Autoregressive Approximations of Multiple Frequency I(1) Processes

Dietmar Bauer and Martin Wagner

No ECO2005/09, Economics Working Papers from European University Institute

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.

Keywords: Unit Roots; Multiple Frequency I(1) Process; Nonrational Transfer Function; Cointegration; VARMA Process; Information Criteria (search for similar items in EconPapers)
JEL-codes: C13 C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2005
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Working Paper: Autoregressive Approximations of Multiple Frequency I(1) Processes (2005)
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