COMPLEX PATTERNS IN FINANCIAL TIME SERIES THROUGH HIGUCHI’S FRACTAL DIMENSION

COMPLEX PATTERNS IN FINANCIAL TIME SERIES THROUGH HIGUCHI’S FRACTAL DIMENSION T. G. GRACE ELIZABETH RANI Research and Development Center, Bharathiar University, Coimbatore 641046, Tamil Nadu, India G. JAYALALITHA Department of Mathematics, Vel’s University, Pallavaram 600117, Tamil Nadu, India

This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.
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