Semantically Enriching the Detrending Step of Time Series Analysis
Lucélia de Souza
1,2
, Maria Salete Marcon Gomes Vaz
2,3
and Marcos Sfair Sunye
2
1
Computer Science Department, State University of Center-West, Guarapuava, Paraná, Brazil
2
Informatics Department, Federal University of Paraná, Curitiba, Paraná, Brazil
3
Informatics Department, State University of Ponta Grossa, Ponta Grossa, Paraná, Brazil
Keywords: OWL Ontology, Modular Development, DBpedia, Nonstationary Time Series, Detrending Methods.
Abstract: In time series analysis, the trend extraction – detrending is considered a relevant step of preprocessing,
where occurs the transformation of nonstationary time series in stationary, that is, free of trends. Trends are
time series components that need be removed because they can hide other phenomena, causing distortions in
further processing. To helping the decision making, by researchers, about how and how often the time series
were detrended, the main contribution of this paper is semantically enriching this step, presenting the
Detrend Ontology (DO prefix), designed in a modular way, by reuse of ontological resources, which are
extended for modeling of statistical methods applied for detrending in the time domain. The ontology was
evaluated by experts and ontologists and validated by means of a case study involving real-world
photometric time series. It is described its extensibility for methods in time-frequency domain, as well as the
association, when applicable, of instances with linked open data from DBpedia semantic knowledge base.
As result of this paper, stands out the semantic enrichment of a relevant step of the analysis, contributing to
the scientific knowledge generation in several areas that analyze time series.
1 INTRODUCTION
Time series (Chatfield, 2004) are observational data,
obtained usually at regular intervals of time, in
several knowledge areas. Time series can present
four main components (Spiegel, 1985): seasonal,
cyclic, irregular (noise or aleatory) and trends.
The trend component is the focus of this
research, characterizing changes in the statistical
measures of the nonstationary time series (which
presenting trends), such as in the mean and/or
variance/covariance, constituting long term
movements. In the frequency domain, the trend is
considered as a low-frequency component (Chandler
and Scott, 2011).
Trends need be extracted from time series
because they can hide other phenomena, as well as,
if it does not occur the trend extraction step –
detrending (Alexandrov et al, 2012), large
distortions can occur in the further processing of
probability density, correlation and spectral
quantities, according to (Bendat and Piersol, 1986).
In an analysis process, usually, the time series
analysis consists of two phases (Wu et al, 2007),
preprocessing and analysis of data. In the
preprocessing phase, occurs the trend extraction
step, where several statistical methods can be
applied for its correction.
The semantic knowledge, by researchers, about
how and how often the stationary time series (free of
trends) were detrended is relevant to decision
making in an analysis process, as well as contributes
to the choose of other statistical methods that can be
applied for best results. However, the knowledge
about the applicability of detrending methods is not
always explicit and easy to interpret.
Time series can be semantically enriched using
metadata - data about data. Nevertheless, these are
free text and they can generate ambiguity in the
generated data, as well as they can be insufficient to
semantically enriching the detrending process.
Another way of generate semantic knowledge is
by means of Ontology Web Language - OWL
Ontologies in the Semantic Web context (Berners-
Lee et al, 2001) which allowing semantically to
enrich the time series, enabling logic inferences and
interoperability, contributing to the understanding of
the methods used and its applicability in the
algorithms.
The main contribution of this paper is to present
475
de Souza L., Marcon Gomes Vaz M. and Sunye M..
Semantically Enriching the Detrending Step of Time Series Analysis.
DOI: 10.5220/0005467504750481
In Proceedings of the 17th International Conference on Enterprise Information Systems (ICEIS-2015), pages 475-481
ISBN: 978-989-758-097-0
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
as the detrending step of time series analysis can be
semantically enriched by means of the definition of
an OWL domain ontology, developed from a
modular design, considering the reuse and the
extension of ontological resources, doing the
association with the DBpedia knowledge base
(DBpedia, 2015) and promoting semantic
interoperability.
