The ACT tobacco expenditure appears to have a clear downward trajectory, decreasing by 90% over decades of tobacco taxes and public health policy. This drop is not linear: There is a distinct temporary “bounce” from around 2000 when expenditure returns to $0.24–0.25 billion, then continues down. Superimposed on this trend is a small regular quarterly wobble, which appears as the “sawtooth” pattern in the time plot. This is reflected in the seasonal plot which shows a relatively flat plot for each year, with most of the explanatory power going into the colour gradient (year) — that is, the seasonal swing within each year is fairly small relative to the trend across the years. The subseries plot also supports this: the quarter means for each of the four quarter periods (Q1–Q4) show a similar downward trend, with the trend for Q4 being slightly higher than the other quarters, suggesting that the seasonal effect is real but minor compared to the overall trend.
The two decompositions show the same trend shape,and both fail to capture the first two quarters of the trend estimation (with the small NA box at the beginning), which is to be expected from the moving-average method at the core of both decompositions. This is why you see the two seasonal panels are looking so alike here, it’s not that STL didn’t have the edge, it’s that this particular spec had it turned off.
The story of the accuracy table is visually apparent from looking at the forecast plot: Mean, Naive, and SNaive all show roughly horizontal lines from the end of the training data, and the true holdout data continues to fall off sharply below all three. The only way the downward slope continues into the forecast period is by drift, which follows the true decline pretty well hence its dominance in all of the accuracy measures: Forecasting methods that ignore the trend (Mean, Naive, SNaive) will systematically over forecast when the trend continues past the training window.
