Some Proposal of the Test for a Random Walk Detection and Its Application in the Stock Market Data Analysis
According to the numerous groups of theoreticians and practitioners, who act in the area of financial markets, changes in the stock prices are random and it is almost infeasible to predict them correctly using historical data. This approach is based on the random walk theory, which states that the price of financial instrument in the subsequent time point is the sum of its price in the previous time point and some random variable with a finite variance, i.e. it is modeled with the use of a stochastic process called a random walk. The random walk hypothesis stands in contradiction to the beliefs of the ordinary technical analysis followers, where the prediction is carried out on the grounds of existing trends, and furthermore, this hypothesis regards such a modeling of financial markets as incorrect. In our work, we construct statistical test for a random walk detection, which is based on the first arcsine law. We also present simulation results that allow to check the quality of the proposed test, as well as we show the application of the introduced test in the stock exchange data analysis.(original abstract)
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