Least Squares Estimation and Tests of Breaks in Mean and Variance under Misspecification

Structural Break, Variance Shifts, Bootstrapping

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 we also obtain the limiting behaviour of a related Wald statistic designed to solely test 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.Structural Breaks, Unit Roots, Nonlinear Dynamics

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.Publicad

On the exact moments of non-standard asymptotic distributions in non stationary autoregressions with dependent errors

In this paper we derive the exact moments of the asymptotic distributions of the OLS estimate and t-statistic in an unstable AR(1) with dependent errors. We can therefore establish theoretically and without simulations, the distortions induced by the presence of non iid errors on inferences as judged by their impact on the moments of the limiting distributions. In addition we study the relationship between the number of lagged dependent variables required for matching the moments of the distribution in the "approximately iid errors" model with those occuring in the purely iid case. Our framework allows us to distinguish explicitly between different types of error processes and study their implications for the lag length selection. A very accurate normal approximation also allows us to obtain approximate magnitudes for the size distortions when the iid based distributions are used for inferences

Regime specific predictability in predictive regressions

Predictive regressions are linear specications linking a noisy variable such as stock returns to past values of a more persistent regressor such as valuation ratios, interest rates etc with the aim of assessing the presence or absence of predictability. Key complications that arise when conducting such inferences are the potential presence of endogeneity, the poor adequacy of the asymptotic approximations amongst numerous others. In this paper we develop an inference theory for uncovering the presence of predictability in such models when the strength or direction of predictability, if present, may alternate across dierent economically meaningful episodes. This allows us to uncover economically interesting scenarios whereby the predictive power of some variable may kick in solely during particular regimes or alternate in strength and direction (e.g. recessions versus expansions, periods of high versus low stock market valuation, periods of high versus low term spreads etc). The limiting distributions of our test statistics are free of nuisance parameters and some are readily tabulated in the literature. Finally our empirical application reconsiders the literature on Dividend Yield based stock return predictability and contrary to the existing literature documents a strong presence of predictability that is countercyclical, occurring solely during bad economic times

Threshold effects in cointegrating relationships

In this paper we introduce threshold type nonlinearities within a single equation cointegrating regression model and propose a testing procedure for testing the null hypothesis of linear cointegration versus cointegration with threshold effects. Our framework allows the modelling of long run equilibrium relationships that may switch according to the magnitude of a threshold variable assumed to be stationary and ergodic and thus constitutes an attempt to deal econometrically with the potential presence of multiple equilibria. The framework is flexible enough to accomodate regressor endogeneity and serial correlation.

Threshold effects In multivariate error correction models

In this paper we propose a testing procedure for assessing the presence of threshold effects in nonstationary Vector autoregressive models with or without cointegration. Our approach involves first testing whether the long run impact matrix characterising the VECM type representation of the VAR switches according to the magnitude of some threshold variable and is valid regardless of whether the system is purely I(1), I(1) with cointegration or stationary. Once the potential presence of threshold effects is established we subsequently evaluate the cointegrating properties of the system in each regime through a model selection based approach whose asymptotic and finite sample properties are also established. This subsequently allows us to introduce a novel non-linear permanent and transitory decomposition of the vector process of interest.

A Novel Approach to Predictive Accuracy Testing in Nested Environments

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample MSE loss differentials between the two competing models, leads to nuisance parameter free Gaussian asymptotics and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g. stationary and local to unit root). A local power analysis also establishes its ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes

Comovements in large systems

In this paper we study various methods for detecting the co integrating rank as the number of variables gets large. We show that the use of standard tools will always lead to misleading inferences in such settings due to excessive size distortions. Particularly the LR test tends to produce too much cointegration. We introduce a new test statistic that displays excellent size properties in both small and large systems. In addition we propose a model selection procedure for selecting the co integrating rank. A new criterion outperforms the standard informationtheoretic criteria (AIC, BIC)

Predictive Regressions

Predictive regressions are a widely used econometric environment for assessing the predictability of economic and financial variables using past values of one or more predictors. The nature of the applications considered by practitioners often involve the use of predictors that have highly persistent smoothly varying dynamics as opposed to the much noisier nature of the variable being predicted. This imbalance tends to affect the accuracy of the estimates of the model parameters and the validity of inferences about them when one uses standard methods that do not explicitly recognise this and related complications. A growing literature that aimed at introducing novel techniques specifically designed to produce accurate inferences in such environments ensued. The frequent use of these predictive regressions in applied work has also led practitioners to question the validity of viewing predictability within a linear setting that ignores the possibility that predictability may occasionally be switched off. This in turn has generated a new stream of research aiming at introducing regime specific behaviour within predictive regressions in order to explicitly capture phenomena such as episodic predictability