Apple Company Daily Closing Price Prediction Based on Time Series Analysis and Monte Carlo Method

Abstract

Accurate forecasting of stock prices is critical for quantitative investment and risk management. This paper investigates the methodology and practical application of time series analysis and the Monte Carlo method in predicting AAPL’s daily closing prices. Time series are decomposed into several components so that models are built to capture the patterns of price change and generate forecasts. Empirical results show that the time series model can achieve acceptable prediction accuracy. But the overly smooth curve of price path indicate that the model fails to reflect fluctuations in real market environment. Meanwhile, the Monte Carlo method is used to extract statistical regularities and randomness from price changes. Specifically, it maps sample data to pseudo-random numbers, which are then employed for stochastic price simulation to generate future price paths. The model effectively simulates AAPL’s general trend and realistic fluctuations over the coming trading days, yet its outputs rely on historical data and random sampling and thus should be used with caution. Despite their different mechanisms, both methods yield consistent overall trend results, offering valuable references for trading or investing AAPL stock.