Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models

TL;DR

This paper introduces an adaptive pointwise estimation method for time-inhomogeneous volatility models, allowing for non-stationarity and varying coefficients, with demonstrated improvements over standard GARCH in financial data.

Contribution

It develops a novel local change-point based estimation approach for non-stationary volatility models, applicable to GARCH and similar frameworks.

Findings

Outperforms standard GARCH in stock-index series

Provides theoretically justified adaptive estimates

Effective in non-stationary financial time series

Abstract

This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.