CUSUM: A Test for Model Constancy (Stationarity)
A description of this test can be found in:
Bos, T., and T. A. Fetherston. 1992.
Market Model Nonstationarity in the Korean Stock
Market. pp. 287-301 in Pacific-Basin Capital Markets Research,
Vol. 3, edited by S. G. Rhee and R. P. Chang. Elsevier Science Publishers B. V. (North-Holland), Amsterdam.
Bos, T., T. A. Fetherston, and C. H. Yang. 1994. Regression-Free Testing of the
Efficiency of T-Bill Markets in Japan and the U.S.. pp. 131-153 in Studies in International Business and Finance, Vol. 11A, edited by T. Bos and T. A.
Fetherston, JAI Press
Inc., Greenwich, Connecticut.
Excel 5.0 Visual Basic Macros
These can be run by anyone with Excel 5.0
- Use QSUMZ.xls to conduct the Bos-Fetherston
test of whether your time series has a constant average of zero, and a constant variance.
- An example of the usage of this test is when one wishes to test whether the return on a mutual fund is equal to the average return of a mutual fund group over time, except for random variations which have a constant variance.
- Use QSUMX.xls to conduct the Bos-Fetherston
test of whether your time series has a constant average, and a constant variance.
- An example of the usage of this test is when one wishes to test whether the difference
between the return of a particular bond and a risk-free bond (in other words, the risk differential)
is constant over time, except for random variations which have a constant variance.
For the Bos-Fetherston CUSUM test:
Critical number of crossings = 0.17772 + 0.31636 (total number of recursive residuals)
For the Bos-Fetherston CUSUM of Squares test:
Critical number of crossings = 0.26275 + 0.24779 (total number of recursive residuals)
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