[R] calculating recursive sequences

From: Vaidotas Zemlys <mpiktas_at_gmail.com>
Date: Thu 29 Dec 2005 - 23:33:32 EST


I was trying to repeat the estimation of threshold GARCH models from the book "Analysis of Financial Time Series" by Ruey S. Tsay, and I was succesfull, but I had to use "for" loop, which is quite slow. The loop is necessary, since you need to calculate recursive sequence. Is there a faster way to do this in R, without using loops?

The model is such:
r_t = \mu + \alpha_2 r_{t-2} + a_t
a_t = \sigma_t\varepsilon_t

\sigma_t^2 =

It is asummed that \varepsilon_t are iid and normal with zero mean and variance one. The data given is r_t, and you have to estimate variables, \mu, \alpha, \beta and \gamma. Since


using the equations we calculate a_t and \sigma_t and estimate the variables using maximum likelihood method. a_t can be estimated directly using first equation and rt. \sigma_t^2 depends on sigma_{t-1}^2, so it should be calculated recursively.

The function calculating negative log-likelihood of this problem I wrote:

garchln <- function(p,rt) {

    n <- length(rt)

    at <- rt[4:n]-p[1]-p[2]*rt[4:n-2]
    u <- as.numeric(at>0)
    h <- rep(0,length(at))
  # h is \sigma_t^2
   for(i in 1:(length(h)-1)) {

        h[i+1] <- p[3]*at[i]^2+p[4]*h[i]+u[i]*(p[5]+p[6]*at[i]^2+p[7]*h[i])     }

   #Maximum likelihood function

For fitting I used optim, with methods "Nelder-Mead" and "BFGS",

Initial parameter values from the book are  0.03 -0.03 0.10 0.60 0.10 0.05 0.10 The fitted values from the book are
 0.043 -0.022 0.098 0.954 0.060 -0.052 -0.069.

The link to the data used:

For this problem recursive sequence is linear, so it is possible to calculate it as a linear equations solution, but it is easy to think of the case where the recursion is non-linear. Is the speed-up possible only by writing C or Fortran code with loops?

Vaidotas Zemlys

Doctorate student, http://www.mif.vu.lt/katedros/eka/katedra/zemlys.php
Vilnius University

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Received on Thu Dec 29 23:41:57 2005

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