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We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. 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 holds significant importance across various scientific disciplines, including finance, physics, and engineering. We harnessed efficient process generators to provide high-quality synthetic training data, enabling the training of scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models. Our neural models outperform conventional statistical methods, even those augmented with neural networks. The precision, speed, consistency, and robustness of our estimators are demonstrated through experiments involving fractional Brownian motion (fBm), the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process, and the fractional Ornstein-Uhlenbeck (fOU) process. We believe that our work will inspire further research in the field of stochastic process modeling and parameter estimation using deep learning techniques., Comment: 14 pages, 16 figures, https://github.com/aielte-research/LMSParEst

This research explores the reliability of deep learning, specifically Long Short-Term Memory (LSTM) networks, for estimating the Hurst parameter in fractional stochastic processes. The study focuses on three types of processes: fractional Brownian motion (fBm), fractional Ornstein-Uhlenbeck (fOU) process, and linear fractional stable motions (lfsm). The work involves a fast generation of extensive datasets for fBm and fOU to train the LSTM network on a large volume of data in a feasible time. The study analyses the accuracy of the LSTM network's Hurst parameter estimation regarding various performance measures like RMSE, MAE, MRE, and quantiles of the absolute and relative errors. It finds that LSTM outperforms the traditional statistical methods in the case of fBm and fOU processes; however, it has limited accuracy on lfsm processes. The research also delves into the implications of training length and valuation sequence length on the LSTM's performance. The methodology is applied by estimating the Hurst parameter in Li-ion battery degradation data and obtaining confidence bounds for the estimation. The study concludes that while deep learning methods show promise in parameter estimation of fractional processes, their effectiveness is contingent on the process type and the quality of training data.

A positive correlation between exposure and counterparty credit risk gives rise to the so-called Wrong-Way Risk (WWR). Even after a decade of the financial crisis, addressing WWR in both sound and tractable ways remains challenging. Academicians have proposed arbitrage-free set-ups through copula methods but those are computationally expensive and hard to use in practice. Resampling methods are proposed by the industry but they lack mathematical foundations. The purpose of this article is to bridge this gap between the approaches used by academicians and industry. To this end, we propose a stochastic correlation approach to asses WWR. The methods based on constant correlation to model the dependency between exposure and counterparty credit risk assume a linear dependency, thus fail to capture the tail dependence. Using a stochastic correlation we move further away from the Gaussian copula and can capture the tail risk. This effect is reflected in the results where the impact of stochastic correlation on calculated CVA is substantial when compared to the case when a high constant correlation is assumed between exposure and credit. Given the uncertainty inherent to CVA, the proposed method is believed to provide a promising way to model WWR.