An Empirical Study of Neural Networks for Trend Detection in Time Series
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ORIGINAL RESEARCH
An Empirical Study of Neural Networks for Trend Detection in Time Series Alexandre Miot1 · Gilles Drigout1 Received: 2 June 2020 / Accepted: 2 October 2020 © Springer Nature Singapore Pte Ltd 2020
Abstract Even if trend is probably one of the most intuitive notions in time series dynamics, this notion is usually ambiguous and model dependent. We first cast the trend detection problem into a sequence-to-sequence classification problem. Then, we simulate various dynamics with labelled trends. Using those simulated time-series we build a baseline trend estimator showing good performance on various dynamics. Comparing this baseline estimator with various other trend estimators, we find that some recurrent neural networks structures compare favourably against other estimators including convolutional neural networks. Those sequence-to-sequence trend classifiers could be used as efficient basic blocks to build more complex time series estimators. Keywords Time series · Trend detection · Classifiers · Neural networks
Introduction A large number of times series, for example financial assets prices (see [18] or [25]), seem to exhibit “trends” and could be seen as the sum of a piecewise linear function -the trendand some noise like Yt = 𝜇(t) + 𝜖(t) with 𝜇(t) a trend process and 𝜖(t) a zero expectation noise process. Being able to identify the trend 𝜇 from the noise 𝜖 is of paramount importance in many domains like finance, economics, marketing... Writing 𝜇(t) = 𝜂t t , where 𝜂t ∈ ℝ , we will focus on trying to predict the sign of 𝜂t , sgn 𝜖 (𝜂t ) ∈ {−1, 0, 1}1 transforming the regression problem into a classification problem. Importantly, 𝜂t can change at each time step and time series data only becomes available as time passes. The main contributions of this article are: – defining the problem as sequence-to-sequence classification with online prediction and building suitably labelled datasets
* Alexandre Miot [email protected] Gilles Drigout [email protected] 1
Société Générale Corporate and Investment Banking, Nanterre, France
– on a simple case and using theory showing how some Recurrent Neural Networks (RNN) can detect trends – identifying empirically which basic building block estimators could be used to build efficient real world trend classifiers Our aim is not to build the “best” sequence-to-sequence classifier for a specific set of time series exhibiting trends. Indeed, in the light of [42] and [21], it seems to us that identifying building blocks that are generally good at this might be more useful. From theoretical and empirical considerations, we have a particular focus on RNNs. Yet, from [34, 38] or [43] for example, it is most likely that building more complex estimators for real life datasets using transfer learning (see [44] for a review) would also use attention mechanisms and convolution neural networks (CNN). After examining related works, we describe our general framework. We then define the time series dynamics used in our simulations. Next, we explore the use
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