Article thumbnail

Nonparametric cointegration analysis

By H.J. Bierens


In this paper we propose consistent cointegration tests, and estimators of a basis of the space of cointegrating vectors, that do not need specification of the data-generating process, apart from some mild regularity conditions, or estimation of structural and/or nuisance parameters. This nonparametric approach is in the same spirit as Johansen s LR method in that the test statistics involved are obtained from the solutions of a generalized eigenvalue problem, and the hypotheses to be tested are the same, but in our case the two matrices in the generalized eigenvalue problem involved are constructed independently of the data-generating process. We compare our approach empirically as well as by a limited Monte Carlo simulation with Johansen s approach, using the series for ln(wages) and ln(GNP) from the extendeStatistical Methods;cointegration;unit root;Testing;statistics

OAI identifier:

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

Suggested articles


  1. (1909). 63Table A.9: Johansen’s test results for the number (r) of cointegrating vectors: intercept and time trend present, with cointegration restrictions on the trend parameters imposed test crit. val. conclusions: test table(*) p r stat.
  2. (1993). A note on Johansen’s cointegration procedure when trends are present,
  3. (1995). Aspects of estimation of cointegrated time series,
  4. (1990). Asymptotic properties of residual based tests for cointegration,
  5. (1992). Asymptotics for linear processes,
  6. (1989). Cointegrated economic time series: a survey with new results, mimeo,
  7. (1987). Cointegration and error correction: representation, estimation, and testing,
  8. (1968). Convergence of probability measures
  9. (1983). Distribution of eigenvalues in multivariate statistical analysis,
  10. (1993). Efficient inference on cointegrating parameters in structural error correction models, to appear in
  11. (1991). Estimation and hypothesis testing of cointegrated vectors in Gaussian vector autoregressive models,
  12. (1994). Finite sample properties of likelihood ratio tests for cointegrating ranks when linear trends are present,
  13. (1987). Forecasting and testing in cointegrated systems,
  14. (1993). Higher-order sample autocorrelations and the unit root hypothesis,
  15. (1995). Impulse response analysis in cointegrated 31processes, mimeo,
  16. (1990). Inference in linear time series models with some unit roots,
  17. (1994). It follows from Lemma 9.6.3 in Bierens
  18. (1980). Martingale limit theory and its applications
  19. (1990). Maximum likelihood estimation and inference on cointegration: with applications to the demand for money,
  20. (1973). Numerical methods for scientists and engineers
  21. (1991). On Bayesian routes to unit roots,
  22. (1987). On the theory of cointegrated economic time series, Invited paper presented at the Econometric Society European Meeting
  23. (1991). Optimal inference in cointegrated systems,
  24. (1994). Proof of Lemma 2: Let F be a typical function Fk, with derivative f, and let x be a cointegrating vector. Using Lemma 9.6.3 in Bierens
  25. (1981). Some properties of time series and their use in econometric model specification,
  26. (1988). Statistical analysis of cointegrated vectors,
  27. (1988). Testing for a unit roots in time series regression,
  28. (1994). Testing for an unstable root in conditional and structural error correction models",
  29. (1988). Testing for common trends,
  30. (1990). Testing for unit root and cointegration by variable addition,
  31. (1993). Testing stationarity and trend stationarity against the unit root hypothesis,
  32. (1994). The role of the constant and linear terms in cointegration analysis of nonstationary variables,
  33. This completes the proof of the second part of Lemma 9. The proof of the first part goes similarly. Q.E.D. 51TABLES Table A.1: Fractiles of the lambda-min test statistic: q-r m 20
  34. (1987). Time series regression with unit roots,
  35. (1994). Topics in advanced econometrics: estimation, testing, and specification of cross-section and time series models (Cambridge, U.K.:
  36. (1982). Trends and random walks in macroeconomic time series,