time series analysis for a 1/tβ memory function and comparison with the lyapunov exponent using volatility scaling

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ID: 249453
2016
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Abstract
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 $\sim 1/t^{\beta},\hskip 0.1truein \beta>0$, and, in terms of a comparative analysis, the Lyapunov Exponent $\lambda$ coupled with an approach whereby both parameters (i.e. $\lambda$ and $\beta-1$) are scaled according to the corresponding Volatility $\sigma$ of the time series. A \lq back-testing' procedure is used to evaluate and compare the performance of the indices $(\beta-1)/\sigma$ and $\lambda/\sigma$ 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.
Reference Key
walsh2016mathematicatime Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Paddy Walsh, Jonathan Blackledge
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Journal membranes
Year 2016
DOI
DOI not found
URL
http://e-hilaris.com/MA/2016/MA6_2_13.pdf
Keywords
filtering strategiesmathematics

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