The tourism forecasting competition

We evaluate the performances of various methods for forecasting tourism data. The data used include 366 monthly series, 427 quarterly series and 518 annual series, all supplied to us by either tourism bodies or academics who had used them in previous tourism forecasting studies. The forecasting methods implemented in the competition are univariate and multivariate time series approaches, and econometric models. This forecasting competition differs from previous competitions in several ways: (i) we concentrate on tourism data only; (ii) we include approaches with explanatory variables; (iii) we evaluate the forecast interval coverage as well as the point forecast accuracy; (iv) we observe the effect of temporal aggregation on the forecasting accuracy; and (v) we consider the mean absolute scaled error as an alternative forecasting accuracy measure. We find that pure time series approaches provide more accurate forecasts for tourism data than models with explanatory variables. For seasonal data we implement three fully automated pure time series algorithms that generate accurate point forecasts, and two of these also produce forecast coverage probabilities which are satisfactorily close to the nominal rates. For annual data we find that Naïve forecasts are hard to beat.     

Reworking wild bootstrap-based inference for clustered errors

Cluster-robust inference is increasingly common in empirical research. With few clusters, inference is often conducted using the wild cluster bootstrap. With conventional bootstrap weights the set of valid $P$-values can create ambiguities in inference. I consider several modifications to the bootstrap procedure to resolve these ambiguities. Monte Carlo simulations provide evidence that both a new 6-point bootstrap weight distribution and a kernel density estimation approach improve the reliability of inference. A brief empirical example highlights the implications of these findings.