Oliver Linton:


  ESTIMATING SEMIPARAMETRIC ARCH(inf) MODELS BY KERNEL SMOOTHING METHODS


by O. Linton and E. Mammen


We introduce a method for the estimation of a new class of semiparametric
ARCH(inf) models that generalizes the standard GARCH(1,1) model to allow
for news impact function of general shape. We show that the news impact
function must satisfy a linear integral equation of second order. We use
this to propose several estimation methods based on alternative approaches
to solving such equations. We also estimate the parameter by profiled
semiparametric likelihood. We establish the distribution theory of both
the parametric and the nonparametric estimators. We investigate the
performance of our procedures on simulated data and on a sample of stock
returns.