Index Numbers and Time Series
Index Numbers and Time Series covers composite measures of price or quantity change and the analysis of data over time. The exam tests weighted index formulas, the consumer price index, and the components and moving-average method of a time series.
Core rules
- A simple aggregative index is (Σp₁/Σp₀) × 100. A simple average of price relatives is (Σ(p₁/p₀ × 100))/n.
- Laspeyres index = (Σp₁q₀/Σp₀q₀) × 100, using base-year quantities.
- Paasche index = (Σp₁q₁/Σp₀q₁) × 100, using current-year quantities.
- Fisher's ideal index = √(Laspeyres × Paasche), a geometric mean; it satisfies the time-reversal and factor-reversal tests.
- Time series components: trend (T), seasonal (S), cyclical (C) and irregular (I). A moving average of period k smooths fluctuations and estimates trend; for an even k, centre the averages.
Worked example
For two items, base prices are 10 and 20 with base quantities 5 and 2; current prices are 12 and 25. Find the Laspeyres price index. Σp₁q₀ = 12(5) + 25(2) = 60 + 50 = 110. Σp₀q₀ = 10(5) + 20(2) = 50 + 40 = 90. Laspeyres = (110/90) × 100 = 122.22. Prices rose by about 22.22% over the base period on base-year quantities.
Traps
Swapping base and current quantities between Laspeyres and Paasche; taking the arithmetic mean instead of the geometric mean for Fisher; using prices rather than quantities in a quantity index; and forgetting to centre a moving average when the period is even.