Selection of future events from a time series in relation to estimations of forecasting uncertainty

A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly different predictability, or, in other words, to heteroskedastic time series. A priori selection of future events in accordance to expected uncertainty of their forecasts may be helpful for making practical decisions. The procedure first implies creation of two neural network based forecasting models, one of which is aimed at prediction of conditional mean and other - conditional dispersion, and then elaboration of the rule for future event selection into groups of more and less predictable events. The method is demonstrated and tested by the example of the computer generated time series, and then applied to the real world time series, Dow Jones Industrial Average index.

[1]  Spyros Makridakis,et al.  Forecasting Methods for Management , 1989 .

[2]  E. Fama,et al.  Efficient Capital Markets : II , 2007 .

[3]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[4]  W. T. Illingworth,et al.  Practical guide to neural nets , 1991 .

[5]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[6]  David Edelson.  Computational Methods in the Chemical Sciences : By A. F. Carley and P. H. Morgan, Ellis Horwood, Chichester, U.K., 1989. ISBN 0-85312-746-8, 335 pp. including index and contents , 1990, Comput. Chem..

[7]  William Remus,et al.  Neural Network Models for Time Series Forecasts , 1996 .

[8]  A. Lo,et al.  Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test , 1987 .

[9]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[10]  D. Sornette,et al.  Stock Market Crashes, Precursors and Replicas , 1995, cond-mat/9510036.

[11]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[12]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[13]  Bernard Widrow,et al.  Neural networks: applications in industry, business and science , 1994, CACM.

[14]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[15]  Anil K. Bera,et al.  ARCH Models: Properties, Estimation and Testing , 1993 .

[16]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[17]  Leonard J. Tashman,et al.  Out-of-sample tests of forecasting accuracy: an analysis and review , 2000 .

[18]  José Neves,et al.  Genetic and Evolutionary Algorithms for Time Series Forecasting , 2001, IEA/AIE.

[19]  Mehmet Emre Çek,et al.  Analysis of observed chaotic data , 2004 .

[20]  A. F. Carley,et al.  Computational Methods in the Chemical Sciences , 1989 .

[21]  A. Gallant,et al.  Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications , 1989 .

[22]  Richard J. Povinelli,et al.  TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS , 1999 .

[23]  Warren S. Sarle,et al.  Stopped Training and Other Remedies for Overfitting , 1995 .

[24]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[25]  B. Curry,et al.  Neural networks: a need for caution , 1997 .

[26]  M. W Gardner,et al.  Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences , 1998 .

[27]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[28]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[29]  Bruce Curry,et al.  Neural networks and non-linear statistical methods: an application to the modelling of price-quality relationships , 2002, Comput. Oper. Res..

[30]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[31]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[32]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[33]  Jacob Boudoukh,et al.  Investigation of a Class of Volatility Estimators , 1997 .

[34]  Richard J. Povinelli,et al.  Identifying Temporal Patterns for Characterization and Prediction of Financial Time Series Events , 2000, TSDM.

[35]  Stephen Gray,et al.  Semiparametric ARCH models , 2001 .

[36]  Yonathan Bard,et al.  Nonlinear parameter estimation , 1974 .

[37]  Pilar Grau-Carles.  Empirical evidence of long-range correlations in stock returns , 2000 .

[38]  Robert Graham,et al.  Quantization of a two-dimensional map with a strange attractor , 1983 .

[39]  Philip E. Gill,et al.  Practical optimization , 1981 .

[40]  David Horn,et al.  Combined Neural Networks for Time Series Analysis , 1993, NIPS.

[41]  D. Sornette,et al.  Finite-time singularity in the dynamics of the world population, economic and financial indices , 2000, cond-mat/0002075.

[42]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .