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Autoregressive Approximations of Multiple Frequency I(1) Processes

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  • Dietmar Bauer
  • Martin Wagner

Abstract

We investigate autoregressive approximations of multiple frequency I(1) processes, of which I(1) processes are a special class. The underlying data generating process is assumed to allow for an infinite order autoregressive representation where the coefficients of the Wold representation of the suitably differenced process satisfy mild summability constraints. An important special case of this process class are VARMA processes. The main results link the approximation properties of autoregressions for the nonstationary multiple frequency I(1) process to the corresponding properties of a related stationary process, which are well known (cf. Section 7.4 of Hannan and Deistler, 1988). First, error bounds on the estimators of the autoregressive coefficients are derived that hold uniformly in the lag length. Second, the asymptotic properties of order estimators obtained with information criteria are shown to be closely related to those for the associated stationary process obtained by suitable differencing. For multiple frequency I(1) VARMA processes we establish divergence of order estimators based on the BIC criterion at a rate proportional to the logarithm of the sample size.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2005/09.

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Date of creation: 2005
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Handle: RePEc:eui:euiwps:eco2005/09

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Keywords: Unit Roots; Multiple Frequency I(1) Process; Nonrational Transfer Function; Cointegration; VARMA Process; Information Criteria;

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  1. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  2. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February.
  3. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  4. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  5. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society.
  6. 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.
  7. Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft.
  8. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  9. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 19-35, January.
  10. repec:cup:etheor:v:9:y:1993:i:1:p:19-35 is not listed on IDEAS
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Cited by:
  1. Christian Kascha & Carsten Trenkler, 2009. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Working Paper 2009/12, Norges Bank.
  2. Bauer, Dietmar & Wagner, Martin, 2009. "Using subspace algorithm cointegration analysis: Simulation performance and application to the term structure," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1954-1973, April.
  3. Christian Kascha & Carsten Trenkler, 2011. "Cointegrated VARMA models and forecasting US interest rates," ECON - Working Papers 033, Department of Economics - University of Zurich.

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