Asymptotic distributions for quasi-efficient estimators in echelon VARMA models

Jean-Marie Dufour () and Tarek Jouini

Computational Statistics & Data Analysis, 2014, vol. 73, issue C, 69-86

Abstract: Two linear estimators for stationary invertible vector autoregressive moving average (VARMA) models in echelon form — to achieve parameter unicity (identification) — with known Kronecker indices are studied. It is shown that both estimators are consistent and asymptotically normal with strong innovations. The first estimator is a generalized-least-squares (GLS) version of the two-step ordinary least-squares (OLS) estimator studied in Dufour and Jouini (2005). The second is an asymptotically efficient estimator which is computationally much simpler than the Gaussian maximum-likelihood (ML) estimator which requires highly nonlinear optimization, and “efficient linear estimators” proposed earlier (Hannan and Kavalieris, 1984; Reinsel et al., 1992; Poskitt and Salau, 1995). It stands for a new relatively simple three-step estimator based on a linear regression involving innovation estimates which take into account the truncation error of the first-stage long autoregression. The complex dynamic structure of associated residuals is then exploited to derive an efficient covariance matrix estimator of the VARMA innovations, which is of order T−1 more accurate than the one by the fourth-stage of Hannan and Kavalieris’ procedure. Finally, finite-sample simulation evidence shows that, overall, the asymptotically efficient estimator suggested outperforms its competitors in terms of bias and mean squared errors (MSE) for the models studied.

Keywords: Stationary invertible VARMA; Echelon form; Kronecker indices; Truncation lag; Linear estimation; Simulation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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Working Paper: Asymptotic distributions for quasi-efficient estimators in echelon VARMA models (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:73:y:2014:i:c:p:69-86

DOI: 10.1016/j.csda.2013.11.002

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