Time series data are broadly collected and analyzed in diverse fields of science and engineering. To cope with such data, the non-stationary multidimensional time series modeling method plays a dominant role and is widely applied to the data for predicting future values and unveiling interesting structure of them.
The remarkable progress of Bayesian nonparametric methodology has expanded the scope of the non-stationary time series modeling methods, not only enabling us to automatically determine the number of parameters in the model according to the complexity of the dataset, but also tolerating a certain class of heterogeneity among a set of time series data. However, there is relatively little literature on utilizing the non-stationary time series modeling method with Bayesian nonparametrics for applications of time series data analysis, despite the recent extensive use of methods that are not based on any temporal or structural assumption of the time series data such as deep neural networks.
In this presentation, we present two application studies of the non-stationary time series modeling method with Bayesian nonparametrics. First, we analyze a set of multiple time series data of driver behaviors, and show that driver behaviors in future can be predicted by using the Bayesian nonparametric Markov-switching vector autoregressive processes without any model selection procedure. Second, we apply the Bayesian nonparametric hidden Markov model to a birdsong dataset, and reveal that distinct syntactic rules are adopted by different groups of birds that have different tutors. These results support the effectiveness of the non-stationary time series modeling method with Bayesian nonparametrics for behavior analysis.