Statistical Models Coupling Allows for Complex Local Multivariate Time Series Analysis

Abstract

The increased availability of multivariate time-series asks for the development of suitable methods able to holistically analyse them. To this aim, we propose a novel flexible method for data-mining, forecasting and causal patterns detection that leverages the coupling of Hidden Markov Models and Gaussian Graphical Models. Given a multivariate non-stationary time-series, the proposed method simultaneously clusters time points while understanding probabilistic relationships among variables. The clustering divides the time points into stationary sub-groups whose underlying distribution can be inferred through a graphical model. Such coupling can be further exploited to build a time-varying regression model which allows to both make predictions and obtain insights on the presence of causal patterns. We extensively validate the proposed approach on synthetic data showing that it has better performance than the state of the art on clustering, graphical models inference and prediction. Finally, to demonstrate the applicability of our approach in real-world scenarios, we exploit its characteristics to build a profitable investment portfolio. Results show that we are able to improve the state of the art, by going from a -%20 profit to a noticeable 80%.

Dynamic Multi-Network Mining of Tensor Time Series

“…• TAGM [43]: combines HMM with a graphical lasso by modeling each cluster as a graphical lasso and assuming clusters as hidden states of HMM. • TICC [14]: uses the Toeplitz matrix to capture lag correlations and inter-variable correlations and penalizes changing clusters to assign the neighboring segments to the same cluster.…”

“…Although the inference of time-varying networks is able to find change points by comparing the networks before and after a change, it cannot find clusters [15,42,48]. TICC [14] and TAGM [43] use graphical lasso and find clusters from time series based on the network of each subsequence, providing the clusters with interpretability and allowing us to discover clusters that other traditional clustering methods cannot find. However, they cannot provide an interpretable insight when dealing with TTS.…”

“…As well as clustering data, the interpretability of the results is also important since we rarely know what each cluster refers to [33,36]. Modeling a cluster as a dependency network [14,40,43], where nodes are variables and an edge expresses a relationship between variables, gives a clear explanation of what the cluster refers to. Considering that a TTS consists of multiple modes [4,11,23], a cluster should be modeled as multiple networks, where each is a dependency network of a corresponding non-temporal mode, to provide a good explanation.…”

Fast and Multi-aspect Mining of Complex Time-stamped Event Streams

“…Modeling Dynamics and Segmentation. Classical approaches such as linear dynamical systems (LDS), and hidden Markov models (HMM) are extended to capture distinct patterns of sequences as described in [40,48,54,83]. TICC [37] characterizes the interdependence between multivariate observations based on a Markov random field.…”