Threshold Models for Trended Time Series

This paper presents the theoretical development of new threshold autoregressive models based on trended time series. The theoretical arguments underlying the models are outlined and a nonlinear economic model is used to derive the specification of the empirical econometric models. Estimation and testing issues are considered and analysed. Additionally, the models are applied to the empirical investigation of US GDP. The results are encouraging and warrant further research

Model Selection in Threshold Models

This paper considers information criteria as model evaluation tools for nonlinear threshold models. Results concerning the consistency of information criteria in selecting the lag order of linear autoregressive models are extended to nonlinear autoregressive threshold models. Extensive Monte Carlo evidence of the small sample performance of a number of criteria is presented

Nonlinear Autoregressive Models and Long Memory

This note shows that regime switching nonlinear autoregressive models widely used in the time series literature can exhibit arbitrary degrees of long memory via appropriate definition of the model regimes.Long memory, Nonlinearity

A New Nonparametric Test of Cointegration Rank

This paper suggests a new nonparametric testing procedure for determining the rank of nonstationary multivariate cointegrated systems. The asymptotic properties of the procedure are determined and a Monte Carlo study is carried out.Cointegration rank, Nonparametric analysis

A Testing Procedure for Determining the Number of Factors in Approximate Factor Models with Large Datasets

The paradigm of a factor model is very appealing and has been used extensively in economic analyses. Underlying the factor model is the idea that a large number of economic variables can be adequately modelled by a small number of indicator variables. Throughout this extensive research activity on large dimensional factor models a major preoccupation has been the development of tools for determining the number of factors needed for modelling. This paper provides builds on the work of Kapetanios (2004) to provide an alternative method to information criteria as a tool for estimating the number of factors in large dimensional factor models. The new method is robust to considerable cross-sectional and temporal dependence. The theoretical properties of the method are explored and an extensive Monte Carlo study is undertaken. Results are favourable for the new method and suggest that it is a reasonable alternative to existing methods.Factor models, Large sample covariance matrix, Maximum eigenvalue

A Note on Covariance Stationarity Conditions for Dynamic Random Coefficient Models

In this note we look at sufficient conditions for stationarity of a simple random coefficient model and find that this model is guaranteed to be stationary under strict conditions. J.E.L. classification codes.Stationarity, Random coefficient models

A Note on an Iterative Least Squares Estimation Method for ARMA and VARMA Models

In this note we suggest a new iterative least squares method for estimating scalar and vector ARMA models. A Monte Carlo study shows that the method has better small sample properties than existing least squares methods and compares favourably with maximum likelihood estimation as well.ARMA models

Testing for Exogeneity in Nonlinear Threshold Models

Most work in the area of nonlinear econometric modelling is based on a single equation and assumes exogeneity of the explanatory variables. Recently, work by Caner and Hansen (2003) and Psaradakis, Sola, and Spagnolo (2004) has considered the possibility of estimating nonlinear models by methods that take into account endogeneity but provided no tests for exogeneity. This paper examines the problem of testing for exogeneity in nonlinear threshold models. We suggest new Hausman-type tests and discuss the use of the bootstrap to improve the properties of asymptotic tests. The theoretical properties of the tests are discussed and an extensive Monte Carlo study is undertaken.Threshold models, Endogeneity, Bootstrap

A Bootstrap Procedure for Panel Datasets with Many Cross-Sectional Units

This paper considers the issue of bootstrap resampling in panel datasets. The availability of datasets with large temporal and cross sectional dimensions suggests the possibility of new resampling schemes. We suggest one possibility which has not been widely explored in the literature. It amounts to constructing bootstrap samples by resampling whole cross sectional units with replacement. In cases where the data do not exhibit cross sectional dependence but exhibit temporal dependence, such a resampling scheme is of great interest as it allows the application of i.i.d. bootstrap resampling rather than block bootstrap resampling. It is well known that the former enables superior approximation to distributions of statistics compared to the latter. We prove that the bootstrap based on cross sectional resampling provides asymptotic refinements. A Monte Carlo study illustrates the superior properties of the new resampling scheme compared to the block bootstrap.Bootstrap, Panel data

Testing for Structural Breaks in Nonlinear Dynamic Models Using Artificial Neural Network Approximations

In this paper we suggest a number of statistical tests based on neural network models, that are designed to be powerful against structural breaks in otherwise stationary time series processes while allowing for a variety of nonlinear specifications for the dynamic model underlying them. It is clear that in the presence of nonlinearity standard tests of structural breaks for linear models may not have the expected performance under the null hypothesis of no breaks because the model is misspecified. We therefore proceed by approximating the conditional expectation of the dependent variable through a neural network. Then, the residual from this approximation is tested using standard residual based structural break tests. We investigate the asymptoptic behaviour of residual based structural break tests in nonlinear regression models. Monte Carlo evidence suggests that the new tests are powerful against a variety of structural breaks while allowing for stationary nonlinearities.Nonlinearity, Structural breaks, Neural networks