. Volatility also scales, but with a cross-over point of 1 day, with long-run correlations being particularly important. …

time series analysis due to the characteristic features of volatility processes. Provided that one can approximate the … volatility process. …

We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in … the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the … portfolio. Finally, we briefly discuss the potential practical effect of the virtual volatility on an investor asset allocation …

analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover … phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in … the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All …

long persistent time lag and slow decay in the autocorrelation functions of volatility. Besides, we find that the … scales; we also find that the PDFs of volatility, for short time horizons, fit better with a log-normal distribution than …

of long-range dependence in the volatility of 14 energy and agricultural commodity futures price series using the …

this method to stock volatility series. The method uses the techniques of the diffusion process and Rényi entropy to focus … on the scaling behaviors of regular volatility and extreme volatility respectively in developed and emerging markets. It … successfully distinguishes their differences where regular volatility exhibits long-range persistence while extreme volatility …

exponent about four or an exponential-type decay, the volatility, and its correlations depend on the opening effect of each …