The Time Function of Stock Price

TL;DR

This paper introduces a mathematical model linking stock prices to time using white noise theory, providing insights into their movement, predictability, and implications for investment analysis.

Contribution

It establishes a novel integral white noise model for stock prices and derives key statistical functions to understand their behavior and predictability.

Findings

Stock price movements can be modeled as integral white noise processes.

Derived auto-correlation, displacement, and spectral density functions.

Provides a theoretical basis for stock price prediction and risk management.

Abstract

This paper tends to define the quantitative relationship between the stock price and time as a time function. Based on the empirical evidence that the log-return of a stock is the series of white noise, a mathematical model of the integral white noise is established to describe the phenomenon of stock price movement. A deductive approach is used to derive the auto-correlation function, displacement formula and power spectral density of the stock price movement, which reveals not only the characteristics and rules of the movement but also the predictability of the stock price. The deductive fundamental is provided for the price analysis, prediction and risk management of portfolio investment.