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Mixed Normality And Ancillarity In I(2) Systems

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  • Boswijk, H. Peter

Abstract

This paper studies asymptotic likelihood inference on cointegration parameters in systems integrated of order two. We start with so-called triangular systems and then extend the analysis to vector autoregressions. We show that even when all unit root restrictions have been imposed, the asymptotic observed information is not (locally) ancillary, which implies that the log-likelihood ratio is not locally asymptotically mixed normal. The results are applied to inference on polynomial cointegration. Some similarities and differences with I(1) systems are also discussed.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 06 (December)
Pages: 878-904

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Handle: RePEc:cup:etheor:v:16:y:2000:i:06:p:878-904_16

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Cited by:
  1. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
  2. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.
  3. Søren Johansen & Katarina Juselius & Roman Frydman & Michael Goldberg, 2007. "Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate," Discussion Papers 07-34, University of Copenhagen. Department of Economics.
  4. H. Peter Boswijk & Jurgen Doornik, 2003. "Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview," Economics Papers 2003-W10, Economics Group, Nuffield College, University of Oxford.
  5. Paruolo Paolo, 2003. "Common trends and cycles in I(2) VAR systems," Economics and Quantitative Methods qf0217bis, Department of Economics, University of Insubria.
  6. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
  7. Takamitsu Kurita, 2009. "A note on testing parameter constancy in cointegrated vector autoregression: the case of near I(2) processes," Economics Bulletin, AccessEcon, vol. 29(2), pages 575-587.
  8. Helmut Luetkepohl, 2011. "Vector Autoregressive Models," Economics Working Papers ECO2011/30, European University Institute.

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