2018/03/02 by Mohammad Mohammadi, Mohammadi, M., Saeid Rezakhah +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1803.00733
openalex publication_date 2018/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the simple semi-Lévy driven continuous-time generalized autoregressive conditionally heteroscedastic (SS-COGARCH) process. The statistical properties of this process are characterized. This process has the potential to approximate any semi-Lévy driven COGARCH processes. We show that the state representation of such SS-COGARCH process can be described by a random recurrence equation with periodic random coefficients. The almost sure absolute convergence of the state process is proved. The periodically stationary solution of the state process is shown which cause the volatility to be periodically stationary under some suitable conditions. Also it is shown that the increments with constant length of such SS-COGARCH process is itself a periodically correlated (PC) process. Finally, we apply some test to investigate the PC behavior of the increments (with constant length) of the simulated samples of proposed SS-COGARCH process.