Financial Forecasting Using the Kolmogorov–Feller Equation
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 chapter using MetaTrader4.
KeywordsGeneralised Kolmogorov-Feller equation Impulse response function MetaTrader4 Mittag-Leffler memory function Time series analysis Trend analysis Stochastic volatility
The authors acknowledges the support of the Science Foundation Ireland and Enterprise Ireland.
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- 13.MT4 Indicators URL (2012) The MetaTrader4 indicators used to generates the results given in this paper are available from http://eleceng.dit.ie/jblackledge/Indicators.zipwhich provides the.mq4 modules requires to compute the Stochastic Volatility, the \(\alpha \)-index and the Lyapunov exponent