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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Towards an Open Book Architecture for Deep Learning Networks: Data Properties and Network Architectures - Evidence from Time Series Analytics</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vera Fleißner</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kai Heinrich</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Michael Seifert</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>TU-Dresden</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>In the field of time series predictions there are effective and consistent inaccuracies which potentially cause wrong economic decisions. Neural networks are seen as a potential option to improve predictions and are already used in some cases. Nevertheless it is unclear so far for which kind of time series data the use of neural networks is the right choice but also what kind of neural networks are feasible for which data characteristics. The main goal of this researchin-progress paper is therefore to conduct a between different time series characteristics and network architectures by using a descriptive analysis based on an extensive literature review. This goal is a step towards developing design guidelines for (deep) neural networks in the context of time series analysis.</p>
      </abstract>
      <kwd-group>
        <kwd>time series</kwd>
        <kwd>deep learning</kwd>
        <kwd>neural network</kwd>
        <kwd>forecasting</kwd>
        <kwd>prediction</kwd>
        <kwd>survey</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        The field of time series prediction through intelligent systems using Artificial Neural
Networks (ANN) is steadily growing [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. A reason for that lies within the potential of
complex intelligent systems such as Long Term Short Memory (LSTM) or
Convolutional Neural Networks (CNN) to overcome shortcomings of traditional algorithms
such as the vast amount of statistical assumptions to model complex non-linear time
series [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        Neural Networks are especially popular in the field of Big Data Analytics and its
subsequent domains like Natural Language Processing (NLP) and Pattern Recognition,
often times ranking first in prediction quality for several benchmark datasets [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        When it comes to the task of time series prediction, neural networks have widely
been adopted for the task [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. However, time series can exhibit multiple characteristics
like non-linearity, noise of deterministic chaos that makes them hard to predict and
demands suitable models for certain characteristics to be caught. While time series
prediction is applied in many fields such as credit scoring, inflation analysis or stock
market prediction, it remains unclear (1) how those black box models catch certain inherent
characteristics of time series and (2) how they react to different problem and sample
characteristics like sample size or prediction window and (3) how they perform in terms
of prediction quality compared to other algorithms [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>Our main goal within the full research project is to present guidelines on deep
learning architectures based on time series data characteristics. Towards this goal we first
aim to reveal the research gap of intransparent behavior of deep learning algorithms in
the context of time series analysis. We therefore propose the following questions:

</p>
      <p>RQ1: What time series characteristics are usually present in the data when
using neural network architectures?</p>
      <p>RQ2: How do different architectures handle different characteristics?
Our paper is structured as follows: We first give some preliminaries on time series
characteristics in Section 2. After we described our research methodology in Section 3,
we present the results of our descriptive analysis in Section 4 in order to answer research
questions RQ1 and RQ2 in Sections 4.1 and 4.2 respectively. The paper closes with a
discussion and an outlook in Section 5.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Time Series Characteristics</title>
      <p>
        The most common characteristic in a time series is stationarity. We can assume a time
series as stationary when it has constant mean, variance and covariance for a given time
step  regardless of time  . When decomposing time series, we can yield a trend and a
seasonality component, if such effects are present in the current time series. If a time
series shows trends and seasonality they are not stationary, since they do not have
constant moments throughout the observation interval. Furthermore a time series can show
signs of non-linearity. Non-linearity can lead to small influences of big shocks and vice
versa. Influences in non-linear time series will also depend on the sign of the shock
effect [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Most of the time series data will show evidence of multiple characteristics
[
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. In addition to that, those characteristics might determine each other. In addition to
that, the prediction error grows with every additional prediction made upon a previous
value, since those values depend themselves on predictions rather than a real data point.
Further characteristics include anomalies and deterministic chaos behavior. Anomalies
can occur in several forms: Additive outlier effects one observation that lies within
normal range but does not reflect a correct value, might be caused by measure errors;
Innovation outlier effects several values (e.g., driving noise during an erroneous
interval); changing trend caused by a shock event in the data or a permanent level shift of
the measurement system (PLS). Dismissing anomalies can lead to significantly worse
and biased predictions [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Deterministic chaos as an additional source for seemingly
unpredictable randomness, while limiting long term prediction, can be facilitated in
short-term prediction models if detected correctly [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. Time series can also exhibit signs
of no deterministic stochastic process at all, which is evidence for the presence of a
noisy component. Noise, like many other characteristics is not an exclusive property
and can be mixed with deterministic parts, so that a time series can just show signs of
partial noise [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
    </sec>
    <sec id="sec-3">
      <title>Research methodology</title>
      <p>
        As a basis for our descriptive analysis we employ a systematic literature review [
        <xref ref-type="bibr" rid="ref10 ref11">10,
11</xref>
        ]. We derive constraints for the review from our RQ1 and RQ2. The technical
constraints of our literature review can be summarized as follows: Only peer-reviewed
journals were included; English is the written language of the paper; Papers are
accessible; List of databases: IEEE; Science Direct; AIS; Springer; JSTOR; Emerald; ACM;
Web of Science. The content constraints can be derived by the research questions: The
focus of the literature review was on application of approaches to time series analysis,
so that we excluded papers that were solely based on theoretical algorithm
introductions. We combined a group of search terms from three different topic areas: algorithm,
task and domain. The task and domain are given by “prediction” and “time series”
respectively. For the area of algorithm we compiled a list of commonly known methods
applied within the field of intelligent systems (e.g., neural networks, deep learning).
