zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Co-integration and error correction: Representation, estimation, and testing. (English) Zbl 0613.62140

The paper explores the relationship between co-integration and error correction models and develops estimation procedures and tests for co- integration. The components of the vector x t are co-integrated of order b,d, if all components of x t are integrated of order d and there exists a vector α (0) such that z t =α ' x t is integrated of order d-b, b>0. The vector α is called the co-integrating vector. Special emphasis is given to the case in which α ' x t =0. This situation has the immediate interpretation of a long-run equilibrium so that co-integration implies that deviations from equilibrium are stationary with finite variance despite of the fact that the series themselves are nonstationary and have infinite variances.

By use of the second author’s representation theorem [Co-integrated variables and error-correcting models. UCSD discussion paper 83-13 (1983)] the authors show how co-integrated systems are connected by moving average, autoregressive, and error correction representations. Furthermore, the authors present an asymptotically efficient two-step estimator. Testing for co-integration combines the problems of testing for unit roots and tests with parameters which are not identified under the null. Several test statistics are suggested and the critical values for these statistics obtained by a Monte Carlo simulation are given. The paper closes with some applications.

Reviewer: H.S.Buscher

MSC:
62P20Applications of statistics to economics
62M10Time series, auto-correlation, regression, etc. (statistics)
91B84Economic time series analysis