Identification, Estimation and Specification in a Class of Semiparametic Time Series Models

In this paper, we consider some identification, estimation and specification problems in a class of semiparametric time series models. Existing studies for the stationary time series case have been reviewed and discussed. We also consider the case where new studies for the integrated nonstationary case are established. In the meantime, we propose some new estimation methods and establish some new results for a new class of semiparametric autoregressive models. In addition, we discuss certain directions for further research

Nonparametric Regression Approach to Bayesian Estimation

Estimation of unknown parameters and functions involved in complex nonlinear econometric models is a very important issue. Existing estimation methods include generalised method of moments (GMM) by Hansen (1982) and others, efficient method of moments (EMM) by Gallant and Tauchen (1997), Markov chain Monte Carlo (MCMC) method by Chernozhukov and Hong (2003), and nonparametric simulated maximum likelihood estimation (NSMLE) method by Creel and Kristensen (2011), and Kristensen and Shin (2012). Except the NSMLE method, other existing methods do not provide closed-form solutions. This paper proposes non- and semi-parametric based closed-form approximations to the estimation and computation of posterior means involved in complex nonlinear econometric models. We first consider the case where the samples can be independently drawn from both the likelihood function and the prior density. The samples and observations are then used to nonparametrically estimate posterior mean functions. The estimation method is also applied to estimate the posterior mean of the parameter-of-interest on a summary statistic. Both the asymptotic theory and the finite sample study show that the nonparametric estimate of this posterior mean is superior to existing estimates, including the conventional sample mean

Solving Replication Problems in Complete Market by Orthogonal Series Expansion

We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The departure of our method from the literature is, using an orthogonal expansion of a process related to the proposed trading strategy, we can construct a complete orthonormal basis for the space of cumulative gains in the complete market so that every self-financing strategy can be expressed as a combination of the basis. Hence, a replication strategy is obtained for a European option. Converse to the traditional Black-Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black-Scholes pricing formula. We then provide an implementation procedure to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black-Scholes theory

A simple nonlinear predictive model for stock returns

In this paper, we propose a simple approach to testing and modelling nonlinea

Semiparametric Methods in Nonlinear Time Series Analysis: A Selective Review

Time series analysis is a tremendous research area in statistics and econometrics. As remarked in a review by Howell Tong in 2001, for about 100 years up to 2001 Biometrika (alone) published over 400 papers on the subject. [Tong (2001)] Furthermore, in the review, Howell Tong is able break down up to fifteen key areas of research interest in time series analysis. Nonetheless, unlike that of Howell Tong, the aim of the review in this paper is not to cover a wide range of topics on the subject, but is to concentrate on a small, but extremely essential, point he made on the semiparametric methods in nonlinear time series analysis and to explore into various aspect of this research area in much more detail. It is also an objective of this review to provide some discussion on a future research where appropriate

A New Test in Parametric Linear Models against Nonparametric Autoregressive Errors

This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is proposed and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially avoid misspecification through the need to parametrically specify the form of the errors. In other words, we propose estimating the form of the errors and testing for stationarity or nonstationarity simultaneously. We establish asymptotic distributions of the proposed test. Both the setting and the results differ from earlier work on testing for unit roots in parametric time series regression. We provide both simulated and real-data examples to show that the proposed nonparametric unit-root test works in practice

An Improved Nonparametric Unit-Root Test

This paper proposes a simple and improved nonparametric unit-root test. An asymptotic distribution of the proposed test is established. Finite sample comparisons with an existing nonparametric test are discussed. Some issues about possible extensions are outlined

A Computational Implementation of GMM

In this paper we study a statistical method of implementing quasi-Bayes estimators for nonlinear and nonseparable GMM models, that is motivated by the ideas proposed in Chernozhukov and Hong (2003) and Creel and Kristensen (2011) and that combines simulation with nonparametric regression in the computation of GMM models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of the use of posterior quantiles. We also show that in this setting, local linear kernel regression methods have theoretical advantages over local kernel methods that are also reflected in finite sample simulation results. Our results also apply to both exactly and over identified models. These estimators do not need to rely on numerical optimization or Markov Chain Monte Carlo simulations. They provide an effective complement to the classical M-estimators and to MCMC methods, and can be applied to both likelihood based models and method of moment based models

Hermite Series Estimation in Nonlinear Cointegrating Models

This paper discusses nonparametric series estimation of integrable cointegration models using Hermite functions. We establish the uniform consistency and asymptotic normality of the series estimator. The Monte Carlo simulation results show that the performance of the estimator is numerically satisfactory. We then apply the estimator to estimate the stock return predictive function. The out-of-sample evaluation results suggest that dividend yield has nonlinear predictive power for stock returns while book-to-market ratio and earning-price ratio have little predictive power

Nonparametric kernel estimation of the impact of tax policy on the demand for private health insurance in Australia

This paper is motivated by our attempt to answer an empirical question: how is private health insurance take-up i