It is generally considered difficult to forecast the behavior of stock prices, and thus many methods have been proposed. For example, fundamental analysis and technical analysis are widely used approaches. Fundamental analysis involves investigating any data that can be expected to impact the price of
It is generally considered difficult to forecast the behavior of stock prices, and thus many methods have been proposed. For example, fundamental analysis and technical analysis are widely used approaches. Fundamental analysis involves investigating any data that can be expected to impact the price of a stock. The advantage of this method is that the estimation is objective because the selected economic indicators such as future growth, return on equity, and profit margins are inputted into a particular relational expression to predict the stock price. However, because there is often a time lag prior to the release of economic indicators, one drawback of this approach is that the economic indicators may be outdated. In contrast, technical analysis focuses only on the trading and price history of a stock. The principle underlying technical analysis is that the market price reflects all available information that could affect the stock market. As a result, there is no need to take new economic developments into account because they are already priced into a given security. Technical analysts generally believe that prices move in trends, and that history tends to repeat itself. However, these trends may be a product of chance, and there may actually be a chance that large hill-like or valley-like fluctuations are also considered to be trends. It seems that the market fluctuates based on psychological aspects. There are two major types of technical analysis: chart patterns and technical indicators. 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. Technical indicators are a statistical form wherein technicians apply various mathematical formulas to prices and volumes. The most common technical indicators are moving averages, which smooth price data to make it easier to spot trends.
Difficulties arise in terms of predicting stock prices because daily changes in stock prices seem to be quite random. In particular, fluctuations in stock prices are considered to follow Brownian motion, fluctuating independently of past stock prices. The notion of using a Brownian motion process to explain the behavior of stock prices was first proposed by Black et al. . A Brownian motion process has the property of independent increments. This means that the present price does not affect future prices. However, the present stock price may influence the stock price at some time in the future. Hence, a Brownian motion process is not suitable for explaining stock price movements. Subsequently, a fractional Brownian motion process, which exhibits the property of long-range dependence, was proposed . Meanwhile, it is also considered that there is a relationship between stock price and volume  . Volume is an important aspect of technical analysis because it is used to confirm trends and chart patterns. Any price motion up or down with relatively high volume is seen as a stronger, more relevant move than a similar move with weak volume. Data that are available to general investors include time series of stock prices and volumes. As pointed out in the past, the trend of the stock price itself is random , and using this data alone, it is completely unpredictable how the price will change in the near future. However, since volume is a measure of how much interest sellers and buyers have in the stock, volume data provide a better understanding of stock price fluctuations.
There is already a famous stochastic differential equation that attempts to mathematically elucidate the transition of one bond and one or more stock prices , but the purpose of this study is to reveal the driving force behind sustainable fluctuations in the price of an arbitrary stock using a mathematical model. The rest of this paper is organized as follows. Sections 2 and 3 clarify the relationship between stock prices and volumes, Section 4 presents a model of the proposed relationship, Sections 5 and 6 present an interpretation of the simulation, and Section 7 discusses the effectiveness of the model by comparing the results of the simulation with real data.
2. Characteristics of the Real Data
It is possible to obtain time-series data (e.g., closing prices and volumes) in relation to stock prices for free via 