| Library: | times |
| See also: | gentar genbil genarma genarch |
| Quantlet: | genexpar | |
| Description: | generates the amplitude-dependent exponential AR (EXPAR) process x that has the following form x_t = a(B)x_t + exp{-delta x^2_(t-thrlag)}b(B)x_t + e_t B is the backshift (or lag) operator. The coefficient delta must be positive. The lag polynoms a(B) and b(B) must have the same order. e_t is a sequence of independently distributed white noise with T>99 observations. |
| Usage: | x = genexpar(thrlag,delta,a,b,e) | |
| Input: | ||
| thrlag | integer; threshold lag that specifies the x values in the exponential function | |
| delta | positive coefficient in the exponential function | |
| a | p x 1 vector with the coefficients of the lag polynom a(B) | |
| b | p x 1 vector with the coefficients of the lag polynom b(B) | |
| e | T x 1 vector with realizations of an independently distributed white noise process. | |
| Output: | ||
| x | T x 1 vector with the realizations of the generated EXPAR process | |
library("times") ; loads the quantlets from times library
randomize(10) ; sets a seed
e = normal(500) ; generates the white noise realizations
x = genexpar(1,5,0.3|0.6,0.2|-0.8,e)
timeplot(x[200:500]) ; plots the generated series
The example is a second-order EXPAR model where -5x_(t-1) is the argument in the exponential function. The display shows 300 realizations of the generated series x.