Sales Forecasting System with ARIMA
An advanced time series forecasting application implementing real ARIMA (AutoRegressive Integrated Moving Average) models with mathematical precision. This client project features their custom frontend design enhanced with a fully functional backend system for accurate sales predictions and statistical analysis.
Project Overview
This Sales Forecasting System is a client-commissioned project where they provided the initial frontend design and requirements. My role was to transform their vision into a fully functional application by implementing the complete backend architecture and mathematical algorithms.
The system implements genuine ARIMA methodology with real mathematical formulas including Yule-Walker equations for AR parameter estimation, Levinson-Durbin algorithm for efficient Toeplitz matrix solving, and Method of Moments for MA parameter estimation. Unlike simplified forecasting tools, this application performs actual statistical computations to deliver professional-grade time series analysis.
Built with Python Flask for robust backend processing and a modern JavaScript frontend using Chart.js for interactive visualizations. The system processes CSV time series data, applies differencing transformations, estimates model parameters through maximum likelihood methods, generates multi-step forecasts with confidence intervals, and provides comprehensive residual diagnostics including ACF/PACF analysis and Ljung-Box statistics.
Technology Stack
Key Features
Real ARIMA Implementation
Genuine ARIMA(p,d,q) modeling with mathematical algorithms: Yule-Walker equations, Levinson-Durbin algorithm, and Method of Moments.
Mathematical Parameter Estimation
AR parameters via Yule-Walker/Levinson-Durbin, MA parameters through moment matching with Newton-Raphson refinement.
Differencing Transformations
Automatic application of d-order differencing to achieve stationarity in time series data before modeling.
Multi-Step Forecasting
Generate forecasts for 1 to 100+ steps ahead with proper error propagation and confidence interval calculations.
95% Confidence Intervals
Calculate forecast standard errors and confidence bounds using theoretical ARIMA variance formulas.
Residual Diagnostics
Complete residual analysis with mean, variance, standard deviation, and visual scatter plots for model validation.
ACF/PACF Analysis
Autocorrelation Function (ACF) visualization with up to 20 lags for model adequacy assessment.
Ljung-Box Test
Statistical test for autocorrelation in residuals using Q-statistic: Q = n(n+2) Σ[ρ²(k)/(n-k)].
Model Selection Criteria
AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) for comparing different ARIMA specifications.
CSV Data Processing
Import time series data from CSV files with date parsing and validation. Supports 10 to 1000+ data points.
Sample Data Generator
Built-in generator creating realistic time series with trend, seasonality, AR components, and Gaussian noise.
Interactive Visualizations
Dynamic Chart.js graphs showing historical data, forecasts, confidence intervals, residuals, and ACF plots.
Detailed Forecast Table
Tabular display of each forecast point with date, predicted value, standard error, and confidence bounds.
Manual Parameter Control
Adjust ARIMA(p,d,q) parameters manually with real-time formula display showing the current model equation.
Mathematical Formula Display
Live rendering of ARIMA equation: ∇^d X_t = φ₁X_{t-1} + ... + φₚX_{t-p} + ε_t + θ₁ε_{t-1} + ... + θₑε_{t-q}
Log-Likelihood Estimation
Calculate model log-likelihood: ℓ = -n/2·log(2π) - n/2·log(σ²) - 1/(2σ²)·Σε²
Trend & Seasonality Handling
Properly handles non-stationary data through differencing, preserving long-term trends and seasonal patterns.
Responsive Design
Client's custom frontend design optimized for desktop and mobile viewing with smooth animations.
Status Notifications
Real-time feedback during data processing, parameter estimation, and forecasting with success/error messages.
Clean Code Architecture
Object-oriented JavaScript implementation with proper separation of concerns and modular Flask backend.
Screenshots
