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Title: Long VAR approximation in I(2) context: Asymptotic theory and simulations Authors:  Yuanyuan Li - University of Bielefeld (Germany) [presenting]
Dietmar Bauer - University Bielefeld (Germany)
Abstract: The asymptotic theory for long VAR approximations is extended to I(2) processes. The analysis is mainly performed in the framework of a triangular representation admitting an infinite-order autoregressive representation subject to summability conditions on the autoregressive coefficients. The results, however, also have implications for more general data generating processes. Similar results as in I(1) cases are achieved including the consistency of the estimated coefficients as well as their asymptotic distributions for properly chosen lag length. Based on these results, tests for linear restrictions on the coefficients can be derived. The results are also the starting point for the derivation of rank tests and the asymptotic distributions of reduced rank estimators. Furthermore, a detailed simulation study examines the finite sample properties of rank testing procedures to specify the integer parameters (the two involved cointegration ranks) in the long VAR approximations for I(2) processes.