Bias corrected minimum distance estimator for short and long memory processes

TL;DR

This paper introduces a bias-corrected minimum distance estimator (BCMDE) for short and long memory processes, improving parameter estimation accuracy by addressing bias in sample autocorrelation, with proven consistency and favorable simulation results.

Contribution

The paper develops a novel bias-corrected minimum distance estimator for ARFIMA models, demonstrating its theoretical consistency and superior performance over existing estimators.

Findings

BCMDE is consistent for ARFIMA models.

BCMDE outperforms maximum likelihood, Whittle, and MDE in simulations.

BCMDE has lower bias and mean squared error in various scenarios.

Abstract

This work proposes a new minimum distance estimator (MDE) for the parameters of short and long memory models. This bias corrected minimum distance estimator (BCMDE) considers a correction in the usual MDE to account for the bias of the sample autocorrelation function when the mean is unknown. We prove the weak consistency of the BCMDE for the general fractional autoregressive moving average (ARFIMA(p, d, q)) model and derive its asymptotic distribution for some particular cases. Simulation studies show that the BCMDE presents a good performance compared to other procedures frequently used in the literature, such as the maximum likelihood estimator, the Whittle estimator and the MDE. The results also show that the BCMDE presents, in general, the smallest mean squared error and is less biased than the MDE when the mean is a non-trivial function of time.