Certain Semi-L\'evy Driven CARMA Processes: Estimation and Forecasting

TL;DR

This paper develops a Kalman recursion-based method for estimating parameters of semi-Lévy driven CARMA processes, demonstrating improved forecasting of financial volatility data over Lévy-driven models.

Contribution

It introduces a novel estimation approach for semi-Lévy CARMA processes using Kalman recursion and applies it to financial data for better forecasting.

Findings

Kalman recursion effectively estimates SSLCARMA parameters.

SSLCARMA outperforms Lévy-driven CARMA in forecasting volatility.

The method is validated through simulation and real data application.

Abstract

Continuous-time autoregressive moving average (CARMA) process driven by simple semi-L\'evy process has periodically correlated property with many potential application in finance. In this paper, we study on the estimation of the parameters of the simple semi-L\'evy CARMA (SSLCARMA) process based on the Kalman recursion technique. We implement this method in conjunction with the state-space representation of the associated process. The accuracy of estimation procedure is assessed in a simulated study. We fit a SSLCARMA(2,1) process to intraday realized volatility of Dow Jones Industrial Average data. Finally, We show that this process provides better in-sample forecasts of these data than the L\'evy driven CARMA process after de-seasonalized them.