Abstract

We investigate the statistical properties of time-averaged fractional Brownian motion (fBm), which naturally arises in the modeling of time series subjected to averaging transformations. The main motivation comes from electricity markets, where daily prices are typically obtained by averaging high-frequency data. While fBm-based models are popular in modeling electricity prices, treating averaged prices as direct realizations of fBm is theoretically inconsistent. Instead, time-integrated versions of fBm should be used to accurately reflect the effects of averaging.

This seminar begins with an overview of electricity markets and an introduction to fractional Brownian motion (fBm) and its main characteristics. We then introduce the integral-mean process of fBm and analyze the impact of time-averaging on its properties. Using ergodic theory, we construct strongly consistent estimators for the Hurst parameter adapted to the averaged process and validate them through an extensive simulation study. Next, we extend our approach to linear combinations of two distinct timeaveraged fBm processes, again estimating the relevant parameters. Finally, we apply our methodology to empirical electricity spot price data and discuss potential future developments in this research area.

This is joint work with Yuliya Mishura, Stefania Ottaviano and Tiziano Vargiolu.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.

Seminario Dottorato