# Temporal Logistic Neural Bag-of-Features for Financial Time series Forecasting leveraging Limit Order Book Data

## TL;DR

This paper introduces a novel Temporal Logistic Neural Bag-of-Features method that enhances deep learning models for financial time series forecasting, effectively handling high-dimensional, non-stationary data with improved stability and adaptability.

## Contribution

The paper proposes a new adaptive scaling mechanism and logistic kernel-based density estimation to improve BoF models for deep neural networks in time series analysis.

## Key findings

- Effective on large-scale financial data with over 4 million limit orders.
- Outperforms traditional BoF models in stability and accuracy.
- Demonstrates robustness to non-stationary feature distributions.

## Abstract

Time series forecasting is a crucial component of many important applications, ranging from forecasting the stock markets to energy load prediction. The high-dimensionality, velocity and variety of the data collected in these applications pose significant and unique challenges that must be carefully addressed for each of them. In this work, a novel Temporal Logistic Neural Bag-of-Features approach, that can be used to tackle these challenges, is proposed. The proposed 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. 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.