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Debate on the stochastic behaviour of stock market returns, macroeconomic variables and their cointegrating residuals remains unsettled. This study examines the stochastic properties of the macroeconomic variables, stock market returns and their cointegrating residuals using an Autoregressive Fractionally Integrated Moving Average (ARFIMA) model. It also investigates Granger causality between the macroeconomic variables and stock market returns. The study uses monthly data from 1st January 1993 to 31st December 2015 drawn from the Nairobi Securities Exchange, Central Bank of Kenya, and Kenya National Bureau of Statistics. The results indicate that the 3-month Treasury Bills rate, lending rate, month-onmonth inflation rate, year-on-year inflation rate, exchange rate and stock market returns are fractionally integrated variables.