Statistics and Computational Methods Seminar Series - Fall 2025

Speaker: Ilia Negri (Università della Calabria)

Title:  Estimation of nonlinear time series models via self-weighted quasi-maximum exponential likelihood

(Joint work with Fumiya Akashi, University of Tokyo)

Abstract:

A class of self-weighted quasi maximum exponential likelihood estimators (QMELE) is introduced for a broad family of nonlinear time series models, encompassing the Functional Autoregressive (FAR) framework, which includes well-known models such as the Threshold Autoregressive (TAR) and Exponential Autoregressive (EXPAR) processes as special cases. The key idea of the method is to introduce data-dependent weights into the loss function, so that large observations, typically responsible for instability in estimation under infinite variance, receive smaller weights. The proposed approach extends the self-weighting methodology originally developed for infinite-variance linear models to a broader nonlinear setting. We establish the consistency and derive the asymptotic distribution of the estimators under mild regularity conditions. As a preliminary step, strict stationarity and ergodicity are proved for the general FAR specification, ensuring the validity of the asymptotic theory. A Monte Carlo simulation study based on a generalized EXPAR model illustrates the finite-sample performance and robustness of the proposed estimators, providing empirical validation of the theoretical results.The proposed framework provides a rigorous theoretical basis for statistical inference in nonlinear time series models, including those with heavy-tailed innovations.