Locally adaptive estimation methods with application to univariate time series

TL;DR

This paper introduces a unified framework for locally adaptive estimation methods in univariate time series, applicable to various distributions, with theoretical insights and empirical validation on financial data.

Contribution

It provides a general approach for adaptive estimation in time series, covering multiple distributions and including a procedure for critical value computation.

Findings

Methods perform well on simulated data.

Effective on real financial data.

Flexible for various distribution models.

Abstract

The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical values is given. The underlying model encompasses all distributions from the exponential family providing for great flexibility. The procedures are applied to simulated and real financial data distributed according to the Gaussian, volatility, Poisson, exponential and Bernoulli models. Numerical results exhibit a very reasonable performance of the methods.