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Temporally Local Maximum Likelihood with Application to SIS Model

Author

Listed:
  • Gourieroux Christian

    (University of Toronto, Toronto, Canada)

  • Jasiak Joann

    (York University, Toronto, Canada)

Abstract

The parametric estimators applied by rolling are commonly used for the analysis of time series with nonlinear patterns, including 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 consider the TLML estimators of (a) constant parameters, (b) stochastic, stationary parameters and (c) parameters with the ultra-long run (ULR) dynamics bridging the gap between the constant and stochastic parameters. We show that the weights used in the TLML estimators have a strong impact on the inference. For illustration, we provide a simulation study of the epidemiological susceptible–infected–susceptible (SIS) model, which explores the finite sample performance of TLML estimators of a time varying contagion parameter.

Suggested Citation

  • Gourieroux Christian & Jasiak Joann, 2023. "Temporally Local Maximum Likelihood with Application to SIS Model," Journal of Time Series Econometrics, De Gruyter, vol. 15(2), pages 151-198, July.
    • Handle: RePEc:bpj:jtsmet:v:15:y:2023:i:2:p:151-198:n:3
    DOI: 10.1515/jtse-2022-0016
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    More about this item

    Keywords

    local maximum likelihood; rolling estimator; omitted heterogeneity; bias reduction; generalized linear model; SIS model; logistic growth; ultra long run;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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