Model selection uncertainty and detection of threshold effects

Inferences about the presence or absence of threshold type nonlinearities in TAR models are conducted within models whose lag length has been estimated in a preliminary stage. Typically the null hypothesis of linearity is then tested against a threshold alternative on which the estimated lag length is imposed on each regime. In this paper we evaluate the properties of test statistics for detecting the presence of threshold effects in autoregressive models when this model uncertainty is taken into account. We show that this approach may lead to important distortions when the underlying model has truly threshold effects by establishing the limiting properties of the estimated lag length in the mispecified linear autoregressive fit and assessing the impact of this model uncertainty on the power of the tests. We subsequently propose a full model selection based approach designed to jointly detect the presence of threshold effects and optimally specify its dynamics and compare its performance with the traditional test based approach.

Model selection uncertainty and detection of threshold effects

Inferences about the presence or absence of threshold type nonlinearities in TAR models are conducted within models whose lag length has been estimated in a preliminary stage. Typically the null hypothesis of linearity is then tested against a threshold alternative on which the estimated lag length is imposed on each regime. In this paper we evaluate the properties of test statistics for detecting the presence of threshold effects in autoregressive models when this model uncertainty is taken into account. We show that this approach may lead to important distortions when the underlying model has truly threshold effects by establishing the limiting properties of the estimated lag length in the mispecified linear autoregressive fit and assessing the impact of this model uncertainty on the power of the tests. We subsequently propose a full model selection based approach designed to jointly detect the presence of threshold effects and optimally specify its dynamics and compare its performance with the traditional test based approach

On the bias of the OLS estimator in a nonstationary dynamic panel data model

This paper derives the joint moment generating function of two quadratic forms appearing in the OLS estimator from a dynamic panel data model. The result is then used to investigate the effect of the cross-section dimension on the asymptotic bias.<br/

Moment generating functions and further exact results for seasonal autoregressions

This paper derives the joint moment generating function of quadratic forms occurring in seasonal autoregressive models under stationary, unit root, and explosive specifications. The results are then used to investigate the impact of the seasonal periodicity parameter on various distributional results for both the normalized ordinary least squares coefficient and t-ratio and its effects on the asymptotic bias of parameter estimates

Joint detection of structural change and nonstationarity in autoregressions

In this paper we develop a test of the joint null hypothesis of parameter stability and a unit root within an ADF style autoregressive specification whose entire parameter structure is potentially subject to a structural break at an unknown time period. The maintained underlying null model is a linear autoregression with a unit root, stationary regressors and a constant term. As a byproduct of our distribution theory we also obtain the limiting behaviour of a related Wald statistic designed to test solely the null of parameter stability in an environment with a unit root. These distributions are free of nuisance parameters and easily tabulated. The finite sample properties of our tests are subsequently assessed through a series of simulations

Specification via model selection in vector error correction models

This paper proposes a model selection approach for the specification of the cointegrating rank in the VECM representation of VAR models. Asymptotic properties of estimates are derived and their features compared with the traditional likelihood ratio based approach