Autoregressive moving average process
ARMAProcess[{a1, …, a p}, {b1, …, b q}, v]
ARMAProcess[{a1, …, a p}, {b1, …, b q}, Σ]
ARMAProcess[{a1, …, a p}, {b1, …, b q}, v, init]
ARMAProcess[c, …]
CovarianceFunction[ARMAProcess[c, {a}, {b}, σ^2], s, t]
→ Piecewise[{{-((a^(-1 + Abs[s - t])*(a + b + a^2*b + a*b^2)*σ^2)/((-1 + a)*(1 + a))), Abs[s - t] > 0}}, -((b*σ^2)/a) - ((a + b + a^2*b + a*b^2)*σ^2)/((-1 + a)*a*(1 + a))]DiscretePlot[CorrelationFunction[ARMAProcess[{.4, .2}, {1, .1}, 1], h], {h, 0, 20}, ExtentSize -> 1 / 2]
→ -Graphics-DiscretePlot[PartialCorrelationFunction[ARMAProcess[{.4, .2}, {1, .1}, 1], h], {h, 1, 20}, ExtentSize -> 1 / 2]
→ -Graphics-