## 1 Introduction
To decrease computing resources demanded by building a prediction model for each series, researchers proposed several approaches. One approach is to assemble a subseries according to sample entropy [22] or the Spearman correlation coefficient [23]. Another approach is to predict the trend only [24; 25; 26]. Researchers also employed a scheme of weighted sums to tackle the problem of error accumulation that occurs when aggregating predictions of each subseries [27; 28]. It is effective to combine the signal processing technique and the prediction model to improve accuracy. However, in most related research studies, the signal decomposition was performed at once, which is called one-time decomposition [29] and is based on the assumption that all data are known. However, in practice, wind speed data come sequentially, which indicate the impracticability of one-time decomposition and require real-time decomposition. Real-time decomposition means that data decomposition is performed every time new data come in. The main problem of real-time decomposition is the end effect. The end effect is manifested as the difference between the end region of decomposition results of the initial series and that of the series updated with new wind speed data. The end effect is caused by the difference between endpoint values of these two series. The influence of the end effect on the prediction model is illustrated as follows. For example, a prediction of the trend of wind speed is needed, and trends obtained by decomposition of the updated series \(r_{1},\ldots,r_{N+1}\) and the initial series \(r_{1},\ldots,r_{N}\) are denoted as \(t_{1}^{u},\ldots,t_{N+1}^{u}\) and \(t_{1}^{i},\ldots,t_{N}^{i}\), respectively. The ideal input should be \(t_{1}^{u},\ldots,t_{N}^{u}\) that is more consistent with the target \(t_{N+1}^{u}\), but the available input is \(t_{1}^{i},\ldots,t_{N}^{i}\). There is a difference between the ideal and the available input due to the end effect, which can be interpreted as the introduction of a kind of noise that is caused by the end effect. As a consequence, the end effect can degrade the improvement of accuracy by data decomposition techniques. The accuracy of the prediction model with this basic real-time decomposition can even be worse than that of the prediction model without signal processing techniques [30; 31]. It was suggested to adopt data decomposition techniques as tools of denoising [31], by which only insignificant changes in the raw series are made, and the end effect can be mitigated. How to further reduce the influence of the end effect has become an important topic. A possible solution is to adopt a new scheme of real-time decomposition that can mitigate end effect. [PERSON] et al. [32] proposed a new scheme of real-time decomposition that is called quasi real-time decomposition, and the scheme is explained as follow. An initial prediction of the raw series is firstly made and supplemented to the raw series, and the updated series is then decomposed to obtain a corresponding subseries, by which the end effect can be mitigated. However, the effectiveness of quasi real-time decomposition depends on the accuracy of the initial prediction. [PERSON] and wang [33] proposed a scheme of real-time decomposition to eliminate the influence of the end effect by discarding the influenced part of the result of decomposition and using the rest as input, which can be regarded as truncated real-time decomposition. Compared to basic real-time decomposition and quasi real-time decomposition, truncated real-time decomposition can eliminate the influence of the end effect explicitly, but it can lose information significantly and transform a single-step prediction problem into a multi-step prediction problem. Thus, the scheme of truncated real-time decomposition requires auxiliary measures. Recently, researchers studied the possibility of applying multi-resolution data to wind speed prediction. [PERSON] et al.