Autoregressive forests for multivariate time series modeling

•A novel autoregressive approach to represent multivariate time series is proposed.•Proposed method is a non-linear, non-parametric vector autoregressive approach.•Proposed method requires few parameters to tune and it is robust to the changes in parameters if they are set in a certain range.•The proposed method can handle large number of features and long time series effectively.•The approach provides competitive results in several multivariate time series classification problems.

Multivariate Time Series (MTS) modeling has received significant attention in the last decade because of the complex nature of the data. Efficient representations are required to deal with the high dimensionality due to the increase in the number of variables and duration of the time series in different applications. For example, model-based approaches such as Hidden Markov Models (HMM) or autoregressive (AR) models focus on finding a model to represent the series with the model parameters to handle this problem. Both HMM and AR models are known to be very successful in the representation of the time series however most of the HMM approaches assume independence and traditional AR models consider linear dependence between the variables of MTS. As most of the real systems exhibit nonlinear relations, traditional approaches fail to represent the time series. To handle these problems, we propose an autoregressive tree-based ensemble approach that can model the nonlinear behavior embedded in the time series with the help of tree-based learning. Multivariate autoregressive forest, namely mv-ARF, is a nonparametric vector autoregression approach which provides an easy and efficient representation that scales well with large datasets. An error-based representation based on the learned models is the basis of the proposed approach. This is very similar to time series kernels used for multivariate time series classification problems. We test mv-ARF on MTS classification problems and show that mv-ARF provides fast and competitive results on benchmark datasets from several domains. Furthermore, mv-ARF provides a research direction for vector autoregressive models that breaks from the linear dependency models to potentially foster other promising nonlinear approaches.