Time Series Characteristics in Real Estate
Interactive visualizations of non-stationarity, autocorrelation, and heteroscedasticity
📈 Non-Stationarity
🔗 Autocorrelation
📊 Heteroscedasticity
Non-Stationary vs Stationary Series
Non-Stationary: Home Prices (Upward Trend)
Stationary: Year-over-Year Price Changes
What You're Seeing:
Top chart: Home prices increase persistently from $200,000 to $400,000 over 20 years. The mean increases over time (non-stationary).

Bottom chart: After differencing (computing year-over-year changes), the series fluctuates around 3-5% with stable variance (stationary). This transformed series is suitable for forecasting models.
Autocorrelation: How Today's Price Depends on Yesterday's
Office Rent Changes (Month-over-Month)
Autocorrelation Function (ACF)
Lag 1: 0.72 (Strong positive correlation) Lag 3: 0.48 (Moderate correlation) Lag 12: 0.15 (Weak correlation)
What You're Seeing:
Top chart: Office rent changes show momentum. When rents increase (above zero), they tend to increase again next month. This is positive autocorrelation.

Bottom chart: The ACF measures correlation at different lags. High values at lags 1-3 show strong short-term dependence. This autocorrelation structure provides forecasting power for time series models like ARIMA.
Changing Variance Over Time (Volatility Clustering)
Monthly Home Price Changes (%)
2000-2006 Std Dev: 0.5% (Calm period) 2008-2010 Std Dev: 2.5% (Turbulent period)
Rolling Standard Deviation (12-Month Window)
What You're Seeing:
Top chart: Price changes show calm periods (2000-2006) with small fluctuations, followed by turbulent periods (2008-2010) with large swings. Variance is not constant.

Bottom chart: Rolling standard deviation reveals volatility clustering. High-volatility periods persist, then markets calm down. Standard forecasting models assume constant variance; GARCH models explicitly handle this changing variance.