Rank-based estimation for all-pass time series models

TL;DR

This paper introduces rank-based estimators for all-pass time series models, proving their asymptotic properties, demonstrating robustness, and showcasing their effectiveness through simulations and a seismogram application.

Contribution

The paper develops and analyzes rank-based estimators for all-pass models, establishing their asymptotic normality, consistency, and efficiency, with practical validation.

Findings

Estimators are asymptotically normal and consistent.

Rank-based estimators achieve efficiency comparable to maximum likelihood.

Simulation studies confirm finite-sample performance and robustness.

Abstract

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.