Estimation and Testing for Fractional Cointegration

Estimation of bivariate fractionally cointegrated models usually operates in two steps: the first step is to estimate the long run coefficient (\beta) whereas the second step estimates the long memory parameter (d) of the cointegrating residuals. We suggest an adaptation of the maximum likelihood estimator of Hualde and Robinson (2007) to estimate jointly \beta and d, and possibly other nuisance parameters, for a wide range of integration orders when regressors are I(1). The finite sample properties of this estimator are compared with various popular estimation methods of parameters \beta (LSE, ADL, DOLS, FMLS, GLS, MLE, NBLS, FMNBLS), and d (LPE,LWE,LPM,FML) through a Monte Carlo experiment. We also investigate the crucial question of testing for fractional cointegration (that is, d < 1). The simulation results suggest that the one-step methodology generally outperforms others methods, both in terms of estimation precision and reliability of statistical inferences. Finally we apply this methodology by studying the long-run relationship between stock prices and dividends in the US case.