Measuring multiscaling in financial time-series

TL;DR

This paper investigates the origins of multiscaling in financial time-series, proposing a methodology to distinguish sources of multifractality and highlighting how aggregation horizon biases can affect measurements.

Contribution

It introduces a method to separate different sources of multifractality in financial data using synthetic time-series analysis.

Findings

Aggregation horizon influences multifractality measures.

Power law tails with exponents [2,5] significantly bias results.

Proper aggregation horizon can mitigate bias.

Abstract

We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of synthetic time-series with known properties. We use the results from the synthetic time-series to interpret the measure of multifractality of real log-returns time-series. The main finding is that the aggregation horizon of the returns can introduce a strong bias effect on the measure of multifractality. This effect can become especially important when returns distributions have power law tails with exponents in the range [2,5]. We discuss the right aggregation horizon to mitigate this bias.