Discrete time approximation of a COGARCH(p,q) model and its estimation

TL;DR

This paper develops a discrete-time approximation for the COGARCH(p,q) model, enabling effective estimation from irregular time series data using a pseudo likelihood approach implemented in the yuima package.

Contribution

It introduces a convergent discrete-time process approximation for COGARCH(p,q) models and provides an estimation method suitable for irregularly spaced data.

Findings

Discrete approximation converges in probability and Skorokhod metric.

Estimation method based on pseudo log-likelihood is implemented in R.

Facilitates analysis of irregularly spaced financial data.

Abstract

In this paper, we construct a sequence of discrete time stochastic processes that converges in probability and in the Skorokhod metric to a COGARCH(p,q) model. The result is useful for the estimation of the continuous model defined for irregularly spaced time series data. The estimation procedure is based on the maximization of a pseudo log-likelihood function and is implemented in the yuima package.