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Autoregressive Approximations of Multiple Frequency I(1) Processes

  • Dietmar Bauer
  • Martin Wagner

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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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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  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:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  3. 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.
  4. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
  5. repec:cup:etheor:v:9:y:1993:i:1:p:19-35 is not listed on IDEAS
  6. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society.
  7. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  8. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February.
  9. 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.
  10. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 19-35, January.
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