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.