The modified conditional sum-of-squares estimator for fractionally integrated models

In this paper, we analyse the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator in a stationary or non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions for the estimator's bias and show that the leading term can be easily removed by a simple modification of the CSS objective function. We call this new estimator the modified conditional sum-of-squares (MCSS) estimator. We show theoretically and by means of Monte Carlo simulations that its performance relative to that of the CSS estimator is markedly improved even for small sample sizes. Finally, we revisit three classical short datasets that have in the past been described by ARFIMA($p_1$,$d$,$p_2$) models with constant term, namely the post-second World War real GNP data, the extended Nelson-Plosser data, and the Nile data.