Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks

Balint Csanady, Lóránt Nagy, Dávid Kovács, Daniel Boros, Ivan Ivkovic, Dalma Tóth-Lakits, Laszlo Markus, András Lukács

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Keywords: Hurst parameter, Fractional Brownian motion, ARFIMA, Fractional Ornstein-Uhlenbeck processes, 1D convolutional neural networks, LSTM

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TL;DR: Deep neural networks for better Hurst exponent estimation in the cases of various stochastic processes.

Abstract: We present a pure deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long range dependence. Long memory parameters such as the Hurst exponent are critical in characterizing the long-range dependence, roughness, and self-similarity of stochastic processes. The accurate and fast estimation of these parameters is of paramount importance in various scientific fields, including finance, physics, and engineering. We harnessed efficient process generators to provide high-quality synthetic training data to train 1D Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) models. Our neural models outperform conventional statistical methods, even if the latter have neural network extensions. Precision, speed as well as consistency and robustness of the estimators are supported by experiments with fractional Brownian motion (fBm), the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process, and the fractional Ornstein-Uhlenbeck process (fOU). We believe that our work will inspire further research in the application of deep learning techniques for stochastic process modeling and parameter estimation.

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Submission Number: 8119