A comparative evaluation of nonlinear dynamics methods for time series prediction View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-04-29

AUTHORS

Francesco Camastra, Maurizio Filippone

ABSTRACT

A key problem in time series prediction using autoregressive models is to fix the model order, namely the number of past samples required to model the time series adequately. The estimation of the model order using cross-validation may be a long process. In this paper, we investigate alternative methods to cross-validation, based on nonlinear dynamics methods, namely Grassberger–Procaccia, Kégl, Levina–Bickel and False Nearest Neighbors algorithms. The experiments have been performed in two different ways. In the first case, the model order has been used to carry out the prediction, performed by a SVM for regression on three real data time series showing that nonlinear dynamics methods have performances very close to the cross-validation ones. In the second case, we have tested the accuracy of nonlinear dynamics methods in predicting the known model order of synthetic time series. In this case, most of the methods have yielded a correct estimate and when the estimate was not correct, the value was very close to the real one. More... »

PAGES

1021

References to SciGraph publications

  • 1981. On the dimension of the compact invariant sets of certain non-linear maps in DYNAMICAL SYSTEMS AND TURBULENCE, WARWICK 1980
  • 1985. On the numerical determination of the dimension of an attractor in DYNAMICAL SYSTEMS AND BIFURCATIONS
  • 1996. Analysis of Observed Chaotic Data in NONE
  • 1989-03-01. AnO(n logn) algorithm for the all-nearest-neighbors Problem in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1981. Detecting strange attractors in turbulence in DYNAMICAL SYSTEMS AND TURBULENCE, WARWICK 1980
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00521-009-0266-y

    DOI

    http://dx.doi.org/10.1007/s00521-009-0266-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1034089468


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/17", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Psychology and Cognitive Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Artificial Intelligence and Image Processing", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0906", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Electrical and Electronic Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1702", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Cognitive Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Applied Science, University of Naples Parthenope, Centro Direzionale Isola C4, 80143, Naples, Italy", 
              "id": "http://www.grid.ac/institutes/grid.17682.3a", 
              "name": [
                "Department of Applied Science, University of Naples Parthenope, Centro Direzionale Isola C4, 80143, Naples, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Camastra", 
            "givenName": "Francesco", 
            "id": "sg:person.0670572515.64", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0670572515.64"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, S1 4DP, Sheffield, UK", 
              "id": "http://www.grid.ac/institutes/grid.11835.3e", 
              "name": [
                "Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, S1 4DP, Sheffield, UK"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Filippone", 
            "givenName": "Maurizio", 
            "id": "sg:person.07706215665.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bfb0091924", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049441366", 
              "https://doi.org/10.1007/bfb0091924"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0075637", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002095214", 
              "https://doi.org/10.1007/bfb0075637"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02187718", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019225055", 
              "https://doi.org/10.1007/bf02187718"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0091916", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006179285", 
              "https://doi.org/10.1007/bfb0091916"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-0763-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033688069", 
              "https://doi.org/10.1007/978-1-4612-0763-4"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009-04-29", 
        "datePublishedReg": "2009-04-29", 
        "description": "A key problem in time series prediction using autoregressive models is to fix the model order, namely the number of past samples required to model the time series adequately. The estimation of the model order using cross-validation may be a long process. In this paper, we investigate alternative methods to cross-validation, based on nonlinear dynamics methods, namely Grassberger\u2013Procaccia, K\u00e9gl, Levina\u2013Bickel and False Nearest Neighbors algorithms. The experiments have been performed in two different ways. In the first case, the model order has been used to carry out the prediction, performed by a SVM for regression on three real data time series showing that nonlinear dynamics methods have performances very close to the cross-validation ones. In the second case, we have tested the accuracy of nonlinear dynamics methods in predicting the known model order of synthetic time series. In this case, most of the methods have yielded a correct estimate and when the estimate was not correct, the value was very close to the real one.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00521-009-0266-y", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1104357", 
            "issn": [
              "0941-0643", 
              "1433-3058"
            ], 
            "name": "Neural Computing and Applications", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "8", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "18"
          }
        ], 
        "keywords": [
          "nonlinear dynamics methods", 
          "model order", 
          "time series prediction", 
          "real data time series", 
          "series prediction", 
          "cross-validation one", 
          "time series", 
          "False Nearest Neighbors", 
          "Grassberger-Procaccia", 
          "synthetic time series", 
          "data time series", 
          "autoregressive model", 
          "past samples", 
          "dynamics method", 
          "Nearest Neighbor", 
          "key problem", 
          "real ones", 
          "correct estimate", 
          "estimates", 
          "alternative method", 
          "estimation", 
          "SVM", 
          "K\u00e9gl", 
          "problem", 
          "prediction", 
          "neighbors", 
          "comparative evaluation", 
          "order", 
          "one", 
          "method", 
          "accuracy", 
          "model", 
          "cases", 
          "different ways", 
          "performance", 
          "second case", 
          "series", 
          "regression", 
          "way", 
          "number", 
          "experiments", 
          "evaluation", 
          "process", 
          "values", 
          "first case", 
          "long process", 
          "samples", 
          "paper", 
          "Levina\u2013Bickel"
        ], 
        "name": "A comparative evaluation of nonlinear dynamics methods for time series prediction", 
        "pagination": "1021", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1034089468"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00521-009-0266-y"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00521-009-0266-y", 
          "https://app.dimensions.ai/details/publication/pub.1034089468"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:20", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_490.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00521-009-0266-y"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00521-009-0266-y'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00521-009-0266-y'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00521-009-0266-y'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00521-009-0266-y'


