School of Management, University of Liverpool, Chatham Street, Liverpool L69 3BX, UK.
A QUASI-LOCALLY MOST POWERFUL TEST FOR CORRELATION IN THE CONDITIONAL VARIANCE OF POSITIVE DATA
Article first published online: 15 MAR 2011
© 2011 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 53, Issue 1, pages 43–62, March 2011
How to Cite
McCabe, B. P. M., Martin, G. M. and Freeland, K. (2011), A QUASI-LOCALLY MOST POWERFUL TEST FOR CORRELATION IN THE CONDITIONAL VARIANCE OF POSITIVE DATA. Australian & New Zealand Journal of Statistics, 53: 43–62. doi: 10.1111/j.1467-842X.2010.00596.x
- Issue published online: 25 MAY 2011
- Article first published online: 15 MAR 2011
- locally most powerful test;
- asymptotic relative efficiency;
- durations data;
- gamma distribution;
- Weibull distribution
A test is derived for short-memory correlation in the conditional variance of strictly positive, skewed data. The test is quasi-locally most powerful (QLMP) under the assumption of conditionally gamma data. Analytical asymptotic relative efficiency calculations show that an alternative test, based on the first-order autocorrelation coefficient of the squared data, has negligible relative power to detect correlation in the conditional variance. Finite-sample simulation results confirm the poor performance of the squares-based test for fixed alternatives, as well as demonstrating the poor performance of the test based on the first-order autocorrelation coefficient of the raw (levels) data. The robustness of the QLMP test, both to misspecification of the conditional distribution and to misspecification of the dynamics, is also demonstrated using simulation. The test is illustrated using financial trade durations data.