We establish sufficient conditions on durations that are stationary with finite variance and memory parameter <inline-graphic>null</inline-graphic> to ensure that the corresponding counting process <italic>N</italic>(<italic>t</italic>) satisfies Var <italic>N</italic>(<italic>t</italic>) ~ <italic>Ct</italic>² (<italic>C</italic> 0) as <italic>t</italic> → ∞, with the same memory parameter <inline-graphic>null</inline-graphic> that was assumed for the durations. Thus,...

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,1/2)$ to ensure that the corresponding counting process $N(t)$ satisfies $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C0$) as $t \rightarrow \infty$, with the same memory parameter...

We establish sufficient conditions on durations that arestationary with finite variance and memory parameter $d \in[0,1/2)$ to ensure that the corresponding counting process $N(t)$satisfies $Var N(t) \sim C t^{2d+1}$ ($Cgt;0$) as $t\rightarrow \infty$, with the same memory parameter $d...

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) raquo; Ct2d+1 (C gt; 0) as t ! 1, with the same memory parameter d 2 [0; 1=2) that was assumed for the...