Modelling and Forecasting Financial Data: Techniques of Nonlinear Dynamics

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Abdol S. Soofi, Liangyue Cao
Springer Science & Business Media, 31.03.2002 - 488 Seiten
Over the last decade, dynamical systems theory and related nonlinear methods have had a major impact on the analysis of time series data from complex systems. Recent developments in mathematical methods of state-space reconstruction, time-delay embedding, and surrogate data analysis, coupled with readily accessible and powerful computational facilities used in gathering and processing massive quantities of high-frequency data, have provided theorists and practitioners unparalleled opportunities for exploratory data analysis, modelling, forecasting, and control.
Until now, research exploring the application of nonlinear dynamics and associated algorithms to the study of economies and markets as complex systems is sparse and fragmentary at best. Modelling and Forecasting Financial Data brings together a coherent and accessible set of chapters on recent research results on this topic. To make such methods readily useful in practice, the contributors to this volume have agreed to make available to readers upon request all computer programs used to implement the methods discussed in their respective chapters.
Modelling and Forecasting Financial Data is a valuable resource for researchers and graduate students studying complex systems in finance, biology, and physics, as well as those applying such methods to nonlinear time series analysis and signal processing.
 

Inhalt

EMBEDDING THEORY INTRODUCTION AND APPLICATIONS TO TIME SERIES ANALYSIS
11
2 Embedding Theories
14
3 Chaotic Time Series Analysis
18
4 Examples of Applications in Economics
32
5 Conclusions
37
DETERMINING MINIMUM EMBEDDING DIMENSION FROM SCALAR TIME SERIES
43
2 Major existing methods
44
3 False nearest neighbor method
45
PROBLEMS IN MODELLING AND PREDICTION
267
SURROGATE DATA TEST ON TIME SERIES
269
1 The Surrogate Data Test
271
2 Implementation of the Nonlinearity Test
275
3 Application to Financial Data
278
4 Discussion
279
VALIDATION OF SELECTED GLOBAL MODELS
285
1 Introduction
286