The Detrend Ontology (DO) defined is combined
with the Time Series Provenance Ontology (de
Souza et al, 2014b) and with a provenance model for
generating information about time series
provenance, detrending methods and which agent
and processes were applied in time series (de Souza
et al, 2014a), contributing to improve the decision
making about a relevant step of time series analysis
(de Souza et al, 2014c).
Beyond this introduction, this paper presenting
more four sections. The second section describes the
theoretical foundation. The third section reports the
methodology and presents the main contribution of
this paper, describing the evaluation and validation
in a real-world case study and its extensibility. In the
fourth section are described and compared the
related works. Finally, are presented the conclusions
and future researches.
2 THEORETICAL FOUNDATION
Ontologies (Guarino, 1998) allow representing the
knowledge in a structured way, enabling logic
inferences by means of reasoners as Pellet; creation
of rules in Semantic Web Rule Language - SWRL
Language; and the development of queries in
SPARQL Protocol and Resource Description
Framework Query Language - SPARQL Language.
OWL is the language used for development of
ontologies in the Web, being used the OWL-DL
version, based on Descriptive Logic (DL).
An ontology is formed by classes, instances and
relationships. A class is a set of individuals or
instances, sharing commons characteristics. A
relationship allows the association between classes.
The association, when applicable, of instances
with the DBpedia knowledge base (DBpedia, 2015)
allows semantic interoperability and the generation
of more knowledge from the linked open data in the
Semantic Web.
Several detrending software using different
statistical methods can be used for trend extraction.
The time series analysis can be done using methods
in its usual domain, that is, in the time domain or, in
the frequency domain, where the trend component is
analysed on the all signal and information about
time domain are lost. Also the analysis can be in the
time-frequency domain, considering both domains
(Meinl, 2011).
One of possibilities for trend extraction is to use
statistical methods that allow its estimation, which is
extracted from time series. Among the methods that
can be used with this objective in time domain, stand
out the parametric methods, such as linear, nonlinear
or multiple regression analysis (Hair et al, 2010), or
nonparametric methods, such as nonparametric
regression, based on some form of time series
smoothing (Shumway and Stoffer, 2006). Other
methods used for its extraction include the use of
digital filters (Chandler and Scott, 2011).
3 DETREND ONTOLOGY
The Ontology Development 101 (Noy and
McGuinness, 2001) and Neon Methodology
(SuarézFigueroa et al, 2012) were used
complementarily for the development of the domain
ontology. The Neon Methodology allows the choice
of nine alternatives scenarios, including specific
scenarios to describe the reuse of ontologies and
semantic declaration, presenting detailed steps for
the development of the ontologies, as well as allows
the use of a modular design. For development of the
DO Ontology, besides of the Scenario 1, also were
used the Scenario 3 for reuse of ontological
resources and the Scenario 8 for its restructuring.
For its development, was considered the reuse of
semantic declarations from Semantic Web for Earth
and Environmental Terminology - SWEET
Ontology (SWEET, 2015) and the
StatisticalAnalysis Ontology (Statistical Analysis,
2015) was used and extended for modeling of other
detrending methods.
According to Neon Methodology, it was
elaborated the Ontology Requirements Specification
Document – ORSD, describing the ontology
proposal, scope, implementation language, users and
requisites. The competence questions were divided
in groups, including questions related with
parametric and non-parametric methods.
About the reuse of ontological resources, to
modeling of software and parameters, the following
ontologies were analysed: i. The Software Ontology
(SWO Ontology, 2014); ii. Core Software Ontology
(CSO Ontology, 2014); Core Ontology of Programs
and Software (Lando et al, 2009); EvoOnt - A
Software Evolution Ontology (EvoOnt, 2014 and
SEON - Software Evolution ONtologies (Seon,
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2014). For other modeling, the following ontologies
also were analysed: i. ACM Ontologies (ACM
Ontologies, 2014); Semantic Web for Earth and
Environmental Terminology (SWEET, 2015);
Ontology Computer Science for Non-Computer
Scientists (CSnCS Ontology, 2014);
reprMathStatistics Ontology (r
eprMathStatistics
Ontology, 2014
) and Sciflow: A Scientific Workflow
Ontology (Sciflow, 2014). By observed reasons, the
above ontologies were not considered for reuse and
extension, including the analysis of experts.
