Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification

263 Pages·2014·5.25 MB·English

by  Antonios K. Alexandridis, Achilleas D. Zapranis

Wavelet Neural Networks

Wavelet Neural Networks
With Applications in Financial Engineering,
Chaos, and Classification
AntoniosK.Alexandridis
SchoolofMathematics,StatisticsandActuarialScience
UniversityofKent
Canterbury,UnitedKingdom
AchilleasD.Zapranis
DepartmentofAccountingandFinance
UniversityofMacedonia
Thessaloniki,Greece
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LibraryofCongressCataloging-in-PublicationData:
Alexandridis,AntoniosK.
Waveletneuralnetworks:withapplicationsinfinancialengineering,
chaos,andclassification/AntoniosK.Alexandridis,Schoolof
Mathematics,StatisticsandActuarialScience,UniversityofKent,
Canterbury,UK,AchilleasD.Zapranis,DepartmentofAccountingand
Finance,UniversityofMacedonia,Thessaloniki,Greece.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-59252-6(cloth)
1.Wavelets(Mathematics) 2.Neuralnetworks(Computerscience)
3.Financialengineering. I.Zapranis,Achilleas,1965– II.Title.
QA403.3.A4282014
006.3′2–dc23
2013047838
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
Toourfamilies

Contents
Preface xiii
1 MachineLearningandFinancialEngineering 1
FinancialEngineering / 2
FinancialEngineeringandRelatedResearchAreas / 3
FunctionsofFinancialEngineering / 5
ApplicationsofMachineLearninginFinance / 6
FromNeuraltoWaveletNetworks / 8
WaveletAnalysis / 8
ExtendingtheFourierTransform:TheWaveletAnalysis
Paradigm / 10
NeuralNetworks / 17
WaveletNeuralNetworks / 19
ApplicationsofWaveletNeuralNetworksinFinancialEngineering,
Chaos,andClassification / 21
BuildingWaveletNetworks / 23
VariableSelection / 23
ModelSelection / 24
ModelAdequacyTesting / 25
BookOutline / 25
References / 27
vii
viii CONTENTS
2 NeuralNetworks 35
ParallelProcessing / 36
ProcessingUnits / 37
ActivationStatusandActivationRules / 37
ConnectivityModel / 39
Perceptron / 41
TheApproximationTheorem / 42
TheDeltaRule / 42
BackpropagationNeuralNetworks / 44
MultilayerFeedforwardNetworks / 44
TheGeneralizedDeltaRule / 45
BackpropagationinPractice / 49
TrainingwithBackpropagation / 51
NetworkParalysis / 54
LocalMinima / 54
NonuniqueSolutions / 56
ConfigurationReference / 56
Conclusions / 59
References / 59
3 WaveletNeuralNetworks 61
WaveletNeuralNetworksforMultivariateProcessModeling / 62
StructureofaWaveletNeuralNetwork / 62
InitializationoftheParametersoftheWaveletNetwork / 64
TrainingaWaveletNetworkwithBackpropagation / 69
StoppingConditionsforTraining / 72
EvaluatingtheInitializationMethods / 73
Conclusions / 77
References / 78
4 ModelSelection:SelectingtheArchitecture
oftheNetwork 81
TheUsualPractice / 82
EarlyStopping / 82
Regularization / 83
Pruning / 84
MinimumPredictionRisk / 86