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An approach to analysing a financial time series using the Kolmogorov-Feller Equation is considered, in particular, the Generalised Kolmogorov-Feller Equation (GKFE) subject to variations in the Stochastic Volatility. Using the Mittag-Leffler memory function, we derive an expression for the Impulse Response Function associated with a short time window of data which is then used to derive an algorithm for computing a new index using a standard moving window process. It is shown that application of this index to financial time series, subject to a low volatility condition, correlates with the start, direction and end of a trend depending on the sampling rate of the time series and the look-back window or "period that is used. An example of this is provided in the paper using MetaTrader4.
Blackledge, J., Lamphiere, M., Murphy, K., Overton. Financial Forecasting Using the Kolmogorov-Feller Equation. IAENG Transactions on Engineering Technologies Lecture Notes in Electrical Engineering, 229. Springer Science+Business Media, 2013. doi:10.1007/978-94-007-6190-2_50