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This paper presents a nonparametric regression model of categorical time series in the setting of conditional tensor factorization and Bayes network. The underlying algorithms are developed to provide a flexible and parsimonious representation for fusion of correlated information from heterogeneous sources, which can be used to improve the performance of prediction tasks and infer the causal relationship between key variables. The proposed method is first illustrated by numerical simulation and then validated with two real-world datasets: (1) experimental data, collected from a swirl-stabilized lean-premixed laboratory-scale combustor, for detection of thermoacoustic instabilities and (2) publicly available economics data for causal inference-making.