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

Tests for Deterministic Parametric Structural Change in Regression Models

The problem of structural change justifiably attracts considerable attention in econometrics. A number of different paradigms have been adopted ranging from structural breaks which are sudden and rare to time-varying coefficient models which exhibit structural change more frequently and continuously. This paper is concerned with parametric econometric models whose coefficients change deterministically and smoothly over time. In particular we provide and discuss tests for the null hypothesis of no structural change versus the alternative hypothesis of smooth deterministic structural change. We provide asymptotic tests for this null hypothesis. However, the finite sample performance of these tests is not good as they overreject significantly. To address this problem we propose and justify bootstrap based tests. These tests perform well in an extensive Monte Carlo study.Structural change, Non-stationarity, Deterministic time-variation

A Note on Joint Estimation of Common Cycles and Common Trends in Nonstationary Multivariate Systems

We provide a new method for jointly consistently estimating common trends and cycles in unit root nonstationary multivariate systems. We concentrate on the MA representation of the differenced data and we jointly impose the reduced rank restriction for the common cycles and the common trends on the MA representation coefficients.Common cycles and trends, Tests of rank, Cointegration

Estimating Deterministically Time-Varying Variances in Regression Models

The problem of structural change justifiably attracts considerable attention in econometrics. A number of different paradigms have been adopted ranging from structural breaks which are sudden and rare to time varying coefficient models which exhibit structural change more frequently and continuously. This paper is concerned with parametric econometric models whose coefficients change deterministically and smoothly over time. In particular we provide a new estimator for unconditional time varying variances in regression models. A small Monte Carlo study indicates that the method works reasonably well for moderately large sample sizes.Structural change, Non-stationarity, Deterministic time-variation

Testing for Strict Stationarity

The investigation of the presence of structural change in economic and financial series is a major preoccupation in econometrics. A number of tests have been developed and used to explore the stationarity properties of various processes. Most of the focus has rested on the first two moments of a process thereby implying that these tests are tests of covariance stationarity. We propose a new test for strict stationarity, that considers the whole distribution of the process rather than just its first two moments, and examine its asymptotic properties. We provide two alternative bootstrap approximations for the exact distribution of the test statistic. A Monte Carlo study illustrates the properties of the new test and an empirical application to the constituents of the S&P 500 illustrates its usefulness.Covariance stationarity, Strict stationarity, Bootstrap, S&P500

Cluster Analysis of Panel Datasets using Non-Standard Optimisation of Information Criteria

Panel datasets have been increasingly used in economics to analyse complex economic phenomena. One of the attractions of panel datasets is the ability to use an extended dataset to obtain information about parameters of interest which are assumed to have common values across panel units. However, the assumption of poolability has not been studied extensively beyond tests that determine whether a given dataset is poolable. We propose an information criterion method that enables the distinction of a set of series into a set of poolable series for which the hypothesis of a common parameter subvector cannot be reject and a set of series for which the poolability hypothesis fails. The method can be extended to analyse datasets with multiple clusters of series with similar characteristics. We discuss the theoretical properties of the method and investigate its small sample performance in a Monte Carlo study.Panel datasets, Poolability, Information criteria, Genetic Algorithm, Simulated Annealing

Modelling Core Inflation for the UK Using a New Dynamic Factor Estimation Method and a Large Disaggregated Price Index Dataset

Recent work in the macroeconometric literature considers the problem of summarising efficiently a large set of variables and using this summary for a variety of purposes including forecasting. This paper applies a new factor extraction method to the extraction of core inflation and forecasting of UK inflation in the recent past.Factor models, Subspace methods, State space models

Testing for Neglected Nonlinearity in Long Memory Models

Interest in the interface of nonstationarity and nonlinearity has been increasing in the econometric literature. The motivation for this development maybe be traced to the perceived possibility that processes following nonlinear models maybe mistakenly taken to be unit root or long-memory nonstationary. This paper considers the possibility that processes may exhibit both long memory and nonlinearity. We test against the possibility that the process u t in the model (1-L) dy t�=�u t is nonlinear. We do not assume a particular parametric form for the nonlinear process but construct a pure significance test. Clearly, such a test could be straightforwardly constructed if d were known. Unfortunately, if a linear model is assumed while estimating d the power of the test will be reduced. We propose new more powerful tests for this problem. We present Monte Carlo evidence on the performance of the new tests and apply them to Yen real exchange rates.Long memory, Nonlinearity, Neural networks, Real exchange rates.

Using Extraneous Information and GMM to Estimate Threshold Parameters in TAR Models

A prominent class of nonlinear time series models are threshold autoregressive models. Recently work by Kapetanios (2000) has shown in a Monte Carlo setting that the superconsistency property of the threshold parameter estimates does not translate to superior performance in small samples. Another issue concerning inference for the threshold parameters relates to estimation of their standard errors. As the asymptotic distribution of the threshold parameters is neither normal nor nuisance parameter free, an outstanding issue is how to obtain standard errors and confidence intervals for them. This paper aims to address these issues. In particular, we suggest that using extraneous information on the location of the threshold parameters may lead to better estimates. The extraneous information comes in the form of moment conditions that relate residuals of standard threshold models to shocks driving other variables. Additionally the paper considers the problem of estimating standard errors and confidence intervals for threshold parameter estimates. We suggest use of the bootstrap for this problem.Threshold Models, GMM, Bootstrap