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Asymptotic inference results for multivariate long-memory processes

Juan J. Dolado and Francesc Marmol
The Econometrics Journal
Vol. 7, No. 1 (2004), pp. 168-190
Published by: Wiley on behalf of the Royal Economic Society
Stable URL: http://www.jstor.org/stable/23115005
Page Count: 23
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Asymptotic inference results for multivariate long-memory processes
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Abstract

In this paper, we extend the well-known Sims, Stock and Watson (SSW) (Sims et al. 1990; Econometrica 56, 113–44), analysis on estimation and testing in vector autoregressive process (VARs) with integer unit roots and deterministic components to a more general set-up where non-stationary fractionally integrated (NFI) processes are considered. In particular, we focus on partial VAR models where the conditioning variables are NFI since this is the only finite-lag VAR model compatible with such processes. We show how SSW's conclusions remain valid. This means that whenever a block of coefficients in the partial VAR can be written as coefficients on zero-mean I(0) regressors in models including a constant term, they will have a joint asymptotic normal distribution. Monte Carlo simulations and an empirical application of our theoretical results are also provided.

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