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Open AccessArticle

Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size

Faculty of Business Administration and Economics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, Germany
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Econometrics 2020, 8(3), 38; https://doi.org/10.3390/econometrics8030038
Received: 4 May 2018 / Revised: 4 September 2020 / Accepted: 8 September 2020 / Published: 17 September 2020
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size. We deal with unrestricted OLS estimators (in the model formulated in levels as well as in vector error correction form) as well as with two stage estimation (2SI2) in the vector error correction model (VECM) formulation. Our main results are analogous to the I(1) case: We show that the long VAR approximation leads to consistent estimates of the long and short run dynamics. Furthermore, tests on the autoregressive coefficients follow standard asymptotics. The pseudo likelihood ratio tests on the cointegrating ranks (using the Gaussian likelihood) used in the 2SI2 algorithm show under the null hypothesis the same distributions as in the case of data generating processes following finite order VARs. The same holds true for the asymptotic distribution of the long run dynamics both in the unrestricted VECM estimation and the reduced rank regression in the 2SI2 algorithm. Building on these results we show that if the data is generated by an invertible VARMA process, the VAR approximation can be used in order to derive a consistent initial estimator for subsequent pseudo likelihood optimization in the VARMA model. View Full-Text
Keywords: vector autoregressions; vector error correction model; integrated processes of order two vector autoregressions; vector error correction model; integrated processes of order two
MDPI and ACS Style

Li, Y.; Bauer, D. Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size. Econometrics 2020, 8, 38.

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