For a general stationary ARMA(<italic>p,q</italic>) process <italic>u</italic> we derive the <italic>exact</italic> form of the orthogonalizing matrix <italic>R</italic> such that <italic>R</italic>′<italic>R</italic> = Σ⁻¹, where Σ = <italic>E</italic>(<italic>uu</italic>′) is the covariance matrix of <italic>u</italic>, generalizing the known formulae for <italic>AR</italic>(<italic>p</italic>) processes. In a linear regression model with an ARMA(<italic>p,q</italic>) error process,...

We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility. We obtain asymptotic properties of the estimators and offer some simulation evidence on small-sample...

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the determinantal equation are well away from the unit circle, and more substantial where one or more roots...

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for...