| Library: | times |
| See also: | gentar genexpar genarma genarch |
| Quantlet: | genbil | |
| Description: | generates the bilinear process x that has the following form x_t = phi(B)x_t + e_t + theta(B)e_t + sum sum c_(i,j)x_(t-i)e_(t-j) B denotes the backshift (or lag) operator. The AR polynom phi(B) has p coefficients and the MA polynom theta(B) has q coefficients. The first sum of the double sum goes from i=1 to p and the second sum goes from j=1 to q. e_t is a sequence of independently distributed white noise with T > 99 observations. The length of the generated process x_t is T. |
| Usage: | x = genbil(phi,theta,c,e) | |
| Input: | ||
| phi | p x 1 vector of coefficients for the AR polynom phi(B) | |
| theta | q x 1 vector of coefficients for the MA polynom theta(B). | |
| c | pq x 1 vector of coefficients c_(i,j) for the double sum. The order of the coefficients must be (c_(1,1),..,c_(1,q),c_(2,1),c_(2,q),..,c_(p,1),..,c_(p,q)) | |
| e | T x 1 vector of realizations of an independently distributed white noise process. T must be greater than 99. | |
| Output: | ||
| x | T x 1 vector of the generated bilinear process | |
library("times") ; loads the quantlets from times library
randomize(10) ; sets a seed
e = normal(580) ; generates white noise realizations
x = genbil(0|0,0,0.75|0,e)
timeplot(x[200:580]^2) ; plots the squared series
The example generates realizations of the simple superdiagonal bilinear model (see Mills, p.153). Whereas the sample ACF indicates that the series is white noise, the display of the squared series reveals the nonlinear structure of the generated series.