×

zbMATH — the first resource for mathematics

A statistical analysis of cointegration for \(I(2)\) variables. (English) Zbl 1274.62597
Summary: This paper discusses inference for \(I(2)\) variables in a VAR model. The estimation procedure suggested consists of two reduced rank regressions. The asymptotic distribution of the proposed estimators of the cointegrating coefficients is mixed Gaussian, which implies that asymptotic inference can be conducted using the \(\chi^2\) distribution. It is shown to what extent inference on the cointegration ranks can be conducted using the tables already prepared for the analysis of cointegration of \(I(1)\) variables. New tables are needed for the test statistics to control the size of the tests. This paper contains a multivariate test for the existence of \(I(2)\) variables. This test is illustrated using a data set consisting of U.K. and foreign prices and interest rates as well as the exchange rate.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M07 Non-Markovian processes: hypothesis testing
62P20 Applications of statistics to economics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/0304-4076(92)90086-7 · Zbl 0850.62905
[2] Kitamura, Estimation of Cointegrated Systems with I(2) Processes (1994)
[3] DOI: 10.1016/0161-8938(92)90003-U
[4] DOI: 10.1002/jae.3950040508
[5] Granger, Long-Run Economic Relations. Readings in Cointegration (1991)
[6] Granger, Cointegrated variables and error correction models (1983)
[7] Engle, Long-Run Economic Relations. Readings in Cointegration pp 237–266– (1991)
[8] Engle, Econometrica 55 pp 251–276– (1987)
[9] DOI: 10.1214/aos/1176350711 · Zbl 0666.62019
[10] Berger, Journal of the American Statistical Association 79 pp 158–163– (1984)
[11] Anderson, Annals of Mathematical Statistics 22 pp 327–351– (1951)
[12] DOI: 10.2307/2289316 · Zbl 0663.62097
[13] DOI: 10.2307/2951763 · Zbl 0801.62097
[14] Johansen, Oxford Bulletin of Economics and Statistics 54 pp 383–397– (1992)
[15] Johansen, Macroeconomic Modeling of the Long Run pp 229–248– (1992)
[16] Johansen, Econometric Theory 8 pp 188–202– (1992) · Zbl 04508526
[17] Johansen, A Likelihood Analysis of the I(2) Model (1992) · Zbl 0923.62094
[18] DOI: 10.2307/2938278 · Zbl 0755.62087
[19] Johansen, An Algorithm for Estimating the Cointegration Relations in Vector Autoregressive Processes Allowing for I(2) Variables (1990)
[20] Johansen, Contemporary Mathematics 80 pp 359–386– (1988)
[21] Johansen, Journal of Economic Dynamics and Control 12 pp 231–254– (1998)
[22] Hall, Martingale Limit Theory and Its Applications (1980) · Zbl 0462.60045
[23] Gregoir, Econometric Theory 9 pp 329–342– (1993)
[24] DOI: 10.1214/aos/1176348666 · Zbl 0759.60021
[25] Phillips, Econometrica 59 pp 256–271– (1991)
[26] DOI: 10.1016/0047-259X(88)90039-5 · Zbl 0629.62091
[27] Paruolo, Asymptotic Efficiency of the 2 Step Estimator in I(2) VAR Systems (1994) · Zbl 1446.62247
[28] Paruolo, Testing for Multicointegration in a Two-Stage Analysis of I(2) Systems (1992)
[29] Pantula, Econometric Theory 5 pp 256–271– (1989)
[30] Johansen, Oxford Bulletin of Economics and Statistics 52 pp 169–210– (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.