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FPP2 §7.3: Holt-Winters additive and multiplicative methods on Australian international visitor nights 2005–2015
| Tool | Forecasting |
| Source | Hyndman, R. J., and Athanasopoulos, G. (2018). Forecasting: Principles and Practice, 2nd ed. OTexts, Melbourne. Section 7.3, Example "International tourist visitor nights in Australia", Tables 7.4 and 7.5 (copy in References/Forecasting-FPP/). |
| Level | Undergraduate |
Problem
Quarterly visitor nights (millions) spent by international tourists in Australia from 2005Q1 to 2015Q4 show a rising trend and strong seasonality. Fit the Holt-Winters additive and multiplicative methods, compare their in-sample RMSE and forecast the eight quarters 2016Q1 to 2017Q4.
Inputs to Enter
- Series: 44 quarterly values 2005Q1–2015Q4 (42.21, 24.65, 32.67, 37.26, … 73.26, 47.70, 61.10, 66.06), loaded by default with their period labels
- Season length 4, horizon 8, confidence 95 %, holdout 8 points, method Holt-Winters multiplicative (default) or additive; α, β, γ left blank
Answers
- Additive: α = 0.3063, β* = 0.0003, γ = 0.4263, RMSE 1.763; forecasts 2016Q1–2017Q4: 76.10, 51.60, 63.97, 68.37, 78.90, 54.41, 66.77, 71.18
- Multiplicative: α = 0.4406, β* = 0.0134, γ = 0.0023, RMSE 1.576; forecasts 80.09, 50.15, 63.34, 68.18, 83.80, 52.45, 66.21, 71.23
- The multiplicative method fits better (lower RMSE), as the book concludes
- Tool: additive RMSE 1.758, multiplicative 1.546; forecasts within 1 % (additive) and 1.5 % (multiplicative) of the printed ones
Notes
The tool's default inputs are this series; press Submit. The book's hw() fits ETS(A,A,A) / ETS(M,A,M) by likelihood with every initial state estimated, while the tool minimizes the one-step SSE with the states as parameters, so the parameters differ slightly and the tool's RMSE is lower; with the book's parameters and states entered, ℓ₄₄ = 63.22 and the 2015Q4 one-step forecast 64.22 are reproduced (test_forecasting.php).