Self-Excited Multifractal Dynamics

Abstract

We introduce the self-excited multifractal (SEMF) model, defined such that the amplitudes of the increments of the process are expressed as exponentials of a long memory of past increments. The principal novel feature of the model lies in the self-excitation mechanism combined with exponential nonlinearity, i.e. the explicit dependence of future values of the process on past ones. The self- excitation captures the microscopic origin of the emergent endogenous self-organization properties, such as the energy cascade in turbulent flows, the triggering of aftershocks by previous earthquakes and the "reflexive" interactions of financial markets. The SEMF process has all the standard stylized facts found in financial time series, which are robust to the specification of the parameters and the shape of the memory kernel: multifractality, heavy tails of the distribution of increments with intermediate asymptotics, zero correlation of the signed increments and long-range correlation of the squared increments, the asymmetry (called "leverage" effect) of the correlation between increments and absolute value of the increments and statistical asymmetry under time reversal.

References in corpus (11)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Multifractality in Human Heartbeat Dynamics
• A multifractal random walk
• The leverage effect in financial markets: retarded volatility and market panic
• Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''
• Log-infinitely divisible multifractal processes
• Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
• Multifractal Scaling of Thermally-Activated Rupture Processes
• Volatility of Linear and Nonlinear Time Series
• Free Decay of Turbulence and Breakdown of Self-Similarity
• Generic Multifractality in Exponentials of Long Memory Processes

Cited by in corpus (9)

• Multifractal analysis of financial markets
• Dependency Structure and Scaling Properties of Financial Time Series Are Related
• Field master equation theory of the self-excited Hawkes process
• Ubiquitous power law scaling in nonlinear self-excited Hawkes processes
• Theory of earthquakes interevent times applied to financial markets
• Exact asymptotic solutions to nonlinear Hawkes processes: a systematic classification of the steady-state solutions
• Power law scaling and "Dragon-Kings" in distributions of intraday financial drawdowns
• The Reactive Volatility Model
• Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models