Small-b and Fixed-b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration

In a standard cointegrating framework, Phillips (1991) introduced the weighted covariance (WC) estimator of cointegrating parameters. Later, Marinucci (2000) applied this estimator to fractional circumstances and, like Phillips (1991), analysed the so-called small-b asymptotic approximation to its sampling distribution. Recently, an alternative limiting theory (fixed-b asymptotics) has been successfully employed to approximate sampling distributions. With the purpose of comparing both approaches, we derive here the fixed-b limit of WC estimators in a fractional setting, filling also some gaps in the traditional (small-b) theory. We also provide some Monte Carlo evidence that suggests that the fixed-b limit is more accurate.