Long memory and multifractality: A joint test

TL;DR

This paper investigates the statistical properties of tests for multifractality and long memory in asset returns, proposing a joint testing approach that improves accuracy, and applies it to currency exchange rate data.

Contribution

It introduces a joint test for long memory and multifractality, addressing over-rejection issues in conventional tests and providing more reliable analysis of financial time series.

Findings

Conventional tests over-reject in the presence of multifractality.

Most currency exchange rates are modeled well by multifractal processes without long memory.

No evidence of long memory was found in the analyzed exchange rate data.

Abstract

The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. In 11 cases, the exchange rate returns are accurately described by compounding a NIID series with a multifractal time-deformation process. There is no evidence of long memory.