Fast calibration of weak FARIMA models

TL;DR

This paper introduces a fast, asymptotically normal estimator for weak FARIMA models that reduces computational time while maintaining statistical properties, useful for remote time series analysis.

Contribution

The paper develops a one-step estimator for weak FARIMA models that is computationally efficient and retains desirable asymptotic properties, extending existing methods.

Findings

Estimator is strongly consistent and asymptotically normal.

Simulation results show reduced computational time.

Application demonstrates utility in remote time series monitoring.

Abstract

In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.