Time Series Analysis
What the domain covers
Time series analysis separates a series into trend, seasonal, cyclical and irregular components and uses moving averages or least squares to estimate trend. The exam tests component identification, moving-average mechanics and seasonal-index interpretation.
Core rules
- Components: long-term trend (T), seasonal variation (S), cyclical fluctuation (C), irregular/random movement (I).
- Additive model: Y = T + S + C + I. Multiplicative model: Y = T × S × C × I.
- A moving average smooths short-term fluctuations. For an odd period m, average m consecutive values; for even m, use a centred moving average.
- Least-squares trend: fit Y = a + bt with t coded from the middle so Σt = 0; then a = ΣY/n and b = ΣtY/Σt².
- Seasonal indices show relative seasonal position; for monthly data they should sum to 1200% under the percentage method.
Worked example
For values 10, 12, 14, 16, a 3-year moving average gives (10+12+14)/3 = 12 and (12+14+16)/3 = 14. These averages are placed against the middle years. For an even period such as 4, a single 4-year average falls between years, so a 2-year average of successive 4-year averages is used to centre it.
Traps
Do not place a 3-year moving average against the first year; it belongs to the middle year. Even-period moving averages need centring. A trend line does not by itself forecast a seasonal series. Do not add seasonal indices to 100 when using monthly percentages; the total is 1200%. Cyclical and irregular components are often merged in short series.