خلاصة:
Fractal analyzing of continuous processes have recently emerged in literatures in various domains. Existence of long memory in many processes including financial time series have been evidenced via different methodologies in many literatures in past decade, which has inspired many recent literatures on quantifying the fractional Brownian motion (fBm) characteristics of financial time series. This paper questions the accuracy of commonly applied fractal analyzing methods on explaining persistent or antipersistent behavior of time series understudy. Rescaled range (R/S) and power spectrum techniques produce fractal dimensions for daily returns of twelve Malaysian stocks from the most well performed firms in Kuala Lumpur stock exchange. Zipf’s law generates linear and logarithmic power-law distribution plots to evaluate the validity of estimated fractal dimensions on prescribing persistent and antipersistent characteristics with less ambiguity. Findings of this study recommend a more thoughtful approach on classifying persistent and antipersistent behaviors of financial time series by utilizing existing fractal analyzing methods.
ملخص الجهاز:
"Findings of this study recommend a more thoughtful approach on classifying persistent and anti-persistent behaviors of financial time series by utilizing existing fractal analyzing methods.
Quantifying financial time series by considering their scale invariance, non-stationary and non-Gaussian behavior flourished following a series of valuable literatures by Mandelbrot [1]-[3] who created and developed the concept of fractal geometry and then the fractal dimension by extending the previous works of Hurst and Hölder [4],[5].
Considering scale invariance feature of financial time series, mining it with Fractal dimension may produce valuable insight for pattern recognition, modeling and forecasting of market behavior, overcoming the shortcomings of commonly used Gaussian based statistical methods.
Meanwhile, the coherence between a non-stationary fractional Brownian motion (fBm) and its counterpart, the fractional Gaussian noise (fGn), encouraged a new structured methodology of fractal analysis in[15], [16] which provide consistent results by applying most of fractal dimension estimation methods on a given class (fBm or fGn) and inconsistent results for the other class.
Therefore, a fractional Brownian motion and a fractional Gaussian noise characterized by the same Hurst exponent have different spectral exponents: fBm=fGn-2 (11) There is a subtle critical fact that put power spectrum analysis ahead of rescaled range analysis in analyzing an unknown self-affine process.
Further similar studies on different financial data sets by applying more diverse fractal dimension estimation methods may end in choosing the best fractal analyzing procedure, reducing the ambiguity of results on this domain."