RandomFunction[ARMAProcess[{.1, .2}, {.3, -.2}, 1],{0,250}];
ListPlot[%,Filling->Axis]

RandomFunction[ARIMAProcess[{-.7},2, {.2}, 1], {0, 250}];
ListPlot[%,Filling->Axis]

RandomFunction[SARIMAProcess[{.4},1,{-1.3},{12,{.7,.3},2,{.7,-.3}},1],{0,250}];
ListPlot[%,Filling->Axis]

RandomFunction[FARIMAProcess[{.1},.45,{.2},1],{0,250}];
ListPlot[%,Filling->Axis]