Time Series Patterns Guide
Core components of a time series
Trend: The long-term direction of the metric. Identified by smoothing out noise (rolling average) and looking at the slope over 4+ periods.
Seasonality: Repeating patterns tied to a fixed calendar period — weekly (Monday dips), monthly (end-of-quarter spikes), or yearly (holiday peaks).
Cyclical variation: Longer, irregular fluctuations not tied to a calendar (economic cycles, product maturity phases). Harder to distinguish from trend changes.
Noise / residual: Random variation after accounting for trend, seasonality, and known events.
Detecting each pattern
Trend detection
- Plot the series with a rolling average (window = 4–8 periods)
- A consistently rising or falling rolling average indicates trend
- Compare first-third vs last-third of the series mean
Seasonality detection
- Plot the same metric across multiple years on the same axis
- Compare average value by day of week, week of year, or month
- High coefficient of variation within each year but low across years suggests seasonality
Anomaly detection
- Z-score:
(value - mean) / std. |z| > 2.5 is a common threshold - IQR method: flag values outside
[Q1 - 1.5×IQR, Q3 + 1.5×IQR] - Residual method: fit a trend + seasonal model; anomalies are large residuals
Period-over-period comparisons
| Comparison | Use case | Caveat |
|---|---|---|
| WoW (week over week) | Operational monitoring | Affected by day-of-week composition |
| MoM (month over month) | Business performance | Affected by different month lengths |
| YoY (year over year) | Strategy, removes seasonality | Affected by prior-year anomalies |
| Rolling 4-week average | Smoothed trend | Lags behind actual changes |
YoY comparisons are the most useful for metrics with strong seasonality. MoM and WoW are better for operational monitoring.
Common time series patterns and their interpretations
Step change: A sudden level shift at a point in time. Usually caused by a product change, policy change, or data pipeline change. Investigate what changed on that date.
Gradual decline: Slow but consistent downward trend. Often indicates product decay, customer churn accumulation, or competitive erosion. Requires understanding the cohort structure.
Hockey stick: Slow growth followed by rapid acceleration. Usually tied to a product or market inflection point. Validate that it's not a data artefact.
Sawtooth pattern: Regular sharp rises followed by drops. Common in metrics driven by monthly billing cycles, quota-based sales activity, or batch processing.
Spike and return: A one-period anomaly that returns to baseline. Usually a one-off event (outage, campaign, holiday). Lower investigation priority than persistent shifts.
Forecasting expectations
For most analytical contexts, a simple forecast is sufficient:
- Baseline extrapolation: Extend the recent trend forward
- Seasonal naive: Next period = same period last year × recent trend adjustment
- Rolling average: Next period ≈ last N-period average
For production forecasting systems, use proper time-series models (ARIMA, ETS, Prophet). For one-off analyses, the above are usually sufficient and far more explainable.
Documentation checklist for time series analysis
- Period covered, data source, and refresh cadence stated
- Seasonal adjustment applied or explicitly skipped (with reason)
- Trend direction and approximate rate quantified
- All anomalies flagged with known or hypothesised explanation
- Forecast produced with explicit assumptions and uncertainty range
- YoY context provided for any metric with visible seasonality