Analysis of Statistical Properties of Ranges and its Application to Estimation of Corporate Status

K. Tan and S. Tokinaga (Japan)


Stock returns, Ranges, Wavelet transform, Kernel-based discriminant Analysis, Genetic algorithm.


In this study we firstly analyze some statistical properties of ranges of stock returns in the real markets. Then, we point out that these statistical properties, especially the fractal dimensions, can be utilized in evaluating the management statuses of those listed firms, namely, to see whether a corporate is making profit or not. This is a completely new approach to support investors’ decision-making. It usually applies linear discriminant analysis to financial ratios for such kind of evaluation. However, it has been well filed that normality seldom holds for the most of financial ratios calculated from Balance Sheet (B/S) and Loss and Profit Sheet (L/P), they sometimes contain outliers as well. It also costs resources to collect account information to calculate ratios. Moreover, to avoid a tumble of stock price, some firms tend to disclose biased or fake information to prevent pepole from understanding their troubled statuses. In this study, we propose to apply estimated fractal dimensions of ranges to nonlinear discriminant analysis, by introducing a kernel-based method. Our numerical results show that our proposed method works well and efficiently compared to the traditional linear discriminant analysis, by mapping the fractal dimensions into a higher dimension. And the parameter in the kernel function is optimized by Genetic Algorithm.

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