Hierarchical Forecasts of Agronomy-Based Data

SYNOPTIC ABSTRACT

In this article we explore the hierarchical nature of time series of various agriculture crops in Pakistan at the subdistrict level and produce short-term forecasts for these time series. The data and forecasts are organized in a hierarchy based on disaggregating the data according to the division and subdistrict levels (geographical regions). Following Athanasopoulos, Ahmed, and Hyndman, we consider five approaches to hierarchical forecasting; two variations of the top-down approach; the bottom-up method; top-down approach where top-level forecasts are disaggregated according to the forecasted proportions of the lower level series; and the new optimal combination approach introduced by Hyndman, Ahmed, Athanasopoulos, and Shang. The forecasts are obtained from these five approaches using two well-known methods; Exponential Smoothing (ES) and an autoregressive integrated moving average (ARIMA). The forecasts are then compared across the two methods and across the various approaches by using various out-of-sample forecast evaluations.

The forecast performance evaluation shows that in most cases either the top-down or the bottom-up approach performs best while the optimal combination method approach is the second best for the major crops production hierarchies we consider. By applying these methods, we produce detailed forecasts of the production of major crops in Pakistan for all levels of hierarchies and draw some useful conclusions for policy makers.

KEY WORDS AND PHRASES:

• ARIMA
• bottom-up method
• crops
• exponential smoothing
• hierarchical forecasting
• optimal combination forecasts
• top-down method

Acknowledgment

We are thankful to anonymous referees and the editor for their valuable comments on the manuscript that led to substantial improvement of the paper.

Funding

This work is partially supported by the Higher Education Commission (HEC) of Pakistan and the University of Agriculture, Faisalabad.