Log return of a Time Series

See also: Time series introduction, Time series in ModelRisk

If S(0) and S(t) are two consecutive observations for a series, the log return r(t) (also called the continuously compounded return) is defined as:

The advantage of looking at log returns of a series is that one can see relative changes in the variable and compare directly with other variables whose values may have very different base values. A similar measure of the relative change in the variable S over time t is the simple return R(t), defined as:

 

R(t) might seem a more intuitive description of relative change, but for a variety of reasons it is much easier to use r(t) in stochastic time series modeling. In any case, there is a simple correspondence between the two measures:

 

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