Estimation of the Vector Moving Average Model by Vector Autoregression

Abstract

We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In nite samples the estimator has a bias which i s low where roots of the determinantal equation are w ell away from the unit circle, and more substantial where one or more roots have m odulus near unity. W e s h ow that the representation estimated by this m ultivariate technique is consistent a n d asymptotically invertible. This estimator has signicant computational advantages over Maximum Likelihood, a n d more importantly may be more r obust than ML to mis-specication o f t h e v ector moving average model. The estimation method is a p plied to a VMA model of wholesale and retail inventories, using Canadian data on overall aggregate, non-durable a n d d u rable inventory investment, and a l lows us to examine the propagation of shocks between the two classes of inventory.

How far do shocks move across borders? Examining volatility transmission in major agricultural futures markets

“…We estimate M based on a vector autoregressive approximation of order p, Galbraith, Ullah, and Zinde-Walsh (2002). The estimator is shown to have a lower bias when the roots of the characteristic equation are su ciently distant from the unit circle, and it declines exponentially with p. Since we work with returns data, the choice of a modest order for the VAR provides a relatively good approximation of M.…”

The Inverse Kullback–Leibler Method for Fitting Vector Moving Averages

“…The covariance matrix Σ can be estimated via the VAR innovation covariance matrix. This will be called the WOLD procedure; it is very similar to the method of Galbraith et al (). [In the method of Galbraith et al (), Π ( B ) Θ ( B ) is approximately equal to the identity matrix, and hence the VMA coefficients can be recursively solved in terms of the coefficients of Π ( B ).]…”

Complete Blind Subspace Deconvolution

“…The innovation can be seen as the observation of an ISA problem because components of s are independent: ISA techniques can be used to identify components s m . Choosing the order of the fitted AR process to x as p = o(T T →∞ − −−− → ∞, where T denotes the number of samples, guarantees that the AR approximation for the MA model is asymptotically consistent [9].…”