Fractionally integrated COGARCH processes

TL;DR

This paper introduces fractional integrated COGARCH models that effectively capture long-range dependence in high-frequency financial data by modifying kernels to ensure well-defined, stationary volatility processes with algebraic decay in covariance.

Contribution

It develops a novel fractional COGARCH model with adjusted kernels to address issues in defining fractional processes, enabling better modeling of long memory in volatility.

Findings

Model exhibits stationarity and algebraic covariance decay.

Successfully fitted to exchange rate data using GMM.

Addresses kernel singularities for non-pathological paths.

Abstract

We construct fractionally integrated continuous-time GARCH models, which capture the observed long range dependence of squared volatility in high-frequency data. Since the usual Molchan-Golosov and Mandelbrot-van-Ness fractional kernels lead to problems in the definition of the model, we resort to moderately long memory processes by choosing a fractional parameter $d\in(-0.5,0)$ and remove the singularities of the kernel to obtain non-pathological sample paths. The volatility of the new fractional COGARCH process has positive features like stationarity, and its covariance function shows an algebraic decay, which make it applicable to econometric high-frequency data. In an empirical application the model is fitted to exchange rate data using a simulation-based version of the generalised method of moments.