Variance-ratio Statistics and High-frequency Data: Testing for Changes in Intraday Volatility Patterns


  • Torben G. Andersen,

  • Tim Bollerslev,

  • Ashish Das

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    • Department of Finance, J. L. Kellogg Graduate School of Management, Northwestern University (Andersen and Das) and Department of Economics, Duke University and NBER (Bollerslev). An earlier version of this paper circulated under the title “Testing for Microstructure Effects in Volatility: Revisiting the Tokyo Experiment.” This work is supported by a grant from the National Science Foundation to the NBER. We are also grateful to Olsen & Associates for making the intraday exchange rate quotations available, and to Mike Melvin for forwarding his version of the data. Finally, we acknowledge comments from brown bag seminar participants at Northwestern University and London School of Economics, Richard Lyons, a referee, and the editor René Stulz.


Variance-ratio tests are routinely employed to assess the variation in return volatility over time and across markets. However, such tests are not statistically robust and can be seriously misleading within a high-frequency context. We develop improved inference procedures using a Fourier Flexible Form regression framework. The practical significance is illustrated through tests for changes in the FX intraday volatility pattern following the removal of trading restrictions in Tokyo. Contrary to earlier evidence, we find nodiscernible changes outside of the Tokyo lunch period. We ascribe the difference to the fragile finite-sample inference of conventional variance-ratio procedures and a single outlier.