This paper examines the statistical properties of the NSE-20 index in the Kenyan stock market over the period 2001 to 2009. The analysis applies both unit root tests and long-range dependence techniques based on the concept of fractional integration. The results indicate that the order of integration of stock prices is significantly above 1, which implies the presence of long memory. This is also detected in the absolute and squared returns. The lowest degrees of integration (very close to zero) are found for Mondays and Fridays, and therefore, a day-of-the-week-effect appears to be present.

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