The ontology called StatisticalAnalysis.owl
(Statistical Analysis Ontology, 2015) is imported,
which is extended for modeling of statistical
methods and its applicability in detrending
algorithms.
For the extension of the ontology, it was done a
search in glossaries, vocabularies, nomenclatures
and norms. About the definition of the concepts, the
same were described from bibliography of the area.
The following references also were analysed: i.
Glossary Of Statistical Terms (OECD Glossary,
2014); ii. Terminology on Statistical Metadata
(TerminologyonStatisticalMetadata, 2014); iii.
International Statistical Institute (ISI, 2014);
Statistics Glossary (STATS, 2014); Statistical
Techniques in the Data Library: A Tutorial
(StatTutorial, 2014); ISO Norms (3534-1:2006,
3534-2:2006 e 3534-3:1999) (ISO Norms, 2014);
Norma Brasileira ABNT NBR ISO 3534-1. 1a. Ed.
2006 - 2010 (Norma Brasileira, 2014); DCMI Type
Vocabulary (DCMI, 2014), from this was created
and defined the (dcmitype:Software) class, which is
extended using the ACM Taxonomy (ACM
Taxonomy, 2014) to modeling of the programming
languages.
Some facts were analysed and considered in the
modeling of the DO Ontology. In the preprocessing
phase of time series analysis, the researcher can
observe the time series components in an isolated
way, applying specific methods for correction of
certain component. In the case of the time series
present the irregular component in an excessive way,
can be necessary the use of a filter method for its
correction, process called denoising.
The DO Ontology considers also this scenario,
where the time series can be corrected from the
noise. Thus, were modeled the algorithms and
software that can be used for this purpose.
In preprocessing phase, a same method can be
used for more once task (Alexandrov et al, 2012).
For example, the Singular Spectrum Analysis – SSA
method (Vautard and Ghil, 1989) can be used to
trend extraction, denoising, prevision and change-
point detection. Likewise, other filter methods can
be used, both to detrending and to denoising
(Flandrin et al, 2004). According to Meinl (2011),
the smoothing methods and denoising sometimes are
used as synonymous. However, the smoothing
denotes the removal of irregulars detail (shark’s
fins), producing a smooth version of raw time series.
Denoising aims the noise removal (short term
changes with low amplitude), from time series that
does not necessarily results in a smooth signal,
according to Meinl (2011).
Aiming to model this scenario, are described
algorithms and software of detrending and
denoising. The filtering algorithms remove the noise
of time series and the detrending algorithms are
related with the estimation and/or removal of trends
from time series. The Classes Diagram (Figure 1)
shows the main classes of the DO Ontology.
From reuse of (math:NumericalEntity),
subclasses (solu:Solution) and (solu:Algorithm), are
created the classes (do:PreprocessingAlgorithm) and
subclasses of filtering and detrending algorithm.
From reuse of (dcmitype:Software) class, it is
created the subclass (do:PreprocessingSoftware) and
its subclasses of detrending and filtering software.
These algorithms/software can be a version of other
algorithms/software, modeled according to an auto-
relationship in the respective class.
In DO Ontology, it is considered that a same
method can be used to realize more once task in the
time series, thus are created the classes
(do:TimeSeriesCorrectionMethod), describing the
methods and the
(do:AlgorithmMethodApplicability), to describe the
applicability of the method in certain algorithm. To
exemplify, the (do:Moving Average) class related
with the moving average method, it can be used in
an algorithm to denoising task, constituting, in
frequency language, a filter that allows to pass the
low-frequency component as the trend, removing the
high-component that is the noise. This method also
can be used in an algorithm to nonparamentric trend
estimation, where the fluctuations are considered
belonging to trend, according to (Chandler and
Scott, 2011).
This choice depends on context, considered in
ontology modeling, being possible to declare the
method and which is its applicability in the
respective algorithm. The objective of this modeling
it is to facilitate the understanding about the method
used and what was done in the time series with its
application. The (do:Domain) class is related with
the domain of the methods, where the instances are
associated with the DBpedia as means of semantic
SemanticallyEnrichingtheDetrendingStepofTimeSeriesAnalysis
477
Figure 1: DO Ontology Classes Diagram.
interoperability. The (do:Statistics) class describes
the Statistics of the methods, Parametric, Semi-
Parametric or Non-Parametric.
