Part I ยท Chapter 4
Visualizing Time Series
Always plot the series before modeling. Trends, seasonality, outliers, breaks, and volatility clustering jump out visually long before any formal test confirms them.
Learning objectives
Spot trend, seasonality, outliers, and structural breaks by eye.
Recognize volatility clustering vs constant variance.
Use moving averages to highlight underlying trend.
Decide what tests to run AFTER inspecting the plot.
Pattern toggles
Seed:
Detective notes
Toggle features and look at the chart.
A modeler must FIRST look at the plot, then choose models that match observed structure.
๐ Decomposition
\[ y_t = \mu_t + s_t + d_t + h_t z_t \]
ฮผ_t trend / level
s_t seasonal pattern
d_t dummy / outlier / break
h_t (possibly time-varying) volatility
๐ Decision tree (what to do next)
- Trend visible? โ check stationarity (ADF, KPSS), consider differencing.
- Seasonality? โ seasonal dummies or SARIMA with seasonal differencing.
- Structural break? โ Chow / Zivot-Andrews tests, intervention dummy.
- Volatility clustering? โ ARCH/GARCH model on residuals.
- Outlier? โ additive outlier dummy; don't delete.
โ ๏ธ Pro Tip: What to Avoid
Student says
"My ARIMA has low AIC and white residuals, so it's a good model."
Why this is wrong
If the series has a visible structural break the student ignored, the "good" model is fitting a process that no longer exists. AIC and diagnostics can't fix a missed regime change.
Correct interpretation
Always plot first. Visible features force model-class choices that no information criterion can correct after the fact.
๐ Mini-quiz
๐ Key Takeaways
| Visible feature | Treatment |
|---|---|
| Trend | Difference or detrend |
| Seasonality | Seasonal differencing, SARIMA, dummies |
| Outlier | AO dummy at that period |
| Structural break | Step dummy + slope dummy; Chow test |
| Volatility clustering | GARCH on residuals |