High-dimensional lag structure optimization of fuzzy time series

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.