This article presents empirical information that links the daily highs and lows of the us dollar exchange rates applied to two other quoted currency pairs over a 15-year period. We find that the logarithmic maximum and the logarithmic minimum of the exchange rate are interrelated, and the duration of error correction is well approximated by a range, depending on how the difference between the logarithmic maximum and the logarithmic minimum is. Then we evaluate the empirical significance of the joint analysis of the highs, lows and ranges by comparing the forecasts of the ranges obtained based on the cointegration structures with the forecasts obtained based on the specifications of the random walk and the autoregressive integrated moving average (arima). The ability of range forecasts as predictors of implied volatility for a european-style currency option is also evaluated. Our results demonstrate that, apart from a limited set of exceptions, the cointegration structure, however, currency rates and converter surpasses the random walk and arima models in this out-of-sample prediction test.
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