Modeling U.S. National Defense Spending (1962–2023)

Author: Mykola Chernyashevskyy
Affiliation: University of Pittsburgh, Department of Physics and Astronomy
Email: myc21@pitt.edu

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🏛️ Introduction

This project explores long-term trends in U.S. national defense spending from 1962 to 2023, adjusted to constant FY 2017 dollars. The data reveals both cyclical and linear behavior—capturing both political cycles and long-term increases.

We fit the data using a combined sinusoidal + linear model and extract local maxima and minima to highlight key turning points in defense budgets. The plot also shades presidential administrations by party to provide historical context.

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📈 Data

• Source: U.S. historical budget data for national defense outlays (in constant FY 2017 USD).
• Years Covered: 1962–2023
• Data Shape:
  • year: 62 time points (1962–2023)
  • Spending: National defense spending (in billions)

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🧪 Methods

🔄 Fitting Function

The spending curve is modeled as:

[ y = A \cdot \sin(Bx + C) + Dx + E ]

Where:

• A: amplitude of oscillation
• B: frequency of oscillation
• C: phase shift
• D: slope of linear trend
• E: intercept

📌 Peak Detection

• Local Maxima: Identified using scipy.signal.find_peaks
• Local Minima: Detected by applying the same method to -y

🟦🟥 Administration Highlighting

U.S. presidential administrations are shaded:

• 🟦 Blue: Democratic
• 🟥 Red: Republican

These intervals are marked using plt.fill_betweenx.

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📊 Output

• ⚫ Scatter plot of original spending data
• 🟢 Sinusoidal + linear best-fit curve
• ❌ Annotated local peaks (green) and troughs (orange)
• 📋 Fit equation displayed directly on the plot
• 🟥🟦 Background shading for political context

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🧰 Dependencies

Make sure you have the following Python libraries installed:

pip install numpy matplotlib scipy