The detrending or filtering algorithm classes are
associated with the respective step by means of the
(do:relatedWithStep) relationship. The
(do:DetrendingStep) and (do:DenoisingStep) classes
are declared as subclass of (do:DataPreprocessing),
disjoint of (do:DataAnalysis), both subclasses of
(do:TimeSeriesAnalysis) class.
Figure 2: Class (do:AlgorithmMethodApplicability).
The Figure 2 presents the applicability of the
methods in the algorithms: trend estimation, trend
removal and filtering. A determined method can be
used for parametrically trend estimation, using a
regression regression analysis method or,
nonparametrically, using nonparametric regression,
based on some smoothing method (Chandler and
Scott, 2011). The method applicability also can be
related with the trend removal, using a filter that
allows to pass the high-frequency component that is
the noise component and removing the trend
component that is of low-frequency. Also it can be
related with the use of some filter method for noise
removal. The Figure 3 presents above an example of
a query in SPARQL Language and bellow the
answer from knowledge base related with detrending
algorithms, methods and its applicability.
The DO Ontology was evaluated according to
the Functional Evaluation (SuarézFigueroa et al,
2012), in its use context, by experts and ontologists.
The feedback from evaluators was considered
essential, due to applicability of the ontology.
As means of validation of the DO Ontology,
after the combination in the Detrend Provenance
Model - dpm prefix (de Souza et al, 2014a), the
ontology was validated with real-world photometric
time series in a case study involving two use cases
which can be seen in Figure 3, among other. The
first use case is related with the Corot Detrend
Algorithm (Mislis et al, 2010) using the regression
analysis method, applied to cubic trend estimation
and using cubic regression analysis. In the second
use case is applied the Corot Detrend Algorithm
Modified (Boufleur, 2012) using the robust moving
average method, a low-pass filter that remove the
high-frequency component, smoothing the trend
component of low-frequency, applied to moving
average filter based smoothing and using the moving
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- Query in SPARQL:
SELECT distinct ?detrendingalgorithm ?detrendingmethod ?detrendingmethodapplicability ?filter ?analysis
WHERE {{ ?detrendingalgorithm do:hasDetrendingMethod ?detrendingmethod ;
do:hasDetrendingMethodApplicability ?detrendingmethodapplicability .
?detrendingmethodapplicability do:hasFilter ?filter .}
UNION { ?detrendingalgorithm do:hasDetrendingMethod ?detrendingmethod ;
do:hasDetrendingMethodApplicability ?detrendingmethodapplicability .
?detrendingmethodapplicability do:hasAnalysis ?analysis .}
Figure 3: Query about methods and its applicability in the detrending algorithms.
average filter. The estimated or smoothed trend is
removed by subtraction operation from raw time
series.
About the extensibility of DO Ontology, are
modeled the following methods of the time-
frequency domain: Singular Spectrum Analysis -
SSA (Vautard and Ghil, 1989), Empirical Mode
Decomposition - EMD (Huang, 1998) and Ensemble
Empirical Mode Decomposition - EEMD (Wu and
Huang, 2009), from (do:Filtering) class. These
methods are data adaptive filter by nonlinear way,
which can be used for trend extraction or noise
removal.
4 RELATED WORKS
The related works with this research are: (Henson et
al, 2009), (Bozic, 2011), (Bozic and Winiwarter,
2012), (Bozic and Winiwarter, 2013), (Bozic et al,
2014), (Compton et al, 2012), (Llaves and
Renschler, 2012), (Sheth et al, 2008), which were
compared according to criteria considered relevant
for the development of the ontology, stand out the
following questions (de Souza et al, 2014c):
Time series observations can be described
using the OWL Language, where domain ontologies
are used to semantically enriching the time series.
A design pattern used to describe time
series observations is the Observations and
Measurements (O&M Model), proposed by Open
Geospatial Consortium/Sensor Web Enablement,
which presenting syntactic interoperability, but it
need be adapted for OWL Language to allow
semantic interoperability.
