Hierarchical forecasts for Australian domestic tourism

Abstract

In this paper we explore the hierarchical nature of tourism demand time series and produce short-term forecasts for Australian domestic tourism. The data and forecasts are organized in a hierarchy based on disaggregating the data for different geographical regions and for different purposes of travel. We consider five approaches to hierarchical forecasting: two variations of the top-down approach, the bottom-up method, a newly proposed top-down approach where top-level forecasts are disaggregated according to forecasted proportions of lower level series, and a recently proposed optimal combination approach. Our forecast performance evaluation shows that the top-down approach based on forecast proportions and the optimal combination method perform best for the tourism hierarchies we consider. By applying these methods, we produce detailed forecasts for the Australian domestic tourism market.

Forecasting with temporal hierarchies

“…We refer to (5) as the temporal reconciliation regression model. It is analogous to the cross-sectional hierarchical reconciliation regression model proposed by Hyndman et al (2011) and also applied in Athanasopoulos et al (2009) for reconciling forecasts of structures of tourism demand. A similar idea has been used for imposing aggregation constraints on time series produced by national statistical agencies (Quenneville and Fortier, 2012).…”

“…In general, Σ is not known and needs to be estimated. Hyndman et al (2011) and Athanasopoulos et al (2009) avoid estimating Σ by using ordinary least squares (OLS), replacing Σ by σ 2 I in (6). This is only optimal under some special conditions, such as when the reconciliation errors are equivariant and uncorrelated, or when the base forecast errors satisfy the same aggregation constraints as the original data (Hyndman et al, 2011), neither of which is likely to be true.…”

“…The top-down approach requires forecasts for only one time series at the very aggregate level. However aggregation implies a large loss of information and it is challenging to disaggregate the forecasts down the hierarchy (see Gross andSohl 1990 andAthanasopoulos et al 2009 for a summary of top-down approaches). In contrast bottom-up implies no loss of information but it requires many and possibly very noisy time series to be forecast.…”

“…To counter this significant limitation Hyndman et al (2011) introduced a regression based approach that instead optimally combines forecasts from all the series of the hierarchy and results in reconciled forecasts. This method is used by Athanasopoulos et al (2009) with good empirical results and further developed by Wickramasuriya et al (2015). As well as achieving reconciliation, this method has been shown to result in significant forecast improvements over the traditional approaches in the cross-sectional setting.…”

Combining country-specific forecasts when forecasting Euro area macroeconomic aggregates

“…The second group of combination weights is based on the original aggregation weights. We apply the novel combination strategy proposed by Athanasopoulos et al (2009) and Hyndman et al (2011) and the shrinkage method suggested by Stock and Watson (2004) to derive combination weights that also use information of the original aggregation weights. It should be noticed that one could also try to improve the forecasting performance of the forecast combination by selecting the most accurate forecast model for each countries' time series and then combine them.…”