4 Averaged false nearest neighbor method
47
5 Examples
51
6 Summary
61
MUTUAL INFORMATION AND RELEVANT VARIABLES FOR PREDICTIONS
63
2 Theoretical Background
66
3 Mutual Information Analysis
71
4 Mutual Information Algorithm
74
5 Examples
80
6 Conclusions
90
Appendix
91
3 A Property of GMI
92
METHODS OF NONLINEAR MODELLING AND FORECASTING
95
STATE SPACE LOCAL LINEAR PREDICTION
97
1 Introduction
98
2 Local prediction
99
3 Implementation of Local Prediction Estimators on Time Series
106
4 Discussion
111
LOCAL POLYNOMIAL PREDICTION AND VOLATILITY ESTIMATION IN FINANCIAL TIME SERIES
117
2 Local polynomial method
119
3 Technical setup for statistical theory
121
4 Prediction methods
125
5 Volatility estimation
128
6 Risk analysis of AOL stock
130
7 Concluding remarks
134
KALMAN FILTERING OF TIME SERIES DATA
139
2 Methods
140
3 Examples
149
RADIAL BASIS FUNCTIONS NETWORKS
161
1 Introduction
162
2 Radial Functions
163
4 An example of using RBF for financial timeseries forecasting
174
5 Discussions
175
6 Conclusions
177
7 Acknowledgements
178
NONLINEAR PREDICTION OF TIME SERIES USING WAVELET NETWORK METHOD
181
2 Nonlinear predictive model
182
3 Wavelet network
183
4 Examples
187
5 Discussion and conclusion
194
MODELLING AND PREDICTING MULTIVARIATE AND INPUTOUTPUT TIME SERIES
199
NONLINEAR MODELLING AND PREDICTION OF MULTIVARIATE FINANCIAL TIME SERIES
201
2 Embedding multivariate data
202
3 Prediction and relationship
204
4 Examples
205
5 Conclusions and discussions
211
ANALYSIS OF ECONOMIC TIME SERIES USING NARMAX POLYNOMIAL MODELS
215
2 NARMAX Polynomial Models
218
3 Algorithms
222
4 Illustrative Results
225
5 Discussion
235
MODELING DYNAMICAL SYSTEMS BY ERROR CORRECTION NEURAL NETWORKS
239
1 Introduction
240
2 Modeling Dynamic Systems by Recurrent Neural Networks
241
3 Modeling Dynamic Systems by Error Correction
248
4 VariantsInvariants Separation
252
5 Optimal State Space Reconstruction for Forecasting
255
6 Yield Curve Forecasting by ECNN
262
2 Bifurcation diagrams for model with parameter dependence
296
3 Synchronization
298
4 Conclusion
302
TESTING STATIONARITY IN TIME SERIES
305
2 Description of the tests
308
3 Applications
314
4 Summary and discussion
325
ANALYSIS OF ECONOMIC DELAYEDFEEDBACK DYNAMICS
329
1 Introduction
330
2 Noiselike behavior induced by a NerloveArrow model with time delay
331
3 A nonparametric approach to analyze delayedfeedback dynamics
334
4 Analysis of NerloveArrow models with time delay
338
5 Model improvement
339
6 Two delays and seasonal forcing
341
7 Analysis of the USA gross private domestic investment time series
343
8 The ACE algorithm
345
9 Summary and conclusion
347
GLOBAL MODELING AND DIFFERENTIAL EMBEDDING
353
2 Global modeling techniques
354
3 Applications to Experimental Data
369
4 Discussion on applications
371
5 Conclusion
373
ESTIMATION OF DETERMINISTIC AND STOCHASTIC RULES UNDERLYING FLUCTUATING DATA
377
2 Stochastic Processes
378
3 Dynamical Noise
380
5 Analysis Examples of Artificially Created Time Series
383
6 Scale Dependent Complex Systems
391
7 Financial Market
392
8 Turbulence
395
9 Conclusions
398
NONLINEAR NOISE REDUCTION
403
1 Noise and its removal
404
2 Local projective noise reduction
405
3 Applications of noise reduction
409
Noise reduction for economic data
415
OPTIMAL MODEL SIZE
419
2 Selection of Nested Models
421
General Estimation Procedures
422
4 Applications and Implementation Issues
427
INFLUENCE OF MEASURED TIME SERIES IN THE RECONSTRUCTION OF NONLINEAR MULTIVARIABLE DYNAMICS
431
2 Non equivalent observables
434
3 Discussions on applications
446
4 Conclusion
450
V APPLICATIONS IN ECONOMICS AND FINANCE
455
NONLINEAR FORECASTING OF NOISY FINANCIAL DATA
457
2 Methodology
459
3 Results
461
4 Conclusions
464
CANONICAL VARIATE ANALYSIS AND ITS APPLICATIONS TO FINANCIAL DATA
469
1 Nonlinear Markov Modelling
472
2 Implementation of Forecasting
475
3 The GARCH11t Model
476
4 Data Analysis
477
5 Empirical Results
478
6 Discussion
481
Index
485
Urheberrecht

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Häufige Begriffe und Wortgruppen

Aguirre algorithm applied attractor autoregressive bifurcation Chaos chaotic attractor chaotic time series chapter coefficient computed data points data sets defined delay determined deterministic dimensional discussed distribution dynamical system ECNN embedding dimension equation estimate example exchange rate false nearest neighbors Figure Fokker-Planck equation forecasting GARCH Gouesbet Ikeda map input Kalman filter Letellier linear Lyapunov exponents matrix measure measurement function minimum embedding dimension model function multivariate time series mutual information nearest neighbor method neural network noise reduction noisy nonlinear time series observed obtained optimal output overfitting parameters phase space Phys Physics polynomial predictor problem radial basis function random rate time series regression regressors RMSE Rössler system samples scalar time series Schreiber series analysis series data signal space reconstruction stationarity stochastic stochastic processes structure surrogate data technique time-delay trajectory transform values variables variance vector volatility wavelet wavelet network

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Bibliografische Informationen

TitelModelling and Forecasting Financial Data: Techniques of Nonlinear Dynamics
Band 2 von Studies in Computational Finance, ISSN 1567-8288
HerausgeberAbdol S. Soofi, Liangyue Cao
Ausgabeillustriert
VerlagSpringer Science & Business Media, 2002
ISBN0792376803, 9780792376804
Länge488 Seiten
  
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