Continuous-time fractional ARMA processes (Q1341364)

Continuous-time fractional ARMA processes \((X_ t)\), \(t \geq 0\), are introduced by \[ X_ t = \int^ t _{-\infty} f(t - s) dW(s). \] Here, \((W(t))\) is a Brownian motion. The impulse response function \(f \in L^ 2(R^ +)\) has a Laplace transform \(F\) of the form \[ F(s) = \prod^ K_ 1 (s - a_ k)^{d_ k} \text{ if Re}(s) > a \] for certain parameters \(a_ k\) and \(d_ k\). The authors study the memory of such processes and the smoothness of their sample paths. Finally, these processes are compared with fractional Brownian motions.