Simple, Parametric and Non-Parametric, Model Misspecification Robust Tests for Unit Root

Description

A considerable amount of research has been devoted to unit root testing in economic and financial time series. It is generally believed that economic and financial time series such as logarithmic real GDP and exchange rates are non-stationary, with time-varying mean and variance. In economics and finance, the general consensus seems to be that a combination of stochastic and deterministic trends is likely to describe the data well. However, distinguishing between these different types of trends (deterministic, stochastic) is difficult in practice. Recent research has primarily focused on stochastic trends caused by unit roots, and how to distinguish these from deterministic trends. One reason for this is that stochastic trends may have important implications for the formulation of economic models. Another reason is that stochastic trends can result in spurious inference, and hence need to be properly accounted for in order to make valid inference when analyzing multivariate time series.From a practitioner's perspective, standard tests for unit root, such as modifications of the augmented Dickey-Fuller (ADF) test, may be hard to fully comprehend with their unknown finite-sample distributions and complicated limiting distributions. In addition, standard unit root tests are known to be sensitive to the initial condition of the data generating process, and to model misspecifications such as serially correlated (autocorrelated) disturbances, with low power and severe size distortions in finite-samples.This project aims to develop simple (easy to implement, easy to use), parametric and non-parametric (distribution-free), initial condition and autocorrelation robust tests for unit root, whose exact finite-sample distributions can be expressed using standard results from order statistics and non-parametric statistics. In addition, some of the proposed tests are, by design, robust to heavy-tailed samples (or outliers) and to certain forms of heteroskedasticity.