Trend vs Seasonality vs Change Points
Three structures that look alike in a chart and mean entirely different things.
Three structures that look alike in a chart and mean entirely different things.
Slow movement in the level that persists across the record. The test is whether it survives lengthening the window. Many reported trends do not.
Repetition at a fixed period, stable in phase. It should be estimated over several complete cycles; two cycles is not evidence of a cycle.
A discrete change in level, slope or variance. The characteristic symptom of an unmodelled break is residuals that are strongly autocorrelated on one side of a date and not the other.
Fit with and without a changepoint and compare the residual structure, not just the score. A model that fits slightly worse but leaves clean residuals is usually describing the data better.
A trend extrapolates. A cycle repeats. A break says the pre-break data is a weaker guide than its volume suggests. Treating a break as a trend produces forecasts that continue a movement which has already finished.