Computing and estimating information matrices of weak ARMA models

Keywords: Asymptotic relative efficiency (ARE), Bahadur's slope\sep Information matrices\sep Lagrange Multiplier test, Nonlinear processes\sep Wald test, Weak ARMA models.

Abstract: Numerous time series admit weak autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. We give analytic expressions and propose consistent estimators of these matrices, at any point of the parameter space. Our results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series.

Computational Statistics and Data Analysis 56, 345--361, 2012.