Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency

TL;DR

This paper introduces a flexible semiparametric approach for time series modeling with log-concave innovations, enabling simultaneous parameter and density estimation with proven consistency and demonstrated effectiveness on real data.

Contribution

It develops a general maximum likelihood framework for semiparametric time series models with log-concave innovations, applicable to ARMA, GARCH, and ARMA-GARCH models, with proven estimator consistency.

Findings

Estimator is consistent in ARMA and ARMA-GARCH models.

Framework performs well in finite sample simulations.

Applied successfully to financial and ecological data.

Abstract

We study semiparametric time series models with innovations following a log-concave distribution. We propose a general maximum likelihood framework which allows us to estimate simultaneously the parameters of the model and the density of the innovations. This framework can be easily adapted to many well-known models, including ARMA, GARCH and ARMA-GARCH. Furthermore, we show that the estimator under our new framework is consistent in both ARMA and ARMA-GARCH settings. We demonstrate its finite sample performance via a thorough simulation study and apply it to model the daily log-return of FTSE 100 index and the rabbit population.