A0703
Title: Self weighted quasi maximum exponential likelihood estimators for non linear time series models
Authors: Ilia Negri - University of Calabria (Italy) [presenting]
Fumiya Akashi - University of Tokyo (Japan)
Abstract: Non-linear time series models are widely used in fields where data exhibit complex dynamic relationships that cannot be captured by traditional linear frameworks. However, the practical application of non-linear models requires attention to fundamental properties, such as strict stationarity and ergodicity, which are crucial for making valid statistical inferences from finite samples. A class of self-weighted quasi-maximum exponential likelihood estimators is proposed for general non-linear time series models. Building on the framework introduced by a prior study, the approach improves robustness to heavy-tailed distributions and efficiency in the estimation of model parameters under non-linear dynamics. The focus is on the class of functional auto-regressive (FAR) models, which includes several well-known non-linear models, such as the threshold auto-regressive and exponential auto-regressive models. FAR models allow for smooth and flexible dependence structures that evolve as functions of past observations. A key contribution is the formal establishment of strict stationarity and ergodicity for the proposed class of models. These results ensure the existence of a stable long-term distribution and justify consistent inference procedures. The theoretical findings provide a solid foundation for applying non-linear time series models in practice, especially in challenging contexts such as financial time series, where heavy tails and volatility are prominent features.