It is possible to associate the necessities of
users with the data (time series), contributing for
decision making by researchers.
In the environmental time series, can occur
different interpretation of fundamental concepts,
such as Sensor. In this cases, it is usually chosen the
broader definition to that the same be specialized in
sub-concepts.
The Simple Knowledge Organization
System Reference Vocabulary (SKOS Vocabulary)
can be used for definition of terms, as in Semantic
Sensor Network - SSN Ontology (Compton et al,
2012).
Terms can be associated with Linked
Sensor Data and Linked Open Data, as means of
promoting semantic interoperability.
SWEET Ontologies are reused as a pattern
to represent environmental and earth sciences.
The modular development can be
considered as the case of SSN Ontology,
conceptually organized in ten modules, which can be
mapped to a physical modularization.
When is done a mapping to a Foundation
Ontology, the ontology considered is the Dolce
Ultralite – DUL (Dul Ontology, 2014), due to its
lightness, considering other Foundation Ontologies.
Ontology Design Patterns (ODPs) are
considered in the domain ontologies design.
Also interoperability questions may occur
from different communities, using the same term to
refer to various occurrences, where this problem
must be treated semantically.
Based on related works, the characteristics
considered relevant and appropriate in the
development of the ontologies were identified and
considered in the DO Ontology definition, such as: i.
modular development; ii. definition of concepts and
of properties using the tags (rdfs:comment) and
(rdfs:label); iii. association of the instances with the
DBpedia; iv. reuse of semantic declaration from
SWEET Ontology; and v. reuse and extension of the
StatisticalAnalysis Ontology.
So, stand out among the related works analysed,
that no studies were found evidencing the semantic
enriching by means of OWL ontologies, developed
SemanticallyEnrichingtheDetrendingStepofTimeSeriesAnalysis
479
in a modular design and considering reuse and the
association with the linked open data of detrending
methods in the time domain, extensible to the
frequency domain, contributing to improving the
decision making in an analysis process.
5 CONCLUSIONS AND FUTURE
RESEARCHES
Nowadays, time series are obtained in several areas,
which need be analysed for generating scientific
knowledge. The focus of this work is the trend
component, constituting changes in the statistical
measures of the time series, characterized as a long
term movement.
The nonstationary time series need be corrected
because the most of statistical methods are
developed for stationarity, also trends can hide other
phenomena, presenting distortions in further
processing. So far, there is not a detrending method
considered as universal in all application areas. So,
several detrending methods can be applied to
detrending the time series.
Given the need to add semantic knowledge in the
detrending step of time series analysis as means of
contributing to improve an important step of
preprocessing, the main contribution of this paper is
presenting a domain ontology, developed in OWL
Language, entitled Detrend Ontology. Its design is
modular, considering the reuse and extension of
ontological resources and association with linked
open data to semantic interoperability. All classes
are defined using nomenclature from time series
analysis. The ontology was evaluated by experts of
the area and by ontologists, where the feedback from
evaluators was considered essential.
The ontology was validated in a case study
where real-world photometric time series were
detrended. Also it is described its extensibility for
modeling of methods in time-frequency domain. It
contributes for the understanding about how and
how often the time series were detrended, allowing
to the researcher to choose other statistical methods
that can be applied for best results. As result, stands
out the semantic enrichment of a relevant step of the
analysis, contributing with the scientific knowledge
generation in many areas that analyze time series.
How futures researches stands out the extension
of modeling of the methods in the frequency
domain, such as Wavelet methods, among other.
Another suggestion is the reuse of the Semantic Web
for Research Communities Ontology (SWRC
Ontology, 2015) for modeling of detrending
publications.
REFERENCES
ACM Ontologies. URL:http://acm.rkbexplorer.com/, Aug.
2014.
ACM Taxonomy. URL:http://dl.acm.org/. Nov. 2014.
Alexandrov, T. et al., 2012. A Review of Some Modern
Approaches to the Problem of Trend Extraction.
Econometric Reviews. Vol. 31, Number 6, pages 593-
624.
