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

Staff - Faculty of Informatics

Date: 15 April 2019 / 15:30 - 17:00

USI Lugano Campus, room SI-003, Informatics building (Via G. Buffi 13)

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)