A wavelet analysis of long-range dependence based on the Hurst exponent is presented in this paper. Numerical comparisons are made against traditional estimators of the exponent based on R/S analysis. The estimator is used to perform an analysis of the long-range dependence in the capital market of a small transition economy (Slovenia). Results of the study suggest that the efficient market hypothesis may not hold for the observed capital market. Furthermore, results also suggest that the estimation of the exponent is sensitive to the frequencies of the data employed and to the sample period. Additionally, the format of the time series has an important impact on the results.