加权极限学习机的多变量时间序列预测方法
Multivariate time series prediction based on weighted extreme learning machine

提出一种基于样本分布的极限学习机预测模型WELMSD. 该模型先用kN近邻密度估计方法估计出样本的密度值，再用估计出的密度值给传统ELM的经验风险项加权，克服传统ELM在对时间序列进行预测时忽略样本分布的缺点. 基于Rossler混沌时间序列和上证、深证股票数据的实验仿真结果证明了所提算法的有效性，且当近邻参数kN取值较小时，所提模型对参数不敏感，是一种更优的多变量时间序列预测模型.
Put forward a kind of extreme learning machine prediction model based on sample distribution which is called WELMSD. WELMSD estimates the density of the sample set by the kN nearest neighbor density estimation firstly，and then weighted for the traditional extreme learning machine by the estimated density. WELMSD overcome the shortcoming of traditional extreme learning machine ignore the sample distribution when it is used for time series prediction. The effectiveness of WELMSD is demonstrated by simulation results on Rossler chaotic time series，Shanghai Composite Index and Shenzhen Component Index. In addition，the prediction results are not sensitive to the parameters of kN nearest neighbor density estimation method when kN is small. It proves that the new model is a better prediction model for multivariate time series