Structure of continuous-time ARMA process driven by semi-Levy measure

TL;DR

This paper introduces a new class of continuous-time ARMA processes driven by semi-Levy measures, analyzing their structure, properties, and statistical characteristics, supported by simulations.

Contribution

It defines and studies a CARMA process driven by semi-Levy measures, providing new insights into its structure and statistical properties without additional measure assumptions.

Findings

Process is well-defined without extra conditions

Kernel representation derived for the process

Simulated data demonstrates model efficiency

Abstract

A class of continuous-time autoregressive moving average (CARMA) process driven by simple semi-Levy measure is defined and its properties are studied. We discuss some new insights on the structure of the semi-Levy measure which is described as periodically divisible measure. This consideration enable us to provide statistical property of the introduced process. We show that this process is well defined without having to assume further conditions on the measure. We find a kernel representation of the process and present the properties of first and second moments of it. Finally we show the efficiency of our model by implying simulated data.