Abstract
We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series.
Acknowledgment
We thank the referee, whose constructive report led to many improvements.
Citation
Download Citation
N. H. Bingham.
"Prediction theory for stationary functional time series."
Probab. Surveys
19
160 - 184,
2022.
https://doi.org/10.1214/20-PS360
Information
Received: 1 December 2020; Published: 2022
First available in Project Euclid: 6 April 2022
Digital Object Identifier: 10.1214/20-PS360
Subjects:
Primary:
60-02
Secondary:
62-02
Keywords:
Beurling-Lax-Halmos theorem
,
Cramér representation
,
functional principal components
,
functional time series
,
Karhunen-Loève expansion
,
kernel methods
,
Kolmogorov isomorphism theorem
,
Szegő alternative
,
Szegő’s theorem
,
Verblunsky coefficients
