Approximated maximum likelihood estimation in multifractal random walks

TL;DR

This paper introduces an approximate maximum likelihood method for multifractal random walks, utilizing Laplace approximation and dependency truncation, implemented in R, and tested on synthetic and financial data.

Contribution

It develops a novel approximate maximum likelihood estimation technique for multifractal processes, enhancing inference accuracy and computational efficiency.

Findings

The method performs well on synthetic data.

It provides reliable parameter estimates for financial indices.

Compared favorably to generalized method of moments.

Abstract

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.