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FPP2 §7.2: Holt's linear trend method on Australian air passengers 1990–2016
| Tool | Forecasting |
| Source | Hyndman, R. J., and Athanasopoulos, G. (2018). Forecasting: Principles and Practice, 2nd ed. OTexts, Melbourne. Section 7.2, Example "Air Passengers", Table 7.3 (copy in References/Forecasting-FPP/). |
| Level | Undergraduate |
Problem
Annual passenger numbers (millions) carried by Australian airlines from 1990 to 2016 rise with a roughly linear trend. Fit Holt's linear trend method with the two smoothing parameters and the initial level and slope estimated from the data, and forecast 2017 to 2021.
Inputs to Enter
- Series (27 values, 1990–2016): 17.55 21.86 23.89 26.93 26.89 28.83 30.08 30.95 30.19 31.58 32.58 33.48 39.02 41.39 41.60 44.66 46.95 48.73 51.49 50.03 60.64 63.36 66.36 68.20 68.12 69.78 72.60
- Method: Holt's linear trend; season length 1; horizon 5; α and β left blank; damped trend off
Answers
- α = 0.8321, β* = 0.0001, ℓ₀ = 15.57, b₀ = 2.102
- Final states ℓ₂₇ = 72.50, b₂₇ = 2.102; one-step forecast of 2016 = 72.02
- Forecasts 2017–2021: 74.60, 76.70, 78.80, 80.91, 83.01
Notes
Paste the 27 values and choose Holt with season length 1. The SSE surface is flat in α, so the tool's α may differ from 0.8321 by up to 0.02 and the forecasts by up to 0.5 (test_forecasting.php); with the book's parameters entered the states reproduce to 0.02 %.