Nonparametric methods for nonstationary time series analysis with application to volatility modelling

You are cordially invited to attend the PhD Dissertation Defense of Ganna Marchenko on Monday April 15th, 2019 at 15:30 in room SI-003 (Informatics building).

Abstract:
Volatility modelling has important applications in risk management, asset pricing and portfolio optimization. The generalized autoregressive conditional heteroskedasticity (GARCH) models are considered to be the state-of-the-art techniques in modelling time-dependent volatility. Such models usually employ parametric assumptions about the data and model volatility as a function of its lagged values and past realizations of squared returns. This dissertation introduces a nonstationary approach for a data-driven modelling of time-dependent volatility under different memory assumptions. The proposed nonparametric method is based on extended Maximum Entropy principle and describes volatility as a persistent nonstationary signal under the assumption of conditionally independent observations. The proposed semi-parametric approach is a nonstationary extension of an ARCH model that allows modelling time-dependent volatility as a mixture of stationary ARCH processes. The unified numerical scheme allows for simultaneous identification of the optimal number of hidden regimes in data and their nonparametric regime-switching dynamic. The Lasso regularization allows for data-driven identification of the redundant parameters of the Maximum Entropy distributions and redundant lags in the memory of the ARCH processes. The empirical results demonstrate that deploying a nonparametric regime-switching process in the context of Maximum Entropy and ARCH problems leads to models that are able to reproduce the long memory property of the stock market returns and provide a better description of the data compared to the state-of-the-art conditional volatility GARCH models with respect to the log-likelihood and information criteria.

Dissertation Committee:

• Prof. Illia Horenko, Università della Svizzera italiana, Switzerland (Research Advisor)
• Prof. Patrick Gagliardini, Università della Svizzera italiana, Switzerland (Research co-Advisor)
• Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Olaf Schenk, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Carsten Hartmann, BTU Cottbus, Germany (External Member)
• Prof. Michael Rockinger, HEC Lausanne, Switzerland (External Member)