Bendat, J. S., and Piersol, A. G., 1986. Random Data:
Analysis and Measurement Procedures, 2nd ed. John
Wiley and Sons, Inc., New York, USA.
Berners-Lee, T., Hendler, J., and Lassila, O., 2001. The
semantic web. Scientific American 284, 5. 34–43.
Boufleur, R. C., 2012. A busca de exoplanetas com as
curvas de luz do corot. Dissertação de mestrado, Curso
de Pós-Graduação em Astronomia, R.J., Brasil.
Bozic, B., 2011. Simulation and modeling of semantically
enriched time series. 19th International Congress on
Modelling and Simulation, 12–16.
Bozic, B., and Winiwarter, W., 2012. Community building
based on semantic time series. iiWAS, 213–222.
Bozic, B., and Winiwarter, W., 2013. A showcase of
semantic time series processing. IJWIS 9, 2 117–141.
Bozic, B., Peters-Andersa, J., and Schimaka, G., 2014.
Ontology mapping in semantic time series processing
and climate change prediction. International
Environmental Modelling and Software Society
(iEMSs).
Chandler, R., and Scott, M., 2011. Statistical Methods for
Trend Detection and Analysis in the Environmental
Sciences, 1nd ed. Wiley.
Chatfield, C., 2004. The Analysis of Time Series: An
Introduction, 6th ed. CRC Press, Florida, US.
Compton, M. et al, 2012. The ssn ontology of the w3c
semantic sensor network incubator group. Web
Semantics: Science, Services and Agents on the WWW
17, 0.
CSO Ontology. Core Software Ontology.
URL:http://cos.ontoware.org/cso, July 2014.
CSnCS Ontology. URL:http://watson.kmi.open.ac.uk/on-
tologies/LT4eL/CSnCSv0.01Lex.owl, June 2014.
DBpedia. URL: http://dbpedia.org/, Jan 2015.
DCMI Type Vocabulary. URL:http://dublincore.org/
documents/2000/07/11/dcmi-type-vocabulary/, Oct.
2014.
de Souza, L., VAZ, M. S. M. G., SUNYE, M. S., 2014a.
Modular development of ontologies for provenance in
detrending time series. In: Eleventh Int. Conf. on Inf.
Tech: New Generations (ITNG). Las Vegas, p. 567-
572.
de Souza, L., VAZ, M. S. M. G., SUNYE, M. S., 2014b.
Domain Ontology for Time Series Provenance. In:
16th International Conference on Enterprise
Information Systems. ICEIS. Lisbon, p. 217-224.
ICEIS2015-17thInternationalConferenceonEnterpriseInformationSystems
480
de Souza, L., 2014c. Um modelo de proveniência para
extração de tendências em séries temporais. Tese de
Doutorado. Or. Sunye, M. S. e Vaz, M. S. M. G.
Programa de Pós-Graduação em Informática. UFPR,
Brazil. 256 pp.
Dul Ontology. URL:http://www.loa-cnr.it/ontologies/
DUL.owl, Feb. 2014.
EvoOnt Ontology. URL:https://files.ifi.uzh.ch/ddis/
oldweb/ddis/research/evoont/, June 2014.
Flandrin, P., Gonçalves, P., and Rilling, G., 2004.
Detrending and denoising with empirical mode
decompositions. In EUSIPCO-04 (2004), pp. 1581–
1584.
Guarino, N., 1998. Formal ontology and information
systems. In Proceedings of FOIS’98, Trento, Italy, 6-
8. Amsterdam, N. Guarino, Ed., IOS Press, pp. 3–15.
Hair, J. F. Jr., Black, W.C., Babin, B.J., Anderson, R. E.,
2010. Multivariate Data Analysis. 7th edition. Pearson
Prentice Hall.
Henson, C. A., H. Neuhaus, H., Sheth, A. P.,
Thirunarayan, K., and Buyya, R., 2009. An
ontological representation of time series observations
on the semantic sensor web. Proc, of 1st Intern.
Workshop on the Semantic Sensor Web. Herkalion,
Greece.
Huang, N. E., and et al., 1998. The empirical mode
decomposition and the Hubert spectrum for nonlinear
and non-stationary time series analysis. Proceedings of
the Royal Society A 454, 1971.
