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

a r t i c l e i n f o Keywords: Fractional cointegration Long memory Range Volatility Daily high and low 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. 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. Daily high and low stock market prices provide valuable information about range-based volatility that is not included in the open and close prices commonly studied by researchers. More specifically, the difference between high and low prices, i.e., the range, provides an efficient es-timator of volatility robust to noise (Parkinson, 1980). To date, stock prices in developed markets have generally been considered to be unpredictable and are assumed to follow a random walk. Hence, most studies consider stock prices to be integrated of order 1 (an I(1) process). However, the choice between stationary I(0) and non-stationary I(1) processes can be too restrictive for the degree of integration of daily high and low prices. Because high and low prices can be modeled together as a possibly fractionally cointegrated relationship (Cheung, 2007; Fiess and MacDonald, 2002), it allows for greater flexibility. This idea is especially interesting because the error correction term from the cointegrating relationship between high and low prices is the range. Hence, a more general fractional or long-memory framework, where the series are assumed to be integrated of order d and cointegrated of …