Temporally Local Maximum Likelihood with Application to SIS Model

TL;DR

This paper investigates the properties of Temporally Local Maximum Likelihood estimators for nonlinear time series, including their application to epidemiological models and finite sample performance.

Contribution

It extends the understanding of TLML estimators to various parameter types and demonstrates their effectiveness in SIS model analysis.

Findings

TLML estimators perform well in finite samples

Application to SIS model shows accurate parameter estimation

Properties of TLML are validated through simulations

Abstract

The parametric estimators applied by rolling are commonly used in the analysis of time series with nonlinear features, such as structural change due to time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of Temporally Local Maximum Likelihood (TLML) estimators. We study the TLML estimators of constant parameters, stochastic and stationary parameters and parameters with the Ultra Long Run (ULR) dynamics bridging the gap between the constant and stochastic parameters. Moreover, we explore the properties of TLML estimators in an application to the Susceptible-Infected-Susceptible (SIS) epidemiological model and illustrate their finite sample performance in a simulation study.