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

TL;DR

This paper introduces the MCSS estimator, a modification of the CSS estimator, which reduces bias in estimating fractionally integrated ARFIMA models, showing improved performance in simulations and real data analysis.

Contribution

The paper proposes the MCSS estimator that corrects bias in CSS estimation for ARFIMA models by a simple modification, enhancing accuracy especially in small samples.

Findings

MCSS estimator reduces bias compared to CSS.

Simulation results show improved performance of MCSS.

Application to classical datasets demonstrates practical effectiveness.

Abstract

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.