The Hilbert-Huang Transform(HHT) algorithm which proposed in recent years escape itself from the requirement of linear and smooth, and it has a clear physical meaning. The data comes from the Shanghai Composite stock index which is decomposed by HHT. It consists of two parts, the first part is empirical mode decomposition(EMD)， the second part is the Hilbert Spectrum. Firstly it gives all Intrinsic Mode Function (IMF) which is decomposed from EMD an interpretation of its physical meaning and introduces the concept of average oscillation cycle and compared the speed of between typical rise and fall times of volatility. On one hand, reconstruct the IMF and estimate its distribution for the purpose of drawing the best characterization cycle of all reconstructed IMF. On the other hand, calculate the average oscillation cycle of the treated IMF and finally derive the quantitative relationship between the two kinds of cycles. At last, to find the curve fits well with the envelope line of each IMF which has been transformed by Hilbert function. | The research of the periodic features of stock index volatility based on Hilbert-huang transformation
