Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T04:16:15.439Z Has data issue: false hasContentIssue false
  • English
  • Français

POWER FUNCTIONS AND ENVELOPES FOR UNIT ROOT TESTS

Published online by Cambridge University Press:  31 January 2003

Ted Juhl  and
Zhijie Xiao
Ted Juhl
Affiliation:
University of Kansas
Zhijie Xiao
Affiliation:
University of Illinois at Urbana-Champaign
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies power functions and envelopes for covariate augmented unit root tests. The power functions are calculated by integrating the characteristic function, allowing accurate evaluation of the power envelope and the power functions. Using the power functions, we study the selection among point optimal invariant unit root tests. An “optimal” point optimal test is proposed based on minimizing the integrated power difference. We find that when there are covariate effects, optimal tests use a local alternative where the power envelope has an approximate value of 0.75.We thank Pentti Saikkonen and two referees for helpful comments.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 2 , April 2003 , pp. 240 - 253
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Cox, D.R. & D.V. Hinkley (1974) Theoretical Statistics. London: Chapman and Hall.
Elliott, G. & M. Jansson (2000) Testing for Unit Roots with Stationary Covariates. Working paper, University of California, San Diego.
Elliott, G., T.J. Rothenberg, & J.H. Stock (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.CrossRefGoogle Scholar
Girsanov, I.V. (1960) On transforming a certain class of stochastic processes by absolutely continuous substitution of measures. Theory of Probability and Its Applications, 5, 285–301.CrossRefGoogle Scholar
Gurland, J. (1948) Inversion formulae for the distribution of ratios. Annals of Mathematical Statistics 19, 228–237.CrossRefGoogle Scholar
Hansen, B.E. (1995) Rethinking the univariate approach to unit root testing. Econometric Theory 11, 1148–1171.CrossRefGoogle Scholar
King, M. (1983) Testing for moving average regression disturbances. Australian Journal of Statistics 25, 23–34.CrossRefGoogle Scholar
King, M. (1988) Towards a theory of point optimal testing. Econometric Reviews 6, 169–218.Google Scholar
Nabeya, S. & K. Tanaka (1990) Limiting powers of unit-root tests in time-series regression. Journal of Econometrics 46, 246–271.CrossRefGoogle Scholar
Nelson, C.R. & C. Plosser (1982) Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics 10, 139–162.CrossRefGoogle Scholar
Perron, P. (1991) A continuous time approximation to the unstable first-order autoregressive process: The case without an intercept. Econometrica 59, 211–236.CrossRefGoogle Scholar
Saikkonen, P. & R. Luukkonen (1993) Point optimal tests for testing the order of differencing in ARIMA models. Econometric Theory 9, 343–362.CrossRefGoogle Scholar
Tanaka, K. (1996) Time Series Analysis. New York: Wiley.