Air Passengers Time Series Forecasting using ARIMA

The number of people who fly on commercial aircraft has grown markedly since the middle of the twentieth century. Reliable forecasts of air passenger demand help airlines and regulators plan fleets, schedules and infrastructure. The AirPassengers data set — monthly counts of international airline passengers from 1949 to 1960 — is a classic benchmark for time series analysis because it exhibits both trend and seasonality [2]. In this report I revisit these data from a practical point of view. Inspired by a publicly available repository of code and plots8, I outline a reproducible workflow that involves exploratory graphics, variance-stabilising transformations, stationarity testing, decomposition of trend and seasonality, autocorrelation analysis and the fitting of a seasonal ARIMA model. I split the series into training and test samples, compare competing models using information criteria, and evaluate out-of-sample forecasts using root mean square error and mean absolute percentage error. The emphasis throughout is on clarity and brevity rather than exhaustiveness. The accompanying scripts and figures make it straightforward for readers to replicate the analysis and adapt the approach to other seasonal time series.