Modelling and Forecasting Financial Data: Techniques of Nonlinear DynamicsAbdol S. Soofi, Liangyue Cao 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. |
Contents
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 |
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 |
485 | |
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Modelling and Forecasting Financial Data: Techniques of Nonlinear Dynamics Abdol S. Soofi,Liangyue Cao No preview available - 2012 |
Common terms and phrases
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