Advances in Financial Machine Learning

CHAPTER 5 Fractionally Differentiated Features

5.1 Motivation

It is known that, as a consequence of arbitrage forces, financial series exhibit low signal-to-noise ratios (López de Prado [2015]). To make matters worse, standard stationarity transformations, like integer differentiation, further reduce that signal by removing memory. Price series have memory, because every value is dependent upon a long history of previous levels. In contrast, integer differentiated series, like returns, have a memory cut-off, in the sense that history is disregarded entirely after a finite sample window. Once stationarity transformations have wiped out all memory from the data, statisticians resort to complex mathematical techniques to extract whatever residual signal remains. Not surprisingly, applying these complex techniques on memory-erased series likely leads to false discoveries. In this chapter we introduce a data transformation method that ensures the stationarity of the data while preserving as much memory as possible.

5.2 The Stationarity vs. Memory Dilemma

It is common in finance to find non-stationary time series. What makes these series non-stationary is the presence of memory, i.e., a long history of previous levels that shift the series' mean over time. In order to perform inferential analyses, researchers need to work with invariant processes, such as returns on prices (or changes in log-prices), changes in yield, or changes in volatility. These data transformations make the ...