The summary of the search terms that were yielding at least one result can be found in
Table 1.
      </p>
      <p>We initially found 226 papers. After we applied the technical constraints and
removed duplicates 192 papers were left. We then filtered out papers with unsuitable non
numeric time series data (170 papers left) and removed papers that were not topic
relevant (e.g., no focus on intelligent systems) to our cause (135). In the next section we
conduct a descriptive analysis and first answering RQ1 in Section 4.1 and subsequently
RQ2 in Section 4.2</p>
    </sec>
    <sec id="sec-4">
      <title>Descriptive analysis and results</title>
      <sec id="sec-4-1">
        <title>Time Series Characteristics</title>
        <p>The majority of the found papers is published in the field of computer science. The
research goals of the papers can be divided into model comparison, prediction (new
problem), improve prediction (existing problem) and improve model. The improve
prediction task makes up the majority of the papers (51%), followed by the improve model
task (22%). The distribution of time series characteristics within the literature review
database is depicted in Fig. 1. We can see that non-linear time series are the subject of
a majority of papers along with trend and seasonal components.
# of results
113
93
5
4
5
226</p>
        <p>
          The different dataset sizes and their frequency of occurrence have a peak at around
500 data points, the majority of the studies does not extend into big data territory in
terms of volume. Only a small fraction of the studies use datasets with 10000
observations or more. This is particularly interesting when applying deep learning algorithms
that often times long for rather large training datasets. Considering the used algorithms
in the studies observed we used a taxonomy approach by [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ] to group them. First we
classified them by basic network architecture where we divide them up into classic
ANNs with standard activation functions (denoted “ANN”), ANNs with different
functions and different architectures (denoted “no ANN”), e.g., Ridge Polynomial or
Abductive Networks and hybrid methods consisting of at least a two stage approach
applying classic ANN and other methods, e.g., fuzzy functions (denoted “hybrid
method”). Secondly we divide them up due to their properties, where we distinguished
between modular networks (“modular”) that can easily be expanded using additional
layers, feedforward and feedbackward architectures, interlayer networks that allow
connections within each layer, convolutional networks and network architectures that
allow recurrence using time features. Since hybrid methods can both be related to
architecture as well as features (e.g., using hybrid activation functions), we added hybrid
to the distinction of properties as well. Fig. 2 shows the correlation between the two
distinction schemes (basic network architecture as blue, red and green bars vs.
properties on the x-axis). It can be derived from Fig 2. that some neural network properties
occur more often than others. While the property of modular networks is uniformly
distributed, networks that do not have a classical ANN as base network (no ANN) are
more frequently used to directly model time dependencies. The same applies to
feedbackward architectures, since they require special base networks in order to work
properly. We rarely see convolution or interlayer architectures in time series analysis,
although recent publications suggest that they are used more frequently now, due to
their ability to reduce dimensionality. Hybrid methods are used more often with classic
ANN based systems rather than with other base networks, since the added method most
of the time replaces the complex and different no ANN network.
4.2
        </p>
      </sec>
      <sec id="sec-4-2">
        <title>Dependencies of neural networks and time series characteristics</title>
        <p>Since in most cases from our literature review hybrid methods or special networks (no
ANN) are used to model time series features we depict the correlation between hybrid
modeling and no ANN with time series characteristics in Fig. 3. We clearly see that
with most of the features like chaos or non-stationary present, hybrid models are far
more often used, since standard ANNs are in some cases not able to achieve satisfactory
results by themselves but rather need another additional method that either precedes or
succeeds the application of the neural network. A special focus should also be given to
the time architectural features of ANNs (e.g., LSTM, RNN) and their over proportional
use when it comes to non-stationarity, chaos and especially noise. As in the classical
models like GARCH or ARIMA, the noise is most likely autocorrelated and therefore
has to be dealt with accordingly or otherwise it will be included into the model and will
introduce a prediction bias. Considering the two advanced ANN classes “no ANN“ and
“hybrid method”, it is apparent from the descriptive analysis, that some special
treatment of time series data is needed and that the data cannot simply be processed by an
out-of-the-box algorithm. When we look into the detailed algorithm classes of either
class, we find a variety of different methods like Ridge Polynomial or Abductive
Networks as well as fuzzy logic operators used as hybrid functions with classical ANNs
that do not correlate with time series features in this small literature sample.
Since time series data plays an increasingly large role in economic applications not only
in the finance sector but also in the context of event and process as well as failure data
in the context of Industry 4.0, the knowledge base is in need of guidelines on how to
design networks in order to handle certain types of time series with different
characteristics. Towards that notion, we conducted an extended literature review with regard to
time series characteristics and neural network architecture. We showed that several of
those characteristics are of great concern in the literature and that certain hybrid or
nonbase ANNs are built for special cases. However, there are is no correlation between
certain types of characteristics and those algorithms. This can be explained by the
special designs of hybrid functions and networks, such as wavelet networks that are
specifically designed and configured to deal with one particular problem. In general the
transparency on how different time series characteristics can be dealt with in the context
of neuronal networks remain foggy. As this work continues it will conduct extensive
benchmarking studies based on simulated and real time events in order to find useful
correlations between time series characteristics and neural network architecture in the
context of prediction problems.</p>
      </sec>
    </sec>
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