Forecasting with Temporal Hierarchies

TLDR: Forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty, and the implied combination mitigates modelling uncertainty.

About: This article is published in European Journal of Operational Research.The article was published on 2017-10-01 and is currently open access. It has received 164 citations till now. The article focuses on the topics: Probabilistic forecasting & Consensus forecast.

Figures

Figure 1: Temporal hierarchy for quarterly series.

Table 3: Estimated parameters for the ARIMA DGP at the monthly frequency. Theoretically derived parameters for the observationally equivalent ARIMA representations for each aggregation level above the monthly level.

Table 5: Entries show the percentage differences in RMSE between ETS and ARIMA base forecasts and reconciled forecasts. A negative (positive) entry represents a percentage decrease (increase) in RMSE relative to the base forecasts at that aggregation level.

Figure 2: Temporal hierarchy for quarterly series using the common index i for all levels of aggregation.

Table 6: The thirteen weekly A&E time series used in the case study.

Table 7: Average MASE for the base and temporally reconciled forecasts across all A&E time series, and percentage change, for different forecast horizons (h). A negative entry indicates a percentage decrease in MASE for the reconciled forecasts compared to the base forecasts.

Frequently asked questions

Q1. What have the authors contributed in "Forecasting with temporal hierarchies" ?

This paper introduces the concept of Temporal Hierarchies for time series forecasting. The authors discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments. 

Q2. What are the advantages of using temporal hierarchies for forecasting?

temporal hierarchies incorporate the advantages of forecast combinations, such as reducing forecast error variance and diverging model uncertainty in terms of model specification and estimation across aggregation levels. 

Q3. What is the effect of using temporal hierarchies on forecast accuracy?

The resulting forecasts from using temporal hierarchies bring the benefits of estimation efficiency and potential seasonal information from the lower levels to the annual level and take the trend information at the aggregate levels to the monthly level. 

Q4. What is the minimum requirement for a reconciliation of forecasts?

To achieve consistent forecasts that support all decisions from operational to strategic, the reconciliation must be done at different data frequencies and different forecast horizons. 

Q5. What types of A&E departments in the UK record a number of demand statistics?

A&E departments in the UK record a number of demand statistics, classified under three types: major A&E, single specialty and other/minor A&E. 

Q6. How many hours should patients be seen, treated and discharged within the first four hours?

since 2004 a four-hour target was introduced for the emergency departments: at least 98% of patients should be seen, treated and subsequently admitted or discharged within four hours. 

Q7. What is the performing temporal hierarchy forecast for the monthly time series?

The best performing temporal hierarchy forecast for the monthly time series obtained an error of 13.61%, usingETS and WLSS , while for the quarterly that was 9.70%, using ARIMA and WLSV . 

Q8. What is the efficient estimation of the correct observationally equivalent DGPs?

The most efficient estimation of the correctly specified observationally equivalent DGPs is achieved at this very bottom aggregation level which provides estimation with the most degrees of freedom. 

Q9. What is the main reason for the use of unweighted combinations of forecasts?

In the context of temporal aggregation, Kourentzes, Petropoulos and Trapero (2014) use unweighted combinations of forecasts from different aggregation levels, but provide evidence that weighted combinations are beneficial using ad-hoc weights. 

Q10. What is the next step in forecasting?

Obviously the next step is an integrated hierarchical forecast that will result in consistent forecasts for organisations to base their plans and decisions on. 

Q11. What can be done to ensure adequate number of nurses and doctors?

patient bed capacity can be planned accordingly while ensuring adequate number of nurses and doctors to make use of them; and (at a longer horizon) to train them accordingly.