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. 2021 Apr 30;23(5):560.
doi: 10.3390/e23050560.

Entropy Based Student's t-Process Dynamical Model

Ayumu Nono  1 , Yusuke Uchiyama  2 , Kei Nakagawa  3
Affiliations

Entropy Based Student's t-Process Dynamical Model

Ayumu Nono et al. Entropy (Basel). .

Abstract

Volatility, which represents the magnitude of fluctuating asset prices or returns, is used in the problems of finance to design optimal asset allocations and to calculate the price of derivatives. Since volatility is unobservable, it is identified and estimated by latent variable models known as volatility fluctuation models. Almost all conventional volatility fluctuation models are linear time-series models and thus are difficult to capture nonlinear and/or non-Gaussian properties of volatility dynamics. In this study, we propose an entropy based Student's t-process Dynamical model (ETPDM) as a volatility fluctuation model combined with both nonlinear dynamics and non-Gaussian noise. The ETPDM estimates its latent variables and intrinsic parameters by a robust particle filtering based on a generalized H-theorem for a relative entropy. To test the performance of the ETPDM, we implement numerical experiments for financial time-series and confirm the robustness for a small number of particles by comparing with the conventional particle filtering.

Keywords: Student’s t-process; entropy based particle filter; finance; relative entropy; volatility fluctuation.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Overview of estimation results in 1-min chart.
Figure 2
Figure 2
Overview of estimation results in 30-min chart.
Figure 3
Figure 3
Overview of estimation results in 1-h chart.
Figure 4
Figure 4
Estimated log-likelihoods of (a) the cp-GARCH, the cp-TPDM and (b) the ETPDM.
Figure 5
Figure 5
Effective particle rates of (a) cp-GARCH, the cp-TPDM and (b) the ETPDM.
Figure 6
Figure 6
Log-likelihoods of the cp-TPDM and the ETPDM in (a) low volatility window and (b) high volatility one.
See this image and copyright information in PMC

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