## 2 The Procedures of Forecasting Strategy
### Elimination of Noisy Data using Wavelet Transform (WT)  
The WT is a method that transforms time series data into time-frequency representation and becomes a superior alternative of the Fourier transform (FT) to analyze stationary and non-stationary data [24; 27]. In the theory of WT, an original signal is decomposed into two parts; a low-frequency signal and a high-frequency signal. The process is called the wavelet decomposition process, which is represented in Figure 3.  
The arrangement in Figure 3 shows the decomposition process of an original signal through the use of a high pass filter and low pass filter to produce a high-frequency signal and a low-frequency signal. The high-frequency signal is known as the detailed signal while the low-frequency signal is identified as the approximation signal. After the first level of the decomposition process, the approximation signal can be further decomposed at several levels. Meanwhile, the detailed signal that exists in the form of noise is filtered through this wavelet decomposition process.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Meteorological Variables** & **Correlation Value** \\ \hline Global Radiation & 0.84 \\ Tilted Radiation & 0.86 \\ Temperature Surrounding & 0.48 \\ Humidity Surrounding & \(-\)0.49 \\ Panel Temperature & 0.60 \\ Wind Speed & 0.41 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlation value between solar power and meteorological variables.  
In this work, the WT technique is applied to remove noise in meteorological data and solar power data. Hence, the application of this noise removal technique is established according to three important processes, namely, decomposition of the noisy input signal, threshold estimation of wavelet coefficient and reconstruction of the denoised signal.  
For the decomposition process, five levels of decomposition trees are chosen because it gives the most reliable result during the wavelet decomposition. Thus, four variables--tilted radiation, global radiation, panel temperature and solar power data--are decomposed five times in this process.  
In wavelet analysis, the approximation signal contains vital information of the signal and is rarely affected by noise, while the detailed signal represents noise in the signal [28]. After the decomposition process, the detailed signal needs to pass through the thresholding process. It is implemented by selecting a threshold value for detailed signal in every level of decomposition. At this threshold stage, the coefficients of the detailed signal that are below the threshold value are set to zero, while the coefficients of the detailed signal that lie above the threshold value are subjected to the scaling process and shrinking process. Note that the threshold value of a detailed signal can be estimated by using various threshold estimation methods. This work chooses the threshold estimation method according to the heuristic approach. The outcome of this heuristic approach has shown excellent performance for the fixed type method, because it depicts the most reliable signals compared to other threshold estimation methods.  
Once the new coefficients of the detailed signal are obtained, they are reconstructed in the reconstruction process to produce a denoised signal. Those above-mentioned processes are illustrated in Figure 4, where s represents the original signal, \(\mathrm{d_{i}}\) denotes the detailed signal, \(\mathrm{a_{i}}\) signifies the approximation signal and symbol i is for the level of decomposition. The original signal in this work can be either the tilted radiation signal, global radiation signal, panel temperature signal or solar power signal. Each of them will pass through the decomposition process, thresholding process and reconstruction process in order to produce a new denoised signal.  
Figure 4: Noise reduction scheme of the wavelet transform (WT).  
Figure 3: Wavelet decomposition scheme.