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Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold-Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

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BACKGROUND: This study aims to show that including pairwise hierarchical interactions of covariates and combining forecasts from individual models improves prediction accuracy. METHODS: The least absolute shrinkage and selection operator via hierarchical pairwise interaction is used in selecting variables that are not correlated and with the greatest predictive power in single forecast models (Gradient boosting method [GBM], Generalized additive models [GAMs], Support vector regression [SVR]) are used in the analysis. The best model was selected based on the mean absolute error (MAE), the best key performance indicator for skewed data. Forecasts from the 5 models were combined using linear quantile regression averaging (LQRA). Box and Whiskers plots are used to diagnose the overall performance of fitted models. RESULTS: Single forecast models (GBM, GAMs, and SVRs) show that including pairwise interactions improves forecast accuracy. The SVR model with interactions based on the radial basis kernel function is the best from single forecast models with the lowest MAE. Combining point forecasts from all the single forecast models using the LQRA approach further reduces the MAE. However, based on the Box and Whiskers plot, the SVR model with pairwise interactions has the smallest range. CONCLUSIONS: Based on the key performance indicators, combining predictions from several individual models improves forecast accuracy. However, overall, the SVM with pairwise hierarchical interactions outperforms all the other models.

Asunto(s)

COVID-19 , Humanos , Zimbabwe/epidemiología , Algoritmos , Modelos Lineales

RESUMEN

Background: The coronavirus pandemic has resulted in complex challenges worldwide, and the Southern African Development Community (SADC) region has not been spared. The region has become the epicentre for coronavirus in the African continent. Combining forecasting techniques can help capture other attributes of the series, thus providing crucial information to address the problem. Objective: To formulate an effective model that timely predicts the spread of COVID-19 in the SADC region. Methods: Using the Quantile regression approaches; linear quantile regression averaging (LQRA), monotone composite quantile regression neural network (MCQRNN), partial additive quantile regression averaging (PAQRA), among others, we combine point forecasts from four candidate models namely, the ARIMA (p, d, q) model, TBATS, Generalized additive model (GAM) and a Gradient Boosting machine (GBM). Results: Among the single forecast models, the GAM provides the best model for predicting the spread of COVID-19 in the SADC region. However, it did not perform well in some periods. Combined forecasts models performed significantly better with the MCQRNN being the best (Theil's U statistic=0.000000278). Conclusion: The findings present an insightful approach in monitoring the spread of COVID-19 in the SADC region. The spread of COVID-19 can best be predicted using combined forecasts models, particularly the MCQRNN approach.

Asunto(s)

COVID-19 , Humanos , COVID-19/epidemiología , Modelos Estadísticos , Modelos Lineales , Predicción , Pandemias

RESUMEN

A common problem that arises in extreme value theory when dealing with several variables (such as weather or meteorological) is to find an appropriate method to assess their joint or conditional multivariate extremal dependence behaviour. The method for choosing an appropriate threshold in peaks-over threshold approach is also another problem of endless debate. In this era of climate change and global warming, extreme temperatures accompanied by heat waves and cold waves pose serious economic and health challenges particularly in small economies or developing countries like South Africa. The present study attempts to address these problems, in particular, to deal with and capture dependencies in extreme values of two variables, by applying bivariate conditional extremes modelling with a time-varying threshold to Limpopo province's monthly maximum temperature series. Limpopo and North West provinces are the two hottest provinces in South Africa characterised by heat waves and the present study is carried out in the Limpopo province at Mara, Messina, Polokwane and Thabazimbi meteorological stations for the period 1994-2009. With the aim to model extremal dependence of maximum temperature at these four meteorological stations, two modelling approaches are applied: bivariate conditional extremes model and time-varying threshold. The latter approach was used to capture the climate change effects in the data. The main contribution of this paper is in combining these two approaches in bivariate extremal dependence modelling of maximum temperature extremes in the Limpopo province of South Africa. The findings of the study revealed both significant positive and negative extremal dependence in some pairs of meteorological stations. Among the major findings were the significant strong positive extremal dependence of Thabazimbi on high-temperature values at Mara and the strong negative extremal dependence of Polokwane on high-temperature values at Messina. The findings of this study play an important role in revealing information useful to meteorologists, climatologists, agriculturalists, and planners in the energy sector among others.

RESUMEN

Natural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000-2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September-April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.