To be or not to be: Roughness or long memory in volatility?

2024/03/19 by Mikkel Bennedsen, Bennedsen, Mikkel, Kim Christensen +3 · 1 citation
Engineering · #Econometrics (econ.EM) #FOS: Economics and business #Fault Detection and Control Systems #Mathematical Finance (q-fin.MF)

paper · pdf · doi:10.48550/arxiv.2403.12653

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that have been proposed to describe the random log-spot variance of financial asset returns. A simulation study shows that it delivers good performance in these settings and improves upon a method-of-moments estimation. In an empirical investigation, we inspect the dynamic of an intraday measure of the spot log-realized variance computed with high-frequency data from the cryptocurrency market. The evidence supports a mechanism, where the short- and long-term correlation structure of stochastic volatility are decoupled in order to capture its properties at different time scales. This is further backed by an analysis of the associated spot log-trading volume.

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• M-estimation for Gaussian processes with time-inhomogeneous drifts from high-frequency data

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