A Unified representation theorem on new algebraic bases for (co)integrated processes up to the second order

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Abstract

The paper establishes a unified representation theorem for (co)integrated processes up to the second order which provides a compact and informative insight into the solution of VAR models with unit roots, and sheds light on the cointegration features of the engendered processes. The theorem is primarily stated by taking a one-lag specification as a reference frame, and it is afterwards extended to cover the case of an arbitrary number of lags via a companion-form based approach. All proofs are obtained by resorting to an innovative and powerful algebraic apparatus tailored to the derivation of the intended results.
Original languageEnglish
Pages (from-to)37-66
Number of pages30
JournalADVANCES AND APPLICATIONS IN STATISTICS
Volume12
Publication statusPublished - 2009

Keywords

  • Laurent expansion in matrix form
  • Unified representation theorem
  • cointegration
  • orthogonal-complement algebra

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