Low and high prices can improve covariance forecasts: The evidence based on currency rates

In this paper we introduce a new specification of the BEKK model, where its parameters are estimated with the use of closing and additionally low and high prices. In an empirical application, we show that the use of additional information related to low and high prices in the formulation of the BEKK model improved the estimation of the covariance matrix of returns and increased the accuracy of covariance and variance forecasts based on this model, compared with using closing prices only. This analysis was performed for the following three most heavily traded currency pairs in the Forex market: EUR/USD, USD/JPY, and GBP/USD. The main result obtained in this study is robust to the applied forecast evaluation criterion. This issue is important from a practical viewpoint, because daily low and high prices are available with closing prices for most financial series.