Time Series Data Analysis Using Fractional Calculus Concepts and Fractal Analysis
A study is conducted on time series data analysis relating the concept of the fractional calculus to fractals and to the fractal dimension. A new definition of the fractal dimension is provided based on a property of the fractional derivative. Using fractional Gaussian noise and fractional Brownian motion, simulations show the information content of a time series can be easily manipulated by the fractional derivative method and generated in real time.
Repperger, D. W.,
Farris, K. A.,
Barton, C. C.,
& Tebbens, S. F.
(2009). Time Series Data Analysis Using Fractional Calculus Concepts and Fractal Analysis. IEEE International Conference on Systems, Man and Cybernetics, 3311-3315.