Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation

Fractionally integrated vector autoregressive models allow to capture persistence in time series data in a very flexible way. Additional flexibility for the short memory properties of the model can be attained by using the fractional lag perator of Johansen (2008) in the vector autoregressive polynomial. However, it also makes maximum likelihood estimation more diffcult. In this paper we first identify parameter settings for univariate and bivariate models that suffer from poor identification in finite samples and may therefore lead to estimation problems. Second, we propose to investigate the extent of poor identification by using expected log-likelihoods and variations thereof which are faster to simulate than multivariate finite sample distributions of parameter estimates. Third, we provide a line of reasoning that explains the finding from several univariate and bivariate simulation examples that the two-step estimator suggested by Tschernig, Weber, and Weigand (2010) can be more robust with respect to estimating the deterministic components than the maximum likelihood estimator.