# 2018-20 Tjalling C. Koopmans Econometric Theory Prize Winners

The winners of the 2018-20 Tjalling C. Koopmans Econometric Theory Prize were announced in the August 2021 issue of *Econometric Theory *by the journal editor and Cowles research staﬀ member, Peter C.B. Phillips.

The biennial prize is supported by the Cowles Foundation for Research in Economics and is named in honor of Tjalling C. Koopmans, the 1975 Nobel Laureate in Economic Science, and comes with a ﬁnancial award of $1,000.

The two winning articles are: “Representation of I(1) and I(2) Autoregressive Hilbertian Processes,” authored by **Brendan K. Beare** (University of Sydney) and **Won-Ki Seo** (Queen’s University); and “Cointegration in Functional Autoregressive Processes,” authored by **Massimo Franchi** and **Paolo Paruolo**. Both articles appear in the October 2020 issue of *Econometric Theory*.

An excerpt from the journal advisory board statement is below:

The selection of the winning articles was made by the Advisory Board of the Journal and all articles published in *Econometric Theory* over 2018-2020 inclusive were candidates for the prize, except those that were authored or coauthored by the Editor and members of the Advisory Board. The citation of the winning paper (written by the Advisory Board and Editor) is as follows:

These articles provide a representation theory for autoregressive models of functional time series, with an emphasis on integration and cointegration. To model functional time series, random variables take values in a complex separable Hilbert space H (thus admitting certain classes of functions, rather than conventional n-dimensional vectors) with linear operators from H to H as autoregressive coeﬀicients. Correspondingly, the autoregressive polynomial A(z) is an operator-valued function of the complex variable z. Analogous to the “classical” case in integration, A(z) is assumed invertible in the closed unit disc except at z=1. The integration and cointegration properties of the corresponding process are based on an analysis of A(z) at z=1. The results obtained show that, under the assumption that 1 is an eigenvalue of ﬁnite type of A(z), the integration and cointegration properties of (generally inﬁnite-dimensional) H-valued processes are the same as for the classical ﬁnite-dimensional VAR case - except for the number of cointegrating relations being inﬁnite.

Citations:

Beare, B.K. and W.-K. Seo (2020): “Representation of I(1) and I(2) Autoregressive Hilbertian Processes”, Econometric Theory, Volume 36, Issue 05, October 2020, 773-802.

Franchi, M. and P. Paruolo (2020): “Cointegration in Functional Autoregressive Processes”, Econometric Theory, Volume 36, Issue 05, October 2020, 803-839.

**Source:**Source: Econometric Theory