selection

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a nonparametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coefficient C_n -> infinity and C_n/n -> 0 as n -> infinity. The limit distribution of the AIC criterion, which is inconsistent, is also obtained. The analysis provides a general limit theory for semiparametric reduced rank regression under weakly dependent errors. The method does not require the specification of a full model, is convenient for practical implementation in empirical work, and is sympathetic with semiparametric estimation approaches to cointegration analysis. Some simulations results on finite sample performance of the criterion are reported.Cointegrating rank, Consistency, Information criteria, Model selection, Nonparametric, Short memory, Unit roots

Cointegrating Rank Selection in Models with Time-Varying Variance

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient C_{n}-> infinity and C_{n}/n -> 0 as n -> infinity. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2008) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application to exchange rate data is provided.Cointegrating rank, Consistency, Heterogeneity, Information criteria, Model selection, Nonparametric, Time varying variances, Unit roots

Bayesian Analysis for Penalized Spline Regression Using WinBUGS

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.

Bayesian Analysis for Penalized Spline Regression Using Win BUGS

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. MCMC mixing is substantially improved from the previous versions by using low{rank thin{plate splines instead of truncated polynomial basis. Simulation time per iteration is reduced 5 to 10 times using a computational trick

Cointegrating Rank Selection in Models with Time-Varying Variance

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient C n → infinity and C n /n → 0 as n → ∞. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2008) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application to exchange rate data is provided

Propriety of Posteriors in Structured Additive Regression Models: Theory and Empirical Evidence

Structured additive regression comprises many semiparametric regression models such as generalized additive (mixed) models, geoadditive models, and hazard regression models within a unified framework. In a Bayesian formulation, nonparametric functions, spatial effects and further model components are specified in terms of multivariate Gaussian priors for high-dimensional vectors of regression coefficients. For several model terms, such as penalised splines or Markov random fields, these Gaussian prior distributions involve rank-deficient precision matrices, yielding partially improper priors. Moreover, hyperpriors for the variances (corresponding to inverse smoothing parameters) may also be specified as improper, e.g. corresponding to Jeffery's prior or a flat prior for the standard deviation. Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations. We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies