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Autoregressive Approximations of Multiple Frequency I(1) Processes


  • Bauer, Dietmar

    (arsenal research, Vienna, Austria)

  • Wagner, Martin

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)


We investigate autoregressive approximations of multiple frequency I(1) processes. 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 filtered process satisfy mild summability constraints. An important special case of this process class are MFI(1) 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. First, uniform error bounds on the estimators of the autoregressive coefficients are derived. 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 filtering. 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.

Suggested Citation

  • Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:174

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    References listed on IDEAS

    1. 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.
    2. repec:cup:etheor:v:9:y:1993:i:1:p:19-35 is not listed on IDEAS
    3. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 19-35, January.
    4. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
    5. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
    6. 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 113-144, January.
    7. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
    8. 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, Universite de Montreal, Departement de sciences economiques.
    9. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February.
    10. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
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    Cited by:

    1. Martin Wagner, 2010. "Cointegration analysis with state space models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 273-305, September.
    2. Kascha, Christian & Trenkler, Carsten, 2011. "Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1008-1017, February.
    3. Christian Kascha & Carsten Trenkler, 2011. "Cointegrated VARMA models and forecasting US interest rates," ECON - Working Papers 033, Department of Economics - University of Zurich.
    4. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
    5. 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.

    More about this item


    Unit roots; Multiple frequency I(1) process; Nonrational transfer function; Cointegration; VARMA process; Information criteria;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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