Functional generalized autoregressive conditional heteroskedasticity

TL;DR

This paper introduces a functional version of GARCH models (fGARCH) for financial time series, providing theoretical foundations, estimation methods, and potential applications to high-frequency volatility data.

Contribution

It develops the theory for fGARCH processes, including stationarity criteria and a consistent estimation procedure, addressing limitations of traditional multivariate GARCH models.

Findings

Established conditions for stationarity of fGARCH(1,1)

Proposed a consistent estimation method for fGARCH

Demonstrated potential for intraday volatility modeling

Abstract

Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the focus of research with attention given to methods seeking an efficient and economic estimation of a large number of model parameters. Due to the need for estimation of many parameters, however, these models may not be suitable for modeling now prevalent high-frequency volatility data. One potentially useful way to bypass these issues is to take a functional approach. In this paper, theory is developed for a new functional version of the generalized autoregressive conditionally heteroskedastic process, termed fGARCH. The main results are concerned with the structure of the fGARCH(1,1) process, providing criteria for the existence of a strictly stationary solutions both in the space of square-integrable and continuous functions. An estimation procedure is introduced and its consistency verified. A small empirical study highlights potential applications to intraday volatility estimation.