We introduce a concept of episode referring to time interval in the development dynamic phenomenon that is characterized by multiple time-variant attributes. A data structure representing single multivariate series. To analyse collections episodes, we propose an approach based on recognition particular patterns temporal variation variables within episodes. Each thus represented combination patt...

The paper is focused on the analysis and design of multivariate time series prediction systems. It addresses mainly practical issues, the main contribution is the developed and implemented conceptual predictive methodology. It is based on designed data management structures that define basic data flow. Despite the fact that the methodology is inspired by problems common for utility companies th...

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regu...

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In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Granger-causality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Granger-causality relations between the variables whereas lines correspond to contemporaneous conditional associa...

One of the important problems in many process industries is how to predict the occurrence of abnormal situations ahead of time in a multivariate time series environment. For example, in an oil refinery, hundreds of sensors (process variables) are installed at different sections of a process unit. These sensors constantly monitor the development of every stage of the process. Typically, each pro...

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such locally adaptive smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time interval...

Canonical correlation analysis has been widely used in the literature to identify the underlying structure of a multivariate linear time series. Most of the studies assume that the innovations to the multivariate system are Gaussian. On the other hand, there are many applications in which the normality assumption is either questionable or clearly inadequate. For example, most empirical time ser...