FORECASTING APPLE INC. STOCK PRICES: A COMPARATIVE TIME SERIES ANALYSIS ACROSS MULTIPLE FORECAST HORIZONS

Abstract

This study evaluates the forecasting performance of time series models for Apple Inc. (AAPL) monthly closing prices from 2020 to 2025. Three methodologies were compared: Multiplicative Seasonal Decomposition, Holt’s Linear Trend, and ARIMA modeling within the Box-Jenkins framework. The analytical process involved Augmented Dickey-Fuller (ADF) stationarity testing, model identification via ACF/PACF, and out-of-sample forecast evaluation using MAE, RMSE, and MAPE metrics. The results indicate that while AAPL stock prices are non-stationary at levels, first-order differencing achieves stationarity (d = 1). The comparative analysis reveals that the ARIMA(0,1,0) model, representing a Random Walk process, demonstrated superior accuracy for a long-term 12-month horizon, consistent with the characteristics of efficient markets. Conversely, Holt’s Linear Trend yielded the lowest error metrics for short-to-medium-term forecasts (3-6 months). Seasonal Decomposition performed poorly across all horizons due to high stochastic volatility. These findings underscore that model effectiveness is horizon-dependent, suggesting that investors must strategically select forecasting tools based on specific investment timeframes and risk management objectives.

Keywords: Time Series Analysis, ARIMA Model, Holt’s Linear Trend, Seasonal Decomposition, Apple Inc. (AAPL)