On Kendall's Autocorrelations

Abstract

This brief article extends the theory of sample Kendall's autocorrelations by providing their exact variances at lags higher than one under the null hypothesis of randomness, by introducing and investigating their weighted modifications, and by numerical demonstration of these results and their usefulness.

Keywords:

• Autocorrelation
• Kendall's tau
• Serial rank coefficient

Mathematics Subject Classification:

• Primary 62M10
• Secondary 62G10

Acknowledgments

This research work of Miroslav Šiman was supported by Project 1M06047 of the Ministry of Education, Youth and Sports of the Czech Republic.

Notes

All the results are taken from Chapters 5 and 6 of the author's PhD thesis; see Šiman (2006).