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Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes

  • Dietmar Bauer
  • Martin Wagner

In this paper we derive (weak) consistency and the asymptotic distribution of pseudo maximum likelihood estimates for multiple frequency I(1) processes. By multiple frequency I(1) processes we denote processes with unit roots at arbitrary points on the unit circle with the integration orders corresponding to these unit roots all equal to 1. The parameters corresponding to the cointegrating spaces at the different unit roots are estimated super-consistently and have a mixture of Brownian motions limiting distribution. All other parameters are asymptotically normally distributed and are estimated at the standard square root of T rate. The problem is formulated in the state space framework, using the canonical form and parameterization introduced by Bauer and Wagner (2002b). Therefore the analysis covers vector ARMA processes and is not restricted to autoregressive processes.

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Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp0205.

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Date of creation: Jun 2002
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Handle: RePEc:ube:dpvwib:dp0205
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  1. Johansen, S. & Schaumburg, E., 1997. "Likelihood Analysis of Seasonal Cointegration," Economics Working Papers eco97/16, European University Institute.
  2. Saikkonen, Pentti, 1993. "Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model," Econometric Theory, Cambridge University Press, vol. 9(02), pages 155-188, April.
  3. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October.
  4. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
  5. Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft.
  6. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  7. repec:cup:etheor:v:9:y:1993:i:2:p:155-88 is not listed on IDEAS
  8. Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part I," Econometric Theory, Cambridge University Press, vol. 15(04), pages 435-468, August.
  9. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  10. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  11. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  12. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(01), pages 1-27, March.
  13. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft.
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