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Cointegration in functional autoregressive processes

Massimo Franchi () and Paolo Paruolo

No 2017/5, DSS Empirical Economics and Econometrics Working Papers Series from Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome

Abstract: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes, where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle. A necessary and sucient condition for integration of order d = 1, 2,... is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces h, h = ,..,d, each one associated with components of the process integrated of order h. These results mirror the ones recently obtained in the nite dimensional case, with the only di erence that the number of cointegrating relations of order 0 is infinite.

Keywords: Functional autoregressive process; Unit roots; Cointegration; Common Trends; Granger-Johansen Representation Theorem. (search for similar items in EconPapers)
JEL-codes: C12 C33 C55 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2017-12
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Working Paper: Cointegration in functional autoregressive processes (2018) Downloads
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