Many methods have been proposed to analyze and forecast time series data. There are different neural network variants for particular tasks, for example, convolutional neural networks for image recognition and recurrent neural networks for time series analysis. Time series forecasting is a crucial component of many important applications, ranging from forecasting the stock markets to energy load prediction. Furthermore, some research has compared deep learning with time series models for predicting time series data. Deep learning techniques for time series data, especially those using long short-term memory (LSTM) models, have shown s results than previous machine learning techniques in different tasks. Among them sentimental analysis, and time series prediction, speech recognition. In recent times, deep learning methods (especially time series analysis) have performed outstandingly for various industrial problems, with better prediction than machine learning methods. Time series forecasting, especially with machine learning techniques is a crucial component of predicting the behavior of financial markets. Moreover, many researchers have used deep learning methods to predict financial time series with various models in recent years.

The large amount of data is collected, what provide an unprecedented opportunity for applying powerful deep learning methods.  Artificial neural networks (ANNs) with multiple hidden layers have become successful machine learning methods to extract features and detect patterns from a large data set. Now the interest is gradually shifting toward using neural network-based methods, including RNN, LSTM and CNN.  It is well-known that ANNs can approximate nonlinear functions and can thus be used to approximate solutions to PDEs. Recent advances in data science have shown that using deep learning techniques even highly nonlinear multi-dimensional functions can be accurately represented.

Trend prediction

Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena. Predicting the trends of financial markets is one of the most important tasks for investors. Many have tried to predict stock market trends using methods such as technical and fundamental analysis. Technical analysis is a traditional method that uses historical stock prices and trading volumes to determine the trends of future stock movements. Fundamental analysis predicts stock prices by using intrinsic values. When using this method, stock values are determined by financial news, market sentiments and economic factors; investors estimate the profits of firms and evaluate whether they are suitable for investment.   In  paper  Lagged correlation-based deep learning for directional trend change prediction in  nancial time series authors proposed the use of deep neural networks that employ step-wise linear regressions with exponential smoothing in the preparatory feature engineering for this task, and apply this method to historical stock market data S&P 500 from 2011 to 2016.

Deep classication model process
Schematic depiction of the gradient calculation and deep classi cation model process (taken from  https://arxiv.org/abs/1811.11287).

They test the hypothesis that deep feedforward neural networks, combined with exponential smoothing for the training inputs, are suitable for learning lagged correlations between the step-wise trends of a large number of time series, and that such models can be successfully applied to current research on real-world forecasting problems. The results demonstrate the viability of the proposed approach, with state-of-the-art accuracies and accounting for the statistical significance of the results for additional validation, as well as important implications for modern financial economics. The experiments that are conducted for this purpose demonstrate the viability of this approach by predicting price trend changes with an accuracy above given market baselines and within a stringent statistical validation framework.

 

Volatility analysis

In paper A deep neural network perspective on pricing and calibration in (rough) volatility models scientists presented a consistent neural network based calibration method for a number of volatility models, including the rough volatility family, that performs the calibration task within a few milliseconds for the full implied volatility surface. Authors highlight how this perspective opens new horizons for quantitative modelling: The calibration bottleneck posed by a slow pricing of derivative contracts is lifted. This brings several model families (such as rough volatility models) within the scope of applicability in industry practice. As customary for machine learning, the form in which information from available data is extracted and stored is crucial for network performance.

Average calibrations times for all models using gradient-based optimizers
Average calibrations times for all models using gradient-based optimizers (from https://arxiv.org/abs/1901.09647)

They present specific architectures for price approximation and calibration and optimize these with respect different objectives regarding accuracy, speed and robustness. Authors report that including the intermediate step of learning pricing functions of (classical or rough) models before calibration significantly improves network performance compared to direct calibration to data.

In paper entitled Temporal Logistic Neural Bag-of-Features for Financial Time series Forecasting leveraging Limit Order Book Data a novel Temporal Logistic Neural Bag-of-Features approach, that can be used to tackle these challenges is proposed. The method can be effectively combined with deep neural  networks, leading to powerful deep learning models for time series analysis. However, combining existing BoF formulations with deep feature extractors pose significant challenges: the distribution of the input features is not stationary, tuning the hyper-parameters of the model can be especially difficult and the normalizations involved in the BoF model can cause significant instabilities during the training process. The proposed method is capable of overcoming these limitations by a employing a novel adaptive scaling mechanism and replacing the classical Gaussian-based density estimation  involved in the regular BoF model with a logistic kernel.

Temporal Logistic Neural BoF (TLo-NBoF) architecture for time series forecasting
Temporal Logistic Neural BoF (TLo-NBoF) architecture for time series
forecasting (from https://arxiv.org/abs/1901.08280)

The effectiveness of the proposed approach is demonstrated using extensive experiments on a large-scale financial time series dataset that consists of more than 4 million limit orders.

The paper  Pricing options and computing implied volatilities using neural networks proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way.

Improvement in the loss
The improvement in the loss, which is an indicator of the model performance (from https://arxiv.org/abs/1901.08943)

The approach is tested on three different types of solvers: the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly

In Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes scientists apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. They train neural network models under different number of layers, neurons per layer, and various different activation functions in order to find which combinations work better empirically. For training, they consider various different loss functions and optimization routines, and demonstrated that deep neural networks exponentially expedite option pricing compared to commonly used option pricing methods, which consequently make calibration and parameter estimation super-fast. In computational finance, it is critical to find a fast and accurate approximation for cases that there is no analytical solution. Some of these approaches could be very time-consuming and to possess a model that is accurate and fast in pricing is central. Hence, with its trained architecture the calculation of prices using neural networks both with and without feedback connections which mimic the idea of context or memory in the brain, becomes elementary and at the same time super-fast.

In  the last paper FINANCIAL SERIES PREDICTION USING ATTENTION LSTM authors compare various deep learning models for financial time series prediction.  They compared multilayer perceptron (MLP), one-dimensional convolutional neural networks (1D CNN), stacked long short-term memory (stacked LSTM), attention networks, and weighted attention networks. In particular, attention LSTM is not only used for prediction, but also for visualizing intermediate outputs to analyze the reason of prediction. Therefore, it was shown an example for understanding the model prediction intuitively with attention vectors.

Attention networks for KOSPI200 prediction
Attention networks for KOSPI200 prediction (from https://arxiv.org/abs/1902.10877)

Authors also analyzed time and factors, which lead to an easy understanding of why certain trends are predicted when accessing a given time series table.