autoregressive hilbertian processes
Recently Published Documents


TOTAL DOCUMENTS

15
(FIVE YEARS 1)

H-INDEX

4
(FIVE YEARS 0)

2019 ◽  
Vol 36 (5) ◽  
pp. 773-802 ◽  
Author(s):  
Brendan K. Beare ◽  
Won-Ki Seo

We develop versions of the Granger–Johansen representation theorems for I(1) and I(2) vector autoregressive processes that apply to processes taking values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. An I(1) or I(2) solution to an autoregressive law of motion is obtained when the inverse of the autoregressive operator pencil has a pole of first or second order at one. We obtain a range of necessary and sufficient conditions for such a pole to be of first or second order. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.


Sign in / Sign up

Export Citation Format

Share Document