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

Contemporaneous Threshold Autoregressive Models: Estimation, Testing and Forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta (1998), in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well-suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finitesample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen (1992) procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.Smooth Transition Threshold Autoregressive, Forecasting, Nonlinear Models

Contemporaneous threshold autoregressive models: estimation, testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta (1998), in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well-suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen (1992) procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed. ; Earlier title: Contemporaneous threshold autoregressive models: estimation, forecasting and rational expectations applicationsRational expectations (Economic theory) ; Forecasting

Multivariate contemporaneous threshold autoregressive models

In this paper we propose a contemporaneous threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. The model is a multivariate generalization of the contemporaneous threshold autoregressive model introduced by Dueker et al. (2007). A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. The stability and distributional properties of the proposed model are investigated. The C-MSTAR model is also used to examine the relationship between US stock prices and interest rates.Time-series analysis ; Capital assets pricing model

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

Multivariate Contemporaneous-Threshold Autoregressive Models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific innovation covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.Nonlinear autoregressive model; Smooth transition; Stability; Threshold.

Testing the Unbiased Forward Exchange Rate Hypothesis Using a Markov Switching Model and Instrumental Variables

This paper develops a model for the forward and spot exchange rate which allows for the presence of a Markov switching risk premium in the forward market and considers the issue of testing for the unbiased forward exchange rate (UFER) hypothesis. Using US/UK data, it is shown that the UFER hypothesis cannot be rejected provided that instrumental variables are used to account for within-regime correlation between explanatory variables and disturbances in the Markov switching model on which the test is based

Forecasting economic variables with nonlinear models

This article is concerned with forecasting from nonlinear conditional mean models. First, a number of often applied nonlinear conditional mean models are introduced and their main properties discussed. The next section is devoted to techniques of building nonlinear models. Ways of computing multi-step ahead forecasts from nonlinear models are surveyed. Tests of forecast accuracy in the case where the models generating the forecasts are nested are discussed. There is a numerical example, showing that even when a stationary nonlinear process generates the observations, future obervations may in some situations be better forecast by a linear model with a unit root. Finally, some empirical studies that compare forecasts from linear and nonlinear models are discussed.Forecast accuracy; forecast comparison; hidden Markov model; neural network; nonlinear modelling; recursive forecast; smooth transition regression; switching regression;