Robust testing for fractional integration using the bootstrap

TLDR: In this paper, the authors discuss how computer intensive methods may be used to adjust the test distribution, such that the actual significance level will coincide with the desired nominal level, and as a concequence, too many true null hypotheses will falsely be rejected.

Abstract: This dissertation contains five essays in the field of time series econometrics. The main issue discussed is the lack of coherence between small sample and asymptotic inference. Frequently, in modern econometrics distributional results are strictly only valid for a hypothetical infinite sample. Studies show that the attained actual level of a test may be considerable different from the nominal significance level, and as a concequence, too many true null hypotheses will falsely be rejected. This leads, in the extension, to applied users that too often reject evidence in the data for theoretical predictions. In large, the thesis discusses how computer intensive methods may be used to adjust the test distribution, such that the actual significance level will coincide with the desired nominal level. The first two essays focus on how to improve testing for persistence in data, through a bootstrap procedure within a univariate framework. The remaining three essays are studies of multivariate time series models. The third essay considers the identification problem of the basic stationary vector autoregressive model, which is also the basic-line econometric specification for maximum likelihood cointegration analysis. In the fourth essay the multivariate framework is expanded to allow for components of different integrating order and in this setting the paper discusses how fractional cointegration affects the inference in maximum likelihood cointegration analysis. The fifth essay consider once again the bootstrap testing approach, now in a multivariate application, to correct inference on long-run relations in maximum likelihood cointegration analysis.