A fractal forecasting model for financial time series
Financial market time series exhibit high degrees of non-linear variability, and frequently have fractal properties. When the fractal dimension of a time series is non-integer, this is associated with two features: (1) inhomogeneity-extreme fluctuations at irregular intervals, and (2) scaling symmetries-proportionality relationships between fluctuations over different separation distances. In multivariate systems such as financial markets, fractality is stochastic rather than deterministic, and generally originates as a result of multiplicative interactions. Volatility diffusion models with multiple stochastic factors can generate fractal structures. In some cases, such as exchange rates, the underlying structural equation also gives rise to fractality. Fractal principles can be used to develop forecasting algorithms. The forecasting method that yields the best results here is the state transition-fitted residual scale ratio (ST-FRSR) model. A state transition model is used to predict the conditional probability of extreme events. Ratios of rates of change at proximate separation distances are used to parameterize the scaling symmetries. Forecasting experiments are run using intraday exchange rate futures contracts measured at 15-minute intervals. The overall forecast error is reduced on average by up to 7% and in one instance by nearly a quarter. However, the forecast error during the outlying events is reduced by 39% to 57%. The ST-FRSR reduces the predictive error primarily by capturing extreme fluctuations more accurately. Copyright © 2004 John Wiley & Sons, Ltd.
Volume (Year): 23 (2004)
Issue (Month): 8 ()
|Contact details of provider:|| Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999.
"Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance,"
The Review of Economics and Statistics,
MIT Press, vol. 81(4), pages 617-631, November.
- Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000. "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance," Working Papers 00-04, Duke University, Department of Economics.
- Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
- Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
- Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
- Hsieh, David A., 1993. "Implications of Nonlinear Dynamics for Financial Risk Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 41-64, March.
- Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
- Laurent-Emmanuel Calvet & Adlai J. Fisher, 2002. "Multifractality in Asset Returns: Theory and Evidence," Post-Print hal-00478175, HAL.
- Johnson, Timothy C, 2002. "Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 390-411, July.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, "undated". "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
- Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
- Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
- Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
- Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
- Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
- Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:jof:jforec:v:23:y:2004:i:8:p:586-601. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.