     

    This table displays all metadata directly associated to this object as RDF triples.

    153 TRIPLES      22 PREDICATES      83 URIs      66 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00521-009-0266-y schema:about anzsrc-for:08
    2 anzsrc-for:0801
    3 anzsrc-for:09
    4 anzsrc-for:0906
    5 anzsrc-for:17
    6 anzsrc-for:1702
    7 schema:author N07957780cc284a5b9b50510dc455c23c
    8 schema:citation sg:pub.10.1007/978-1-4612-0763-4
    9 sg:pub.10.1007/bf02187718
    10 sg:pub.10.1007/bfb0075637
    11 sg:pub.10.1007/bfb0091916
    12 sg:pub.10.1007/bfb0091924
    13 schema:datePublished 2009-04-29
    14 schema:datePublishedReg 2009-04-29
    15 schema:description A key problem in time series prediction using autoregressive models is to fix the model order, namely the number of past samples required to model the time series adequately. The estimation of the model order using cross-validation may be a long process. In this paper, we investigate alternative methods to cross-validation, based on nonlinear dynamics methods, namely Grassberger–Procaccia, Kégl, Levina–Bickel and False Nearest Neighbors algorithms. The experiments have been performed in two different ways. In the first case, the model order has been used to carry out the prediction, performed by a SVM for regression on three real data time series showing that nonlinear dynamics methods have performances very close to the cross-validation ones. In the second case, we have tested the accuracy of nonlinear dynamics methods in predicting the known model order of synthetic time series. In this case, most of the methods have yielded a correct estimate and when the estimate was not correct, the value was very close to the real one.
    16 schema:genre article
    17 schema:inLanguage en
    18 schema:isAccessibleForFree true
    19 schema:isPartOf N8812ba589ec142efadb2e13ad8fc12f9
    20 Nf1804be61eba4fea9658207895ce042f
    21 sg:journal.1104357
    22 schema:keywords False Nearest Neighbors
    23 Grassberger-Procaccia
    24 Kégl
    25 Levina–Bickel
    26 Nearest Neighbor
    27 SVM
    28 accuracy
    29 alternative method
    30 autoregressive model
    31 cases
    32 comparative evaluation
    33 correct estimate
    34 cross-validation one
    35 data time series
    36 different ways
    37 dynamics method
    38 estimates
    39 estimation
    40 evaluation
    41 experiments
    42 first case
    43 key problem
    44 long process
    45 method
    46 model
    47 model order
    48 neighbors
    49 nonlinear dynamics methods
    50 number
    51 one
    52 order
    53 paper
    54 past samples
    55 performance
    56 prediction
    57 problem
    58 process
    59 real data time series
    60 real ones
    61 regression
    62 samples
    63 second case
    64 series
    65 series prediction
    66 synthetic time series
    67 time series
    68 time series prediction
    69 values
    70 way
    71 schema:name A comparative evaluation of nonlinear dynamics methods for time series prediction
    72 schema:pagination 1021
    73 schema:productId N4d9b15f65e1940f1a07abe6482758959
    74 Nbc9c2238c11c49569e33eaadca1f8920
    75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034089468
    76 https://doi.org/10.1007/s00521-009-0266-y
    77 schema:sdDatePublished 2022-01-01T18:20
    78 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    79 schema:sdPublisher Na8f79959a89b4bf3b9e2df2e1e871623
    80 schema:url https://doi.org/10.1007/s00521-009-0266-y
    81 sgo:license sg:explorer/license/
    82 sgo:sdDataset articles
    83 rdf:type schema:ScholarlyArticle
    84 N07957780cc284a5b9b50510dc455c23c rdf:first sg:person.0670572515.64
    85 rdf:rest Nddf8bdb4c56c4c55844e95be045dce6a
    86 N4d9b15f65e1940f1a07abe6482758959 schema:name doi
    87 schema:value 10.1007/s00521-009-0266-y
    88 rdf:type schema:PropertyValue
    89 N8812ba589ec142efadb2e13ad8fc12f9 schema:issueNumber 8
    90 rdf:type schema:PublicationIssue
    91 Na8f79959a89b4bf3b9e2df2e1e871623 schema:name Springer Nature - SN SciGraph project
    92 rdf:type schema:Organization
    93 Nbc9c2238c11c49569e33eaadca1f8920 schema:name dimensions_id
    94 schema:value pub.1034089468
    95 rdf:type schema:PropertyValue
    96 Nddf8bdb4c56c4c55844e95be045dce6a rdf:first sg:person.07706215665.03
    97 rdf:rest rdf:nil
    98 Nf1804be61eba4fea9658207895ce042f schema:volumeNumber 18
    99 rdf:type schema:PublicationVolume
    100 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    101 schema:name Information and Computing Sciences
    102 rdf:type schema:DefinedTerm
    103 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
    104 schema:name Artificial Intelligence and Image Processing
    105 rdf:type schema:DefinedTerm
    106 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    107 schema:name Engineering
    108 rdf:type schema:DefinedTerm
    109 anzsrc-for:0906 schema:inDefinedTermSet anzsrc-for:
    110 schema:name Electrical and Electronic Engineering
    111 rdf:type schema:DefinedTerm
    112 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
    113 schema:name Psychology and Cognitive Sciences
    114 rdf:type schema:DefinedTerm
    115 anzsrc-for:1702 schema:inDefinedTermSet anzsrc-for:
    116 schema:name Cognitive Sciences
    117 rdf:type schema:DefinedTerm
    118 sg:journal.1104357 schema:issn 0941-0643
    119 1433-3058
    120 schema:name Neural Computing and Applications
    121 schema:publisher Springer Nature
    122 rdf:type schema:Periodical
    123 sg:person.0670572515.64 schema:affiliation grid-institutes:grid.17682.3a
    124 schema:familyName Camastra
    125 schema:givenName Francesco
    126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0670572515.64
    127 rdf:type schema:Person
    128 sg:person.07706215665.03 schema:affiliation grid-institutes:grid.11835.3e
    129 schema:familyName Filippone
    130 schema:givenName Maurizio
    131 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07706215665.03
    132 rdf:type schema:Person
    133 sg:pub.10.1007/978-1-4612-0763-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033688069
    134 https://doi.org/10.1007/978-1-4612-0763-4
    135 rdf:type schema:CreativeWork
    136 sg:pub.10.1007/bf02187718 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019225055
    137 https://doi.org/10.1007/bf02187718
    138 rdf:type schema:CreativeWork
    139 sg:pub.10.1007/bfb0075637 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002095214
    140 https://doi.org/10.1007/bfb0075637
    141 rdf:type schema:CreativeWork
    142 sg:pub.10.1007/bfb0091916 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006179285
    143 https://doi.org/10.1007/bfb0091916
    144 rdf:type schema:CreativeWork
    145 sg:pub.10.1007/bfb0091924 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049441366
    146 https://doi.org/10.1007/bfb0091924
    147 rdf:type schema:CreativeWork
    148 grid-institutes:grid.11835.3e schema:alternateName Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, S1 4DP, Sheffield, UK
    149 schema:name Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, S1 4DP, Sheffield, UK
    150 rdf:type schema:Organization
    151 grid-institutes:grid.17682.3a schema:alternateName Department of Applied Science, University of Naples Parthenope, Centro Direzionale Isola C4, 80143, Naples, Italy
    152 schema:name Department of Applied Science, University of Naples Parthenope, Centro Direzionale Isola C4, 80143, Naples, Italy
    153 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...