|Description:||generates an autoregressive moving average process (ARMA) in deviations from the mean form y_t = a(B)y_t + eps_t + b(B)eps_t B denotes the backshift (or lag) operator. You have to deliver the AR coefficients vector a, the MA coefficients vector b and the (T x 1) white noise series eps. The output y is a (T x 1) ARMA series. The simulation routine sets the necessary initial values to 0 (that is y_t=eps_t=0 for t<1).|
|Usage:||y = genarma(a,b,eps)|
|a||(p x 1) vector of AR coefficients|
|b||(q x 1) vector of MA coefficients|
|eps||(T x 1) vector of white noise disturbances|
|y||(T x 1) vector with the generated ARMA process|
library("times") ; loads the quantlets from times library randomize(0) ; sets the seed y = genarma(0.5,0.5,normal(1000)) pacfplot(y,12) ; display of the sample pacf for y_t acfplot(y,12) ; display of the sample acf for y_t
Two displays that show the acf and the pacf of the generated ARMA(1,1) process y_t. The series y has T=1000 observations. The displays resemble the exhibits in Mills (cited above), p. 89.