Parameter stability and semiparametric inference in time-varying ARCH models

TL;DR

This paper introduces a comprehensive methodology for detecting and estimating time-varying and non time-varying parameters in ARCH models, using kernel estimation and statistical testing, with applications to real data.

Contribution

It develops a semiparametric framework for inference in tv-ARCH models, including estimation, testing, and model selection procedures, extending existing econometric models.

Findings

Non time-varying parameters can be estimated at parametric rates.

Estimates are asymptotically efficient for Gaussian noise.

The methodology is validated with real data applications.

Abstract

In this paper, we develop a complete methodology for detecting time-varying/non time-varying parameters in ARCH processes. For this purpose, we estimate and test various semiparametric versions of the time-varying ARCH model (tv-ARCH) which include two well known non stationary ARCH type models introduced in the econometric literature. Using kernel estimation, we show that non time-varying parameters can be estimated at the usual parametric rate of convergence and for a Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non time-varying parameters or for testing the second order dynamic. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.