What Is a Hurst Exponent?

The Hurst exponent, named after British hydrologist Harold Hurst, was originally used to analyze the inflow and outflow between reservoirs and rivers, and has been widely used in fractal analysis in various industries.

Relabeling

A system with Hurst statistics does not require independent random event assumptions for general probability statistics. It reflects the results of a long list of interconnected events. What happens today will affect the future, and what happened in the past will also affect the present. This is exactly the theory and method we need to analyze the capital market. Traditional probability statistics are difficult to do. ^[2]

HURST

In studying the time series of floods using moment methods,

Hurst Index Stock Market Analysis

Many scholars have studied the chaotic characteristics of the Chinese stock market, not only explaining the chaotic characteristics in the process of the stock market operation, but also giving quantitative indicators of the chaotic characteristics. However, they did not give the structure of the chaotic attractor, but it is the basic characteristic of the chaotic state and the basic tool for describing chaos. Chaotic attractors have a fractal structure. Chaos and fractal are closely related. This thesis takes the Shanghai stock market as an example to analyze the fractal characteristics of the Chinese stock market.

The Chinese stock market has a complex chaotic structure, and we also give a quantitative index of the chaotic structure of the stock index return sequence. "These quantitative indicators are characteristic indicators of chaos." Another feature of chaos is that it has a chaotic attractor. The attractor is a fractal, and the fractal dimension is the most important index for dividing the shape. There are many definitions of fractal dimension. The two most commonly used fractal dimensions are Hausdorff dimension and box dimension. In 1983, Grassberger and Procaccia used the embedding theory and phase space reconstruction techniques to propose an algorithm for directly calculating the correlation dimension from a time series. This paper also uses this method to calculate the fractal dimension of chaotic attractors in the Chinese stock market. Let {xk: k = 1, N} be the time series obtained by observing a system, and embed it in m-dimensional Euclidean space to get the point set in this space. Its elements are: xn (m, ) = (xn, xn + , ..., xn + (m-1) ), n = 1, ... Nm, where: Nm = N- (m-1) . Calculate the distance rij from each of the remaining points to this point by selecting any point xi from Nm points. Repeat this process for all xi (i = 1, ..., Nm) to get the correlation integral function, where H (x ) Take 1 when x> 0, 0 when x0, and the associated dimension D is the limit of the function logCm (r) / logr when r 0.

Take the logarithmic return sequence of the daily closing value of the Shanghai Composite Index as an example to analyze the structure of the Shanghai stock market. The calculation is performed according to the aforementioned method, and the sequences are grouped, each group has 5 elements. Figure 2 shows the ln (R / S) -ln (N) logarithmic plot of the daily rate of return. Before taking the abscissa 5.01, the data is almost on a straight line. Regression calculation of ln (R / S) -ln (N) shows that the value of H is 0.683, which is greater than 0.5. It is a random walk, which is persistent. When the index was rising (declining) at the previous moment, the possibility of rising (declining) at the next moment is relatively large. From a relatively long time span, the H-index of the daily rate of return dropped significantly, approaching 0.5, which basically followed a random walk. Consider the V-statistic again, which is defined as V (N) = (R / S) /. As shown in Figure 3, a turning point is apparent around the abscissa of 5.01, and this value is obtained by taking the logarithm. This translates into exp (5.01), which is about 150 days. In the 150-day cycle, the volatility of the Shanghai Composite Index has obvious persistence. Over 150 days, the persistence diminishes and the characteristics of the system change significantly.

The fractal dimension of the chaotic attractor of the security index return sequence is estimated using the GP algorithm to be between 3 and 4, indicating that the market is globally determinative behind local randomness, that is, the operating system of the securities market will eventually converge to four Chaos attractor determined by several variables. Hurst index measures the statistical correlation of a time series. Through empirical analysis, the H index of the Shanghai Composite Index is 0.683, which is greater than 0.5, which indicates that the Shanghai Composite Index yield series has obvious persistence.

Excel Hurst Index Excel

Hurst index is an important indicator to describe the long period of non-function. It is different from the traditional unit root test. It can find the ultra-long periodicity of the time series, which can be used to judge the market risk, but the calculation is quite tedious. The Excel calculation alone is time-consuming and labor-intensive. Based on this, the macro program written in Excel's macro language VBA is used to easily calculate the Hurst index. Through this work, it is also hoped that the Hurst index can be widely used.