In this paper, we test if stock index prices follow random walks in the Spanish Stock Market by means of variance ratios. We find strong evidence of positive autocorrelation for both IGBM and IBEX35 daily returns until 1977, but not after that date. Although weekly and monthly index positive autocorrelations are not significant during the years 1972-2002, there is significant positive monthly cross-correlation between portfolios based on size. In particular, large stock portfolios seem to lead to the small stock ones.
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