Certain Semi-Lévy Driven CARMA Processes: Estimation and Forecasting
arXiv:1912.10083
Abstract
Continuous-time autoregressive moving average (CARMA) process driven by simple semi-Lévy 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-Lévy 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 Lévy driven CARMA process after de-seasonalized them.
16 pages