(eng): This work provides empirical support for the fractional cointegration relationship between daily high and low stock prices, allowing for the non-stationary volatility of stock market returns. The recently formalized fractionally cointegrated vector autoregressive (VAR) model is employed to explain both the cointegration dynamics between daily high and low stock prices and the long memory of their linear combination, i.e., the range. Daily high and low stock prices are of particular interest because they provide valuable information about range-based volatility, which is considered a highly efficient and robust estimator of volatility. We provide a comparison of the Czech PX index with other world market indices: the German Deutscher Aktienindex (DAX), U.K. Financial Times Stock Exchange (FTSE) 100, U.S. Standard and Poor’s (S&P) 500 and Japanese Nihon Keizai Shimbun (NIKKEI) 225 during the 2003-2012 period, that is, before and during the financial crisis.