Self-Normalization Inference for Linear Trends in Cointegrating Regressions

This article highlights the importance of statistical tests on the trend coefficient in cointegrating regressions when the stochastic regressors contain a deterministic linear trend. In addition to deriving asymptotic theory for t statistics constructed using integrated and modified ordinary least squares (IMOLS, Vogelsang and Wagner (2014)) estimation results, this paper proposes a novel self-normalization inference using the recursive IMOLS estimator. The new test does not require studentization with the heteroskedasticity and autocorrelation consistent (HAC) estimator, and the limit null distribution of the proposed statistic is shown to be pivotal. The simulation results reveal that the new test controls the size better compared to existing methodologies considered in this paper, with moderate loss of power