When working with a single TimeSeries of Foreign Exchange price data (EUR/USD : OHLC) on a minute by minute level, is it better to use the % difference of the close vs the lognormal difference of the close?

When scaling up to use a basket of fx pairs, do the differences between the two become more prevalent?


closed as off-topic by LocalVolatility, Alex C, msitt, amdopt, Attack68 Aug 1 '18 at 16:57

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A practical hint is given by Campbell/Lo/MacKinlay p. 11f.:

When returns are measured over short intervals of time, and are therefore close to zero, the continuously compounded return on a portfolio is close to the weighted average of the continuously compounded returns on the individual asset [...]. Nonetheless it is common to use simple returns when a cross-section of assets is being studied [...] and continuously compounded returns whe the temporal behavior of returns is the focus of interest.

So as you are analyzing the temporal behavior, it is recommended to use lognormal differences. You may also look at this detailed answer for the advantages of log returns. Nevertheless, you have to be aware, that the simple return of a portfolio $R_p$ of $N$ asset returns $R_{it}$ with weight $w_i$ is not the weighted average of log-returns, i.e. the convenient weighting calculation $R_p = \sum_{i=1}^N{w_i*R_{it}}$ does not hold.


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