Using Probability Theory and the Discrete Fourier Transform to Develop Equity Trading Strategies

Abstract:

Although stock prices depend on a wide array of economic factors, the purpose of this research is to analyze them from a mathematical standpoint. This analysis consists of two approaches: one of probability theory, and one of Fourier analysis. First, probability theory is used to calculate the theoretical probabilities of short-term trends in random data. Then, these are compared to the probabilities of the same short-term trends in stock price data. This comparison is accomplished via the Kolmogorov-Smirnov test, which reveals that the probabilities differ from their theoretical values in random data. Second, Fourier analysis, accomplished via the Discrete Fourier Transform, is used to detect periodicity in data. If there is periodicity in stock price data, this could hint at where optimal entry and exit points may lie. However, the data analyzed here does not exhibit any notable periodicities. Hypothetically, a combination of the above strategies – the probability of short-term trends, and periodic behavior – could be used to construct a profitable trading strategy. Such a strategy could be applied in the short term on a daily level, or over a longer time period, depending on the frequency of observations..