Abstract
Predicting and forecasting weather time series has always been a difficult field of research analysis with a very slow progress rate over the years. The main challenge in this project—The Optimal Challenges in Irrigation (TO CHAIR)—is to study how to manage irrigation problems as an optimal control problem: the daily irrigation problem of minimizing water consumption. For that it is necessary to estimate and forecast weather variables in real time in each monitoring area of irrigation. These time series present strong trends and high-frequency seasonality. How to best model and forecast these patterns has been a long-standing issue in time series analysis. This study presents a comparison of the forecasting performance of TBATS (Trigonometric Seasonal, Box-Cox Transformation, ARMA errors, Trend and Seasonal Components) and regression with correlated errors models. These methods are chosen due to their ability to model trend and seasonal fluctuations present in weather data, particularly in dealing with time series with complex seasonal patterns (multiple seasonal patterns). The forecasting performance is demonstrated through a case study of weather time series: minimum air temperature.
Highlights
In a world where climate change and increasing social conflicts are a reality, a proper management of the existing scarce resources is vital
The results obtained from the application of TBATS and regression models (RM) with correlated errors methods are reported
The methods considered in this study are applied to two sets: training data and testing data in order to testify the accuracy of the proposed forecasting models
Summary
In a world where climate change and increasing social conflicts are a reality, a proper management of the existing scarce resources is vital. Understanding the behaviour of humidity in the soil by mathematical/statistical modeling allows, among others, an efficient planning of water use via irrigation systems [1]. 2017 was an extremely dry year and, considering the data from January 1st, 2017 to December 27th, 2017, it will be among the 4 driest years since 1931 (all occurred after 2000), and the average annual total precipitation will be about 60% of what is deemed normal. Our data source are the records of the variable minimum air temperature observed in a farm located in Vila Real County, in northern Portugal, in the field of agriculture irrigation, registered in the period from January 23rd, 2015 to August 11th, 2018 on a daily basis. The main goal is to forecast these environmental variables at a location (in this case, at the farm), where there are historical observations but current measurements are not available (including various steps for forecasting (i.e., 7 days))
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