Estimating FARIMA models with uncorrelated but non-independent error terms

TL;DR

This paper extends the estimation theory of FARIMA models to cases where errors are uncorrelated but not independent, providing new asymptotic results, covariance estimation, and confidence intervals, supported by simulations and stock market data.

Contribution

It relaxes independence assumptions in FARIMA models, deriving new asymptotic properties and proposing a consistent covariance estimator and confidence interval method.

Findings

Asymptotic properties established under uncorrelated but dependent errors.

Proposed a consistent estimator for the asymptotic covariance matrix.

Simulation and real data demonstrate the effectiveness of the methods.

Abstract

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of fractionally integrated autoregressive moving-average (FARIMA) models under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. We relax considerably the independence and even the martingale difference assumptions on the innovation process to extend the range of application of the FARIMA models. We propose a consistent estimator of the asymptotic covariance matrix of the LSE which may be very different from that obtained in the standard framework. A self-normalized approach to confidence interval construction for weak FARIMA model parameters is also presented. All our results are done under a mixing assumption on the noise. Finally, some simulation studies and an application to the daily returns of stock market indices are presented to corroborate our theoretical work.