  Data normalization is one of the most important preprocessing steps when
building a machine learning model, especially when the model of interest is a
deep neural network. This is because deep neural network optimized with
stochastic gradient descent is sensitive to the input variable range and prone
to numerical issues. Different than other types of signals, financial
time-series often exhibit unique characteristics such as high volatility,
non-stationarity and multi-modality that make them challenging to work with,
often requiring expert domain knowledge for devising a suitable processing
pipeline. In this paper, we propose a novel data-driven normalization method
for deep neural networks that handle high-frequency financial time-series. The
proposed normalization scheme, which takes into account the bimodal
characteristic of financial multivariate time-series, requires no expert
knowledge to preprocess a financial time-series since this step is formulated
as part of the end-to-end optimization process. Our experiments, conducted with
state-of-the-arts neural networks and high-frequency data from two large-scale
limit order books coming from the Nordic and US markets, show significant
improvements over other normalization techniques in forecasting future stock
price dynamics.
