Time Series Characteristics
When examining a time series plot, identify these features to determine preprocessing needs:
Non-constant Variation
Amplitude of fluctuations changes over time. If present → variance-stabilizing transformation (e.g., log) first.
Trend
Systematic upward/downward drift. Mean $E(X_t)$ depends on $t$.
Seasonality
Repeating periodic pattern with known period $d$. Monthly: $d=12$; quarterly: $d=4$.
Outlier / Change Point
Isolated extreme values or abrupt shifts in level/variance.
Random Noise
What remains after removing trend, seasonality, and outliers. This is the component we model as stationary.
Visual Rule for Stationarity
If any of the following are visible, the series is not stationary: trend, seasonality, non-constant variance, change point.