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Please give a mathematical explanation to the scientific nature of the BOll indicator?

The technical indicator boll does use standard deviation. Standard deviation is a very important concept in statistics. Let me first briefly explain what statistics are. Statistics is a method of obtaining information from data. Suppose we know some data, such as [19, 35, 25, 24, 68, 44, 17, 22, 34, 55] Maybe this data is the bust size of your female colleagues that you have painstakingly collected, or it is some kind of financial asset. price. No matter what it is, we can use statistics as a tool to analyze and obtain some information. For example, draw a histogram to see the distribution of data. Or find the average or median to see where the center of the data is, etc. These are descriptive statistics, which describe the data. If your data is just a sample, such as the closing price of a certain stock for one month, you can obtain some statistics of this sample through descriptive statistics based on the sample, such as the mean, variance, etc. But what you want to know are the overall parameters. Then we can make an inference about the population from the sample. This is the way of inferential statistics. Anyway, the larger the standard deviation, the greater the variation in the data. It reflects that the price of financial assets is more volatile. According to Chebyshev's law, in any sample, the proportion of data located between k times the standard deviation of the mean is at least 0. That is to say, at least 3/4 of the data fall between 2 times the standard deviation of the mean. 8/9 of the data are within 3 standard deviations of the mean. By default, boll uses the mean plus or minus 2 times the standard deviation. Form an upper and lower track. The calculation formula of the BOLL indicator is that the middle rail line = N-day moving average, the upper rail line = the middle rail line + 2 times the standard deviation, the lower rail line = the middle rail line - 2 times the standard deviation. If you are using 20ma. I have played with all the indicators such as macd, kdj, and other miscellaneous indicators using the boll method. Of course, not only the closing price can be bolled, but also the highest price, lowest price, and opening price. In this way, other oscillation indicators can also be programmed in the form of a K-line chart. Therefore, the boll indicator is a descriptive statistics for the closing price sample, using the average and standard deviation tools. This can also be used in other data processing. I'm just throwing ideas out there. Interested friends can study on their own and build their own trading system.