Time Series Forecasting: US Accidental Deaths (1973-1978)

Project Overview

This project performs time series analysis and forecasting on monthly accidental deaths data in the USA from 1973 to 1978. It implements three forecasting problems using statistical models and provides comprehensive visualizations.

Objectives

1. Problem 1: Use Exponential Smoothing to predict January 1978 deaths
2. Problem 2: Use ARIMA to predict all 12 months of 1978
3. Problem 3: Calculate and visualize 95% confidence intervals for ARIMA forecasts

Dataset

File: usdeaths.csv Source: US Department of Transportation Period: January 1973 - December 1978 Frequency: Monthly Rows: 72 months Columns: Month index and Death count

Data Characteristics

• Seasonality: Strong yearly pattern (peaks in summer, lows in winter)
• Trend: Slight decreasing trend over 6 years
• Range: 6,981 to 11,317 deaths per month
• Average: ~8,700 deaths per month

Technical Implementation

Models Used:

Model	Purpose	Parameters	Library
Holt-Winters Exponential Smoothing	Single month prediction	trend='add', seasonal='add', period=12	statsmodels
ARIMA	Full year prediction	(p,d,q)×(P,D,Q)_m optimized via auto_arima	pmdarima
Confidence Intervals	Uncertainty quantification	95% confidence level	statsmodels

Key Features:

• Complete data preprocessing and visualization
• Model training on 1973-1977 data
• Testing on 1978 data
• Error metrics calculation (MAE, RMSE, MAPE)
• Confidence interval coverage analysis
• Publication-ready visualizations

Results Summary

Problem 1: Exponential Smoothing

• Predicted Jan 1978: 8,236 deaths
• Actual Jan 1978: 7,836 deaths
• Error: +400 deaths (+5.1%)

Problem 2: ARIMA Model

• Best Model: ARIMA(0,1,1)×(0,1,1)₁₂
• MAE: 392.5 deaths
• RMSE: 450.2 deaths
• MAPE: 4.8%

Problem 3: Confidence Intervals

• Coverage: 75% (9/12 months within 95% CI)
• Average CI Width: 1,650 deaths

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How to Use

1. Clone the repository:

   git clone https://github.com/Rahul950951/Time-Series-Forecasting-US-Accidental-Deaths.git
   

Author Rahul kapar