Abstract
Is it true that there is an implicit understanding that Brownian motion or fractional Brownian motion is the driving force behind stock price fluctuations? An analysis of daily prices and volumes of a particular stock revealed the following findings: 1) the logarithms of the moving averages of stock prices and volumes have a strong positive correlation, even though price and volume appear to be fluctuating independently of each other, 2) price and volume fluctuations are messy, but these time series are not necessarily Brownian motion by replacing each daily value by 1 or –1 when it rises or falls compared to the previous day’s value, and 3) the difference between the volume on the previous day and that on the current day is periodic by the frequency analysis. Using these findings, we constructed differential equations for stock prices, the number of buy orders, and the number of sell orders. These equations include terms for both randomness and periodicity. It is apparent that both randomness and periodicity are essential for stock price fluctuations to be sustainable, and that stock prices show large hill-like or valley-like fluctuations stochastically without any increasing or decreasing trend, and repeat themselves over a certain range.
Highlights
It is generally considered difficult to forecast the behavior of stock prices, and many methods have been proposed
Is it true that there is an implicit understanding that Brownian motion or fractional Brownian motion is the driving force behind stock price fluctuations? An analysis of daily prices and volumes of a particular stock revealed the following findings: 1) the logarithms of the moving averages of stock prices and volumes have a strong positive correlation, even though price and volume appear to be fluctuating independently of each other, 2) price and volume fluctuations are messy, but these time series are not necessarily Brownian motion by replacing each daily value by 1 or –1 when it rises or falls compared to the previous day’s value, and 3) the difference between the volume on the previous day and that on the current day is periodic by the frequency analysis
A preliminary study indicated that RND1, RND2, RND3, and RND4 are required for P, B, and S to fluctuate daily in the same manner as real data. These findings suggest that fluctuations in stock prices are characterized by both randomness and periodicity
Summary
It is generally considered difficult to forecast the behavior of stock prices, and many methods have been proposed. Technical analysts generally believe that prices move in trends, and that history tends to repeat itself. These trends may be a product of chance, and there may be a chance that large hill-like or valley-like fluctuations are considered to be trends. Chart patterns are a subjective form of analysis wherein technicians attempt to identify areas of support and resistance on a chart by observing specific patterns These patterns, identified based on experience and behavioral economics, are designed to predict where prices are headed following a breakout or breakdown from a specific price point. The most common technical indicators are moving averages, which smooth price data to make it easier to spot trends
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