Home
Estimating
structural VARMA models with uncorrelated but non-independent error
terms
Yacouba Boubacar Mainassara and Christian Francq
Keywords: Echelon form;
Lagrange Multiplier test; Likelihood Ratio test; Nonlinear
processes; QMLE; Structural representation; VARMA models; Wald
test.
Abstract: The asymptotic properties of the
quasi-maximum likelihood estimator (QMLE) of vector autoregressive
moving-average (VARMA) models are derived under the assumption that
the errors are uncorrelated but not necessarily independent.
Relaxing the independence assumption considerably extends the range
of application of the VARMA models, and allows to cover linear
representations of general nonlinear processes. Conditions are given
for the consistency and asymptotic normality of the QMLE. A
particular attention is given to the estimation of the asymptotic
variance matrix, which may be very different from that obtained in
the standard framework. Modified versions of the Wald, Lagrange
Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the
parameters.
MPRA working paper