📊 Time Series Stationarity Visualizer

Created by Dr. Pedram Jahangiry | Enhanced with Claude

Generate any number of white-noise, random-walk, and cyclical series side by side and watch each one's conditional expectation E[X_t | X_(t-1), X_(t-2), ...] play out — constant for one, drifting or oscillating for the other two, which is the entire practical difference between a stationary process and a non-stationary one.

Explore conditional expectations E[X_t | X_(t-1), X_(t-2), ...] across different time series processes

📋 Usage Guide

Add Series: Click "Add Series" to generate multiple realizations of each process

Different Colors: Each series gets a unique color for easy identification

Teaching Tool: Use to manually demonstrate conditional expectations for different time horizons

1. White Noise Process

E[X_t | X_(t-1), X_(t-2), ...] = E[X_t] = μ (constant for all t) → STATIONARY

Mean (μ)

Variance (σ²)

Length

2. Random Walk with Drift

E[X_t | X_(t-1), X_(t-2), ...] = X_(t-1) + δ (depends on past values) → NON-STATIONARY

Drift (δ)

Variance (σ²)

Initial Value

Length

3. Cyclical/Seasonal Process

E[X_t | X_(t-1), X_(t-2), ...] = A·sin(ωt + φ) (time-varying pattern) → NON-STATIONARY

Amplitude (A)

Frequency (ω)

Phase (φ)

Noise (σ)

🎓 Teaching Points

White Noise: Conditional expectation is always μ regardless of conditioning set - perfectly stationary
Random Walk: Conditional expectation depends on the most recent value - non-stationary
Cyclical: Conditional expectation follows a predictable time-varying pattern - non-stationary but deterministic
Multiple Series: Generate several realizations to show the consistency of these properties across different samples