Temporally Local Maximum Likelihood with Application to SIS Model

Area of Science:

• Statistics
• Econometrics
• Epidemiological Modeling

Background:

• Rolling parametric estimators are crucial for analyzing time series with nonlinear patterns, local trends, and time-varying parameters.
• Temporally Local Maximum Likelihood (TLML) estimators offer a flexible approach within this domain.
• Understanding the properties of these estimators is essential for accurate time series analysis.

Purpose of the Study:

• To examine the properties of TLML estimators for various parameter types: constant, stochastic stationary, and ultra-long run (ULR) dynamics.
• To investigate the impact of weighting schemes within TLML estimators on statistical inference.
• To assess the finite sample performance of TLML estimators in a practical epidemiological context.

Main Methods:

• Theoretical analysis of TLML estimators for constant, stochastic stationary, and ULR parameters.
• Simulation study using the susceptible-infected-susceptible (SIS) epidemiological model.
• Evaluation of the influence of different weight functions on estimator properties and inference.

Main Results:

• The choice of weights in TLML estimators critically affects the accuracy and reliability of statistical inference.
• TLML estimators demonstrate varying performance depending on the parameter dynamics (constant, stochastic, ULR).
• Simulation results illustrate the practical implications of these findings in modeling time-varying contagion parameters.

Conclusions:

• The weighting scheme is a key determinant of the effectiveness of TLML estimators in time series analysis.
• The study provides insights into the behavior of TLML estimators across different parameter scenarios.
• Findings are relevant for applications requiring robust estimation of time-varying parameters, such as in epidemiology.