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Is oanda.com data trustworthy?

The prices are very different if you do not sample synchronously or if you take average prices as Oanda does (Go to http://www.oanda.com/convert/fxhistory get a rate and read the text at the bottom). For example the daily low of EUR/USD on 11/04 was around 1.1802 and the daily high around 1.1996 (194 basis points difference!).Hence both numbers - Oanda and Fed - you report above are "correct". Further if you look at correlations of increments between different sources and use the fact that there is almost no autocorrelation on each series it is not a surprise that there is low correlation between the returns of the different sources.

Best regards
Adrian