On the Causal Models of Fuzzy Time Series

There is a growing interest in fuzzy time series (FTS) forecasting, and several improvements are presented in the last few decades. Among these improvements, the development of causal models (i.e., multiple factor FTS) has sparked a particular literature dealing with the causal inference and its integration in the FTS framework. However, causality among variables is usually introduced as a subjective assumption rather than empirical evidence. As a result of arbitrary causal modeling, the existing multiple factor FTS models are developed with implicit forecasting failure. Since post-sample control (unknown future, as in the business practice) is usually ignored, the spurious accuracy gain through increasing factors is not identified by scholars. This paper discloses the use of causality in the FTS method, and investigates the spurious causal inference problem in the literature with a justification approach. It invalidates the contribution of dozens of previously published papers while justifying its claim with illustrative examples and a comprehensive set of experiments with random data, as well as real business data from maritime transportation (Baltic Dry Index).