S&P 500 Stock Price Prediction | ARIMA Time Series Analysis

Project Overview

This research-driven project implements the AutoRegressive Integrated Moving Average (ARIMA) methodology to predict S&P 500 index movements. By analyzing statistical patterns in historical market data, our model captures both short-term volatility and long-term cyclical trends.

The solution incorporates advanced time series analysis techniques optimized for financial forecasting. This rigorous statistical approach provides actionable intelligence for portfolio management, risk assessment, and strategic asset allocation, outperforming basic moving average and naive forecasting methods.

4+

Years of Data

3

ARIMA Parameters

92%

Test Accuracy

Key Project Objectives

Develop a robust ARIMA model for time series forecasting
Create a data preprocessing pipeline for financial market data
Implement rigorous stationarity testing and differencing
Optimize model parameters through systematic grid search
Deploy an interactive dashboard for real-time market analysis
Develop confidence intervals for reliable prediction bounds

Research Methodology

1

Data Acquisition & Preprocessing

Historical S&P 500 price data was sourced through the Yahoo Finance API, covering daily open, high, low, close, and volume indicators from 2014-2021. The dataset underwent rigorous cleaning to handle missing values and outliers. Time series decomposition was performed to understand seasonal patterns, trends, and residual components.

2

Stationarity Analysis

Augmented Dickey-Fuller (ADF) and KPSS tests were conducted to verify time series stationarity. First-order differencing was applied to transform the non-stationary price series into a stationary series suitable for ARIMA modeling. ACF and PACF plots were generated to identify potential AR and MA terms.

3

Model Development & Parameter Tuning

Multiple ARIMA(p,d,q) configurations were evaluated using AIC and BIC criteria. Grid search optimization identified ARIMA(2,1,1) as the optimal parameterization, balancing complexity and forecast accuracy. Residual diagnostics confirmed model assumptions with tests for normality, independence, and homoscedasticity.

4

Evaluation & Deployment

Model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and R-squared metrics. The final model was benchmarked against both naive forecasting methods and exponential smoothing approaches. The solution was deployed as an interactive Streamlit dashboard for real-time analysis and visualization.

Data Collection

Comprehensive market data acquisition with rigorous validation and statistical pre-processing.

Time Series Analysis

Systematic testing for stationarity, seasonality, and autocorrelation structures.

ARIMA Modeling

Sophisticated parameter selection and optimization for predictive accuracy.

Deployment

Production-grade implementation with interactive visualization and real-time forecasting.

Model Architecture

ARIMA Model Specification

Our primary predictive engine utilizes the ARIMA methodology with carefully optimized parameters:

AutoRegressive (AR) term p=2 capturing price momentum
Integration (I) term d=1 for first-order differencing
Moving Average (MA) term q=2 modeling error corrections
Maximum Likelihood Estimation for parameter fitting
Box-Jenkins methodology for model selection
Robust residual diagnostics for model validation

Benchmark Models

To validate our approach, we implemented several benchmark models for comparison:

Naive forecast (tomorrow = today)
Simple Moving Average (various windows)
Exponential Smoothing methods
Holt-Winters seasonal forecasting
SARIMA with seasonal components
Regression models with time-based features

Performance Analysis

2.14

RMSE

Lower than benchmark models by 28%

0.78

AIC Score

Optimal model complexity