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A new goodness-of-fit process for varma (p,q) models: construction and empirical properties

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2013-12
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Abstract
As an extension of the univariate technique in Ubierna and Velilla (2007), we present a goodness-of-fit process for VARMA (p,q) models in which the residuals of the fit are considered. We also formulatean explicit form of the asymptotic covariance function, as well as a suitable representation of the limitprocess. More importantly, we propose a new goodness-of-fit process based on a transformed correlationmatrix sequence. The new goodness-of-fit process is proved to converge weakly to the Brownian bridge.Several simulations, comparisons, and examples are presented. These results illustrate the scope of bothour theoretical findings and contributions. Our method is shown to be sensitive to detect lack of fit.Thus, it can be considered as a useful tool tool for identifying a proper time series model.
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Brownian bridge, Error sample correlation matrix, Goodness-of-fit process, Model selection, VARMA(p,q) models, Weak convergence
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