Lag-selection is a high dimensional hyper-parameter in the fuzzy time series (FTS) which requires complex optimization process and computational capacity particularly in high frequency dataset (e.g. daily, hourly). Multivariate high order FTS suffers from establishing long logical relationships, and the difficulty of rule matching is proportional to the time lags and number of variables. In the vast majority of FTS literature, a grid search algorithm or evolutionary algorithms are run to find singular time-lags. In addition, some researchers determine the lag structure arbitrarily. However, grid search in high dimensional problems is not practical especially when recursive predictions are generated and evolutionary algorithms suffer from the randomness which may generate different solutions. This paper proposes an alternative approach to the lag selection problem by utilizing supervised principal component analysis (SPCA), and the lag structure is reduced to low dimensional space. SPCA has been developed to project the high dimensional lagged variables into the first principal component. An empirical study is conducted to validate the proposed approach by using global shipping industry data in the world.

滞后选择是模糊时间序列（FTS）中的高维超参数，它需要复杂的优化过程和计算能力，尤其是在高频数据集中（例如每天，每小时）。多元高阶FTS难以建立长逻辑关系，规则匹配的难度与时间滞后和变量数量成正比。在绝大多数FTS文献中，都运行网格搜索算法或进化算法来查找奇异的时滞。另外，一些研究人员任意确定滞后结构。但是，在高维问题中进行网格搜索是不切实际的，特别是在生成递归预测并且演化算法具有随机性的情况下，随机性可能会产生不同的解决方案。本文提出了一种利用监督主成分分析（SPCA）解决滞后问题的替代方法，并将滞后结构简化为低维空间。SPCA已开发为将高维滞后变量投影到第一个主成分中。进行了一项实证研究，通过使用全球航运业的全球数据来验证所提出的方法。