Apparent multifractality in financial time series

TL;DR

This paper introduces a solvable financial time series model that exhibits apparent multiscaling due to finite-scale effects, highlighting challenges in distinguishing true multifractality from artifacts in financial data.

Contribution

It presents a monofractal model that mimics multiscaling, revealing how finite-scale effects can produce apparent multifractality in financial time series.

Findings

Model reproduces long-range volatility correlations.

Apparent multiscaling arises from finite-scale crossover effects.

Challenges in differentiating true and apparent multifractality in data.

Abstract

We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is `monofractal' by construction, it shows apparent multiscaling as a result of a slow crossover phenomenon on finite time scales. Our results suggest that it might be hard to distinguish apparent and true multifractal behavior in financial data. Our model also leads to a new family of stable laws for sums of correlated random variables.