An empirical model of fractionally cointegrated daily high and low stock market prices

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), the U.K. Financial Times Stock Exchange (FTSE) 100, the U.S. Standard and Poor's (S&P) 500 and the Japanese Nihon Keizai Shimbun (NIKKEI) 225 during the 2003–2012 period, that is, before and during the financial crisis. We find that the ranges of all of the indices display long memory and are mostly in the non-stationary region, supporting the recent evidence that volatility might not be a stationary process. No common pattern is detected among all of the studied indices, and different behaviors are also observed in the pre-crisis and post-crisis periods. We conclude that the fractionally cointegrated VAR approach allowing for long memory is an interesting alternative for modelling range-based volatility.