Time Series Analysis for a 1/tb Memory Function and Comparison with the Lyapunov Exponent using Volatility Scaling

Being able to provide accurate forecasts on the trending behaviour of time series is important in a range of applications involving the real time evolution of signals, most notable in financial time series analysis but control engineering in general. A critical solution for providing high accuracy forecasts is the filtering operation used to identify the position in time at which a trend occurs subject to a time delay factor that is inherent in the filtering strategy used. The paper explores this strategy and presents some example results that provide a quantitative measure of the accuracy used.