  In this paper we study the simple semi-L\'evy 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-L\'evy 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.
