Modeling and Forecasting Financial Data

by Soofi, Abdol S.; Cao, Liangyue

• ISBN13: 9780792376804
• ISBN10: 0792376803
• Format: Hardcover
• Copyright: 2002-03-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

List of Figures	vii
List of Tables	xv
Preface	xvii
Contributing Authors	xxi
Introduction	1	(10)
Abdol S. Soofi
Liangyue Cao
Part I EMBEDDING THEORY: TIME-DELAY PHASE SPACE RECONSTRUCTION AND DETECTION OF NONLINEAR DYNAMICS
Embedding Theory: Introduction and Applications to Time Series Analysis	11	(32)
F. Strozzi
J. M. Zaldivar
Introduction	11	(3)
Embedding Theories	14	(4)
Chaotic Time Series Analysis	18	(14)
Examples of Applications in Economics	32	(5)
Conclusions	37	(6)
Determining Minimum Embedding Dimension	43	(18)
Liangyue Cao
Introduction	43	(1)
Major existing methods	44	(1)
False nearest neighbor method	45	(2)
Averaged false nearest neighbor method	47	(2)
Examples	49	(10)
Summary	59	(2)
Mutual Information and Relevant Variables for Predictions	61	(34)
Bernd Pompe
Introduction	61	(3)
Theoretical Background	64	(5)
Mutual Information Analysis	69	(3)
Mutual Information Algorithm	72	(6)
Examples	78	(10)
Conclusions	88	(1)
Appendix	89	(6)
The Best LMS Predictor	89	(1)
A Property of MI	89	(1)
A Property of GMI	90	(5)
Part II METHODS OF NONLINEAR MODELING AND FORECASTING
State Space Local Linear Prediction	95	(20)
D. Kugiumtzis
Introduction	96	(1)
Local prediction	96	(8)
Implementation of Local Prediction Estimators on Time Series	104	(5)
Discussion	109	(6)
Local Polynomial Prediction and Volatility Estimation in Financial Time Series	115	(22)
Zhan-Qian Lu
Introduction	115	(2)
Local polynomial method	117	(2)
Technical setup for statistical theory	119	(4)
Prediction methods	123	(3)
Volatility estimation	126	(2)
Risk analysis of AOL stock	128	(4)
Concluding remarks	132	(5)
Kalman Filtering of Time Series Data	137	(22)
David M. Walker
Introduction	137	(1)
Methods	138	(9)
Examples	147	(9)
Summary	156	(3)
Radial Basis Functions Networks	159	(20)
A. Braga
A. C. Carvalho
T. Ludermir
M. de Almeida
E. Lacerda
Introduction	160	(1)
Radial Functions	161	(1)
RBF Neural Networks	161	(11)
An example of using RBF for financial time-series forecasting	172	(1)
Discussions	173	(2)
Conclusions	175	(1)
Acknowledgements	176	(3)
Nonlinear Prediction of Time Series Using Wavelet Network Method	179	(20)
Liangyue Cao
Introduction	179	(1)
Nonlinear predictive model	180	(1)
Wavelet network	181	(4)
Examples	185	(7)
Discussion and conclusion	192	(7)
Part III MODELLING AND PREDICTING MULTIVARIATE AND INPUT-OUTPUT TIME SERIES
Nonlinear Modelling and Prediction of Multivariate Financial Time Series	199	(14)
Liangyue Cao
Introduction	199	(1)
Embedding multivariate data	200	(2)
Prediction and relationship	202	(1)
Examples	203	(6)
Conclusions and discussions	209	(4)
Analysis of Economic Time Series Using NARMAX Polynomial Models	213	(24)
Luis Antonio Aguirre
Antonio Aguirre
Introduction	213	(3)
NARMAX Polynomial Models	216	(4)
Algorithms	220	(3)
Illustrative Results	223	(10)
Discussion	233	(4)
Modeling dynamical systems by Error Correction Neural Networks	237	(30)
Hans-Georg Zimmermann
Ralph Neuneier
Ralph Grothmann
Introduction	238	(1)
Modeling Dynamic Systems by Recurrent Neural Networks	239	(7)
