# A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration

@article{Shin1994ART, title={A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration}, author={Yongcheol Shin}, journal={Econometric Theory}, year={1994}, volume={10}, pages={91 - 115} }

This paper proposes a residual-based test of the null of cointegration using a structural single equation model. It is shown that the limiting distribution of the test statistic for cointegration can be made free of nuisance parameters when the cointegrating relation is efficiently estimated. The limiting distributions are given in terms of a mixture of a Brownian bridge and vector Brownian motion. It is also shown that this test is consistent. Critical values are given for standard, demeaned…

## 501 Citations

A Test for the Null of Multiple Cointegrating Vectors

- Mathematics
- 2013

This paper examines a test for the null of cointegration in a multivariate system based on the discrepancy between the OLS estimator of the full set of n cointegrating relationships in the n + k…

Testing the Null of Cointegration with Structural Breaks

- Mathematics, Economics
- 2006

In this paper we propose an LM-Type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vector.…

Testing for Cointegration in a System of Equations

- MathematicsEconometric Theory
- 1995

This paper introduces various consistent tests for the null of cointegration against the alternative of noncointegration that can be applied to a system of equations as well as to a single equation.…

Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics

- Mathematics, Economics
- 2004

A Lagrange multiplier test of the null hypothesis of cointegration in fractionally cointegrated models is proposed. The test statistic uses fully modified residuals to cancel the endogeneity and…

Test for the null hypothesis of cointegration with reduced size distortion

- Mathematics, Economics
- 2008

Abstract. This article considers a single‐equation cointegrating model and proposes the locally best invariant and unbiased (LBIU) test for the null hypothesis of cointegration. We derive the local…

The Fourier approximation and testing for the null of cointegration

- Economics
- 2016

In this paper, we propose a test to investigate the null of cointegration allowing for structural breaks of unknown form in deterministic trend by using the Fourier form. The test is developed on the…

A MULTIVARIATE TEST OF THE NULL OF COINTEGRATION USING COVARIATES

- Mathematics, Economics
- 2004

A multivariate test for stationarity is proposed in this paper. We develop Lagrange Multiplier type tests based on using additional stationary covariates. We show that the tests can be used to…

Testing for the Null Hypothesis of Cointegration with a Structural Break

- Mathematics, Economics
- 2005

In this paper we propose residual-based tests for the null hypothesis of cointegration with a structural break against the alternative of no cointegration. The Lagrange Multiplier (LM) test is…

## References

SHOWING 1-10 OF 41 REFERENCES

Parameter constancy in cointegrating regressions

- Mathematics, Economics
- 1993

This paper proposes an approach to testing for coefficient stability in cointegrating regressions in time series models. The test statistic considered is the one-sided version of the Lagrange…

Tests for Parameter Instability in Regressions with I(1) Processes

- Mathematics
- 1992

This article derives the large-sample distributions of Lagrange multiplier (LM) tests for parameter instability against several alternatives of interest in the context of cointegrated regression…

An Alternative Approach to the Asymptotic Theory of Spurious Regression, Cointegration, and Near Cointegration

- Economics, MathematicsEconometric Theory
- 1993

An alternative approach is taken to the asymptotic theory of cointegration. The present approach gives a different expression for the limiting distributions of statistics associated with…

Asymptotic Properties of Residual Based Tests for Cointegration

- Mathematics
- 1990

This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript "alpha") and Z(subscript "t")…

Canonical Cointegrating Regressions

- Economics, Mathematics
- 1992

A new procedure for statistical inference in cointegrating regressions is developed. The author introduces canonical cointegrating regressions (regressions formulated with the transformed data). The…

Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models

- Mathematics, Economics
- 1991

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic…

Co-integration and error correction: representation, estimation and testing

- Economics
- 1987

The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of…

Optimal Inference in Cointegrated Systems

- Mathematics
- 1991

Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate…

Testing for a Unit Root in Time Series Regression

- Mathematics, Economics
- 1986

This Paper Proposes Some New Tests for Detecting the Presence of a Unit Root in Quite General Time Series Modesl. Our Approach Is Nonparametric with Respect to Nuisance Parameters and Thereby Allows…

Spectral Regression for Cointegrated Time Series

- Mathematics
- 1988

This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including efficient and band spectral…