《A Fractal Forecasting Model for Financial Time Series》.pdf

Journal of Forecasting J. Forecast. 23, 587–602 (2004) Published online in Wiley InterScience (). DOI: 10.1002/for.927 A Fractal Forecasting Model for Financial Time Series GORDON R. RICHARDS* Sprint, Kansas, USA ABSTRACT 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 princi- ples 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-F