ISI. International Statistical Institute. URL:http://
isi.cbs.nl/glossary/bloken00.htm, Sept. 2014.
ISO Norms (3534-1:2006, 3534-2:2006 e 3534-3:1999).
URL:http://www.iso.org/iso/home/, Oct. 2014.
Lando, P., Lapujade, A., Kassel, G., and Furst, F., 2009.
An ontological investigation in the field of computer
programs. In Software and Data Tech.,
Communications in Computer and Inf. Science. 22,
371–383.
Llaves, A., and Renschler, C. S., 2012. Observing changes
in real-time sensor observations. In Multidisciplinary
Research on Geographical Information in Europe and
Beyond.
Meinl, T., 2011. A Novel Wavelet Based Approach for
Time Series Data Analysis. PhD thesis, Karlsruhe.
Mislis, D., Schmitt, J. H. M. M., Carone, L., Guenther, E.
W. and Patzold, M., 2010. An algorithm for correcting
corot raw light curves. arXiv/1008.0300.
Norma brasileira abnt nbr iso 3534-1. 1a. ed. 2006 - 2010.
URL:http://www.abntcatalogo.com.br/, Oct. 2014.
Noy, N. F., and McGuinness, D. L., 2001. Ontology
development 101: A guide to creating your first
ontology. Development 32, 1 (2001), 1–25.
OECD Glossary. URL:http://stats.oecd.org/glossary/
index.htm, Aug. 2014.
ReprMathStatistics Ontology. URL:http://sweet.jpl.
nasa.gov.gov/2.3/reprMathStatistics.owl, Sept. 2014.
Sciflow a scientific workflow ontology.
URL:http://www.lbd.dcc.ufmg.br/colecoes/sbbd/2011/
0016.pdf, Oct. 2014.
Seon Ontologies. URL:http://www.se-on.org/, July 2014.
Sheth, A., Henson, C., and Sahoo, S. S., 2008. Semantic
sensor web. IEEE Internet Computing 12, 4. 78–83.
Shumway, R.H., and Stoffer, D. S. 2006. Time series
analysis and its applications: with R examples. 2
nd
ed.
Springer.
Spiegel, M. R., 1985. Estatística. McGraw-Hill, São
Paulo, Brazil.
Statistical Analysis Ontology. URL: URL:http://a.com/
StatisticalAnalysis.owl. Dec, 2015.
StatTutorial. Statistical techniques in the data library: A
tutorial. URL:http://iridl.ldeo.columbia.edu/dochelp/
Stat.
Tutorial/, Sept. 2014.
STATS. Statistics glossary. URL:http://www.stats.gla.
ac.uk/steps/glossary/paired_data.html, Oct. 2014.
SuarézFigueroa, M. C., Gomez-Perez, A., Motta, E., and
Gangemi, 2012. A. Ontology Engineering in a
Networked World. Springer-Verlag Berlin Heidelberg.
SWEET Ontology. URL: http://sweet.jpl.nasa.gov/2.3/
sweetAll.owl, Dec, 2015.
SWO Ontology. The Software Ontology.
URL:http://purl.bioontology.org/ontology/SWO, June
2014.
SWRC Ontology. Semantic Web for Research
Communities Ontology. URL:http://ontoware.org/
swrc/, Jan, 2015.
Terminology on statistical metadata. URL:http://
www.unece.org/fileadmin/DAM/stats/publica-
tions/53metadaterminology.pdf, July 2014.
Vautard, R. P. Y., and Ghil, M., 1989. Singular spectrum
analysis in nonlinear dynamics with applications to
paleoclimatic time series. Physica D 35, 395–424.
Wu, Z., and Huang, N. E., 2009. Ensemble empirical
mode decomposition: a noise-assisted data analysis
method. Advances in Adaptive Data Analysis 1, 1, 1–
41.
Wu, Z., Huang, N. E., Long, S. R., and Peng, C., 2007. On
the trend, detrending, and variability of nonlinear and
nonstationary time series. Proc. Nat. Academy of
Sciences 104, 38, 14889–14894.
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