Multiple Testing for No Cointegration Under Nonstationary Volatility

29 Pages Posted: 8 May 2018

See all articles by Matei Demetrescu

Matei Demetrescu

Goethe University Frankfurt - Faculty of Economics and Business Administration

Christoph Hanck

University of Dortmund - Department of Statistics

Date Written: June 2018

Abstract

With cointegration tests often being oversized under time‐varying error variance, it is possible, if not likely, to confuse error variance non‐stationarity with cointegration. This paper takes an instrumental variable (IV) approach to establish individual‐unit test statistics for no cointegration that are robust to variance non‐stationarity. The sign of a fitted departure from long‐run equilibrium is used as an instrument when estimating an error‐correction model. The resulting IV‐based test is shown to follow a chi‐square limiting null distribution irrespective of the variance pattern of the data‐generating process. In spite of this, the test proposed here has, unlike previous work relying on instrumental variables, competitive local power against sequences of local alternatives in 1/T‐neighbourhoods of the null. The standard limiting null distribution motivates, using the single‐unit tests in a multiple testing approach for cointegration in multi‐country data sets by combining P‐values from individual units. Simulations suggest good performance of the single‐unit and multiple testing procedures under various plausible designs of cross‐sectional correlation and cross‐unit cointegration in the data. An application to the equilibrium relationship between short‐ and long‐term interest rates illustrates the dramatic differences between results of robust and non‐robust tests.

Suggested Citation

Demetrescu, Matei and Hanck, Christoph, Multiple Testing for No Cointegration Under Nonstationary Volatility (June 2018). Oxford Bulletin of Economics and Statistics, Vol. 80, Issue 3, pp. 485-513, 2018, Available at SSRN: https://ssrn.com/abstract=3174999 or http://dx.doi.org/10.1111/obes.12214

Matei Demetrescu (Contact Author)

Goethe University Frankfurt - Faculty of Economics and Business Administration ( email )

Statistics and Econometric Methods
Frankfurt am Main
Germany

Christoph Hanck

University of Dortmund - Department of Statistics ( email )

D-44221 Dortmund
Germany

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