ckARMA0 {longmemo} | R Documentation |
Compute the Autocovariances of a fractional ARIMA(0,d,0) process (d = H - 1/2).
ckARMA0(n, H)
n |
sample size (length of time series). |
H |
self-similarity (`Hurst') parameter. |
The theoretical formula,
C(k) = (-1)^k Γ(1-2d) / (Γ(k+1-d) Γ(1-k-d)) ,
where d = H - 1/2, leads to over-/underflow for larger lags k; hence use the asymptotical formula there.
numeric vector of length n
of covariances
C(0) ... C(n-1).
Jan Beran (principal) and Martin Maechler (speedup, fine tuning)
Jan Beran (1994), p.63, (2.35) and (2.39).
ckFGN0
which does the same for fractional
Gaussian noise.
str(C.8 <- ckARMA0(50, H = 0.8)) yl <- c(0,max(C.8)) plot(0:49, C.8, type = "h", ylim = yl) plot(0:49, C.8, type = "h", log = "xy", main = "Log-Log ACF for ARIMA(0,d,0)")