Modeling Dynamic Systems by Error Correction	246	(4)
Variants-Invariants Separation	250	(3)
Optimal State Space Reconstruction for Forecasting	253	(7)
Yield Curve Forecasting by ECNN	260	(2)
Conclusion	262	(5)
Part IV PROBLEMS IN MODELLING AND PREDICTION
Surrogate Data Test on Time Series	267	(16)
D. Kugiumtzis
The Surrogate Data Test	269	(4)
Implementation of the Nonlinearity Test	273	(3)
Application to Financial Data	276	(1)
Discussion	277	(6)
Validation of Selected Global Models	283	(20)
C. Letellier
O. Menard
L. A. Aguirre
Introduction	284	(10)
Bifurcation diagrams for model with parameter dependence	294	(2)
Synchronization	296	(4)
Conclusion	300	(3)
Testing Stationarity in Time Series	303	(24)
Annette Witt
Jurgen Kurths
Introduction	303	(3)
Description of the tests	306	(6)
Applications	312	(11)
Summary and discussion	323	(4)
Analysis of Economic Delayed-Feedback Dynamics	327	(24)
Henning U. Voss
Jurgen Kurths
Introduction	328	(1)
Noise-like behavior induced by a Nerlove-Arrow model with time delay	329	(3)
A nonparametric approach to analyze delayed-feedback dynamics	332	(4)
Analysis of Nerlove-Arrow models with time delay	336	(1)
Model improvement	337	(2)
Two delays and seasonal forcing	339	(2)
Analysis of the USA gross private domestic investment time series	341	(2)
The ACE algorithm	343	(2)
Summary and conclusion	345	(6)
Global Modeling and Differential Embedding	351	(24)
J. Maquet
C. Letellier
G. Gouesbet
Introduction	351	(1)
Global modeling techniques	352	(15)
Applications to Experimental Data	367	(2)
Discussion on applications	369	(2)
Conclusion	371	(4)
Estimation of Rules Underlying Fluctuating Data	375	(26)
S. Siegert
R. Friedrich
Ch. Renner
J. Peinke
Introduction	375	(1)
Stochastic Processes	376	(2)
Dynamical Noise	378	(1)
Algorithm for Analysing Fluctuating Data Sets	378	(3)
Analysis Examples of Artificially Created Time Series	381	(8)
Scale Dependent Complex Systems	389	(1)
Financial Market	390	(3)
Turbulence	393	(3)
Conclusions	396	(5)
Nonlinear Noise Reduction	401	(16)
Rainer Hegger
Holger Kantz
Thomas Schreiber
Noise and its removal	402	(1)
Local projective noise reduction	403	(4)
Applications of noise reduction	407	(6)
Conclusion and outlook: Noise reduction for economic data	413	(4)
Optimal Model Size	417	(12)
Jianming Ye
Introduction	417	(2)
Selection of Nested Models	419	(1)
Information Criteria: General Estimation Procedures	420	(5)
Applications and Implementation Issues	425	(4)
Influence of Measured Time Series in the Reconstruction of Nonlinear Multivariable Dynamics	429	(26)
C. Letellier
L. A. Aguirre
Introduction	429	(3)
Non equivalent observables	432	(12)
Discussions on applications	444	(4)
Conclusion	448	(7)
Part V APPLICATIONS IN ECONOMICS AND FINANCE
Nonlinear Forecasting of Noisy Financial Data	455	(12)
Abdol S. Soofi
Liangyue Cao
Introduction	455	(2)
Methodology	457	(2)
Results	459	(3)
Conclusions	462	(5)
Canonical Variate Analysis and its Applications to Financial Data	467	(16)
Berndt Pilgram
Peter Verhoeven
Alistair Mees
Michael McAleer
Non-linear Markov Modelling	470	(3)
Implementation of Forecasting	473	(1)
The GARCH(1,1)-t Model	474	(1)
Data Analysis	475	(1)
Empirical Results	476	(3)
Discussion	479	(4)
Index	483