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Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes

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  • Dietmar Bauer

    (Department of Business Administration and Economics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, Germany)

Abstract

When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the corresponding estimators are well documented in great generality in the book Hannan and Deistler (1988). If the data-generating process is not a finite-order VAR, the selected lag length typically tends to infinity as a function of the sample size. For invertible vector autoregressive moving average (VARMA) processes, this typically happens roughly proportional to log T . The same approach for lag length selection is also followed in practice for more general processes, for example, unit root processes. In the I(1) case, the literature suggests that the behavior is analogous to the stationary case. For I(2) processes, no such results are currently known. This note closes this gap, concluding that information-criteria-based lag length selection for I(2) processes indeed shows similar properties to in the stationary case.

Suggested Citation

  • Dietmar Bauer, 2023. "Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes," Econometrics, MDPI, vol. 11(2), pages 1-11, April.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:2:p:11-:d:1128372
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    References listed on IDEAS

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    2. Jostein Paulsen, 1984. "Order Determination Of Multivariate Autoregressive Time Series With Unit Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 115-127, March.
    3. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    4. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575.
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