# Short-Term Wind Speed Forecasting Using Statistical and Machine Learning Methods
## 3 Analysis of the Forecasting Results  
### Source and Description of Case Study  
The dataset contains meteorological data with features such as wind speed, wind direction, humidity, barometric pressure and air temperature recorded from different wind turbine (WT) hub heights [47, 48]. The response variable is the mean wind speed measured at 62-m altitude of the WT (i.e., WS_62_mean); all other measured quantities from the wind power plant at varying heights were fed into the variable selection model. The data were obtained from the Wind Atlas South Africa website ([[http://wasadata.csir.co.za/wasa1/WASAData](http://wasadata.csir.co.za/wasa1/WASAData)]([http://wasadata.csir.co.za/wasa1/WASAData](http://wasadata.csir.co.za/wasa1/WASAData))). Many data for various locations where readings were carried out are available on this website. The data corresponding to Location 3 (WM03), which is the Vredendal in the Western Cape province of South Africa, were used for this research. WM03 was picked because it has a small amount of null and nan values, also known as missing data. The missing values were imputed and cleaned up during the data pre-processing stage. Another reason for choosing WM03 is because the needed properties for time series forecasting, such as trend, periodic seasonality and residuals, were observed in the visualisation of the decomposition of its response variable (mean wind speed measured at 62 m, i.e., WS_62_mean) compared to those of the other points (see Appendix A, Figure A2 for the visualisation of the decomposition for the response variable of the dataset). Vredendal is located at longitude 18.419916\({}^{\circ}\) E and latitude 31.730507\({}^{\circ}\) S. The data were curated from 1 January 2018 to 1 March 2019. The dataset contains 61,057 rows of observations and was reduced to 60,769 by the final two days lagged variable added to the selected variables making a total of 48 variables. The data were divided into training and testing data. While training data correspond to data for 1 January-30 November 2018, taking 45,576 observations of 10-min recordings, testing data span 1 December-1 March 2019 with 15,193 observations of 10-min interval recordings. A map of the point location of Vredendal is shown in Figure 1.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Model** & **Description** & **Motivation** \\ \hline ANN, SGB and GAM & \begin{tabular}{l} Machine and Statistical learning, \\ Deterministic methods \\ \end{tabular} & Point forecasting \\ \hline LQRA and AQRA & Statistical and Probabilistic Methods & \
\begin{tabular}{l} Forecasts combination and Prediction interval \\ construction \\ \end{tabular} \\ \hline The LASSO & Mathematical & Variable/feature selection \\ \hline MAE, RMSE, and MAPE & Mathematical & Point forecast evaluation metrics \\ \hline PIW, PICP, PINAW, PINAD and PICAW &
\begin{tabular}{l} Mathematical formulations and \\ Interval forecasting metrics \\ \end{tabular} & To quantify uncertainties in the forecasts \\ \hline Simple Average and Median PI & Mathematical & Prediction Interval combination (Improves forecast) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of models, description and motivations,