Multivariate analysis in vector time series

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed

Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related Field

Detecting nonlinearity in multivariate time series

We propose an extension to time series with several simultaneously measured variables of the nonlinearity test, which combines the redundancy -- linear redundancy approach with the surrogate data technique. For several variables various types of the redundancies can be defined, in order to test specific dependence structures between/among (groups of) variables. The null hypothesis of a multivariate linear stochastic process is tested using the multivariate surrogate data. The linear redundancies are used in order to avoid spurious results due to imperfect surrogates. The method is demonstrated using two types of numerically generated multivariate series (linear and nonlinear) and experimental multivariate data from meteorology and physiology.Comment: 11 pages, compressed and uuencoded postscript file, figures included. Also available by anonymous ftp at ftp://ftp.santafe.edu/pub/mp/multi, E-mail: [email protected], [email protected]

MULTIVARIATE ANALYSIS IN VECTOR TIME SERIES

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.

Scaling analysis of multivariate intermittent time series

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk forecasts: the probability of observing next day a large price movement is (super-universally) inversely proportional to the length of the ongoing low-variability period. Finally, a method is devised for a multi-factor scaling analysis. We apply the simplest, two-factor model to equity index and trading volume time series.Comment: 16 pages, 5 figures, accepted for publication in Physica

Variance changes detection in multivariate time series

This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures are considered. The first is based on the likelihood ratio test and the second on cusum statistics. These two procedures are compared in a simulation study and we conclude that the cusum procedure is more powerful. The procedures are illustrated in two examples.