Autoregressive Approximations of Multiple Frequency I(1) Processes
AbstractWe 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 InfoPaper provided by European University Institute in its series Economics Working Papers with number ECO2005/09.
Date of creation: 2005
Date of revision:
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More information through EDIRC
Unit Roots; Multiple Frequency I(1) Process; Nonrational Transfer Function; Cointegration; VARMA Process; Information Criteria;
Other versions of this item:
- Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-08-13 (All new papers)
- NEP-ECM-2005-08-13 (Econometrics)
- NEP-ETS-2005-08-13 (Econometric Time Series)
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