Perspectives on full and fractional differencing of investment time series.

It is well known that asset prices are nonstationary, while most statistical models require the data to be (at least locally) stationary.

Hence, we must somehow preprocess the data to make it easier for our statistical models to learn.

A standard approach is to perform full differencing, for example, compute log returns.

In recent years, fractional differencing has been presented as an alternative that preserves “memory”.

One major issue with fractional differencing is that we cannot recover the original time series in full generality, only when we impose additional assumptions.

This creates severe disadvantages for investment simulation.

Another point missing from the fractional differencing argument is that we estimate our models on the entire training set, not just the last observation.

Good models should be able to capture market state and “memory” given the path of log returns, because the original time series is still encoded in those.

Fractional differencing might be useful in some applications, but it has its limitations. It is definitely not the solution to all your modeling problems :-)