Paddy Walsh and Jonathan Blackledge
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 notably in financial time series analysis, but control engineering in general. This paper reports on the use of an indicator that is based on a Memory Function of the form ∼ 1/tβ , β > 0, and, in terms of a comparative analysis, the Lyapunov Exponent λ coupled with an approach whereby both parameters (i.e. λ and β − 1) are scaled according to the corresponding Volatility σ of the time series. A ‘back-testing’ procedure is used to evaluate and compare the performance of the indices (β − 1)/σ and λ/σ for forecasting and quantifying trends over a range of time scales. However, in either case, 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 obtained.