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This article considers the use of the long memory volatility process, FIGARCH, in representing Deutschemark - US dollar spot exchange rate returns for both high and low frequency returns data. The FIGARCH model is found to be the preferred specification for both high frequency and daily returns data, with similar values of the long memory volatility parameter across frequencies, which is indicative of returns being generated by a self similar process. The BDS test for non-linearity is applied to the residuals of the model for the high frequency returns. No evidence is found to suggest that the procedure for filtering the high frequency returns to remove the intraday periodicity has induced any non-linearities in the residuals; and the FIGARCH specification is found to be adequate.

High Frequency Deutsche Mark-US Dollar Returns: FIGARCH Representations and Non Linearities