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

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.

Compression and Conditional Emulation of Climate Model Output

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. The statistical model can be used to generate realizations representing the full dataset, along with characterizations of the uncertainties in the generated data. Thus, the methods are capable of both compression and conditional emulation of the climate models. Considerable attention is paid to accurately modeling the original dataset--one year of daily mean temperature data--particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers

Modelling multiple time series via common factors

We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable (nonstationary) factors are identified via expanding the white noise space step by step; therefore solving a high-dimensional optimization problem by several low-dimensional subproblems. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets

Analysis of a Japan government intervention on the domestic agriculture market

We investigate an economic system in which one large agent - the Japan government changes the environment of numerous smaller agents - the Japan agriculture producers by indirect regulation of prices of agriculture goods. The reason for this intervention was that before the oil crisis in 1974 Japan agriculture production prices exhibited irregular and large amplitude changes. By means of analysis of correlations and a combination of singular spectrum analysis (SSA), principal component analysis (PCA), and time delay phase space construction (TDPSC) we study the influence of the government measures on the domestic piglet prices and production in Japan. We show that the government regulation politics was successful and leaded (i) to a decrease of the nonstationarities and to increase of predictability of the piglet price; (ii) to a coupling of the price and production cycles; (iii) to increase of determinism of the dynamics of the fluctuations of piglet price around the year average price. The investigated case is an example confirming the thesis that a large agent can change in a significant way the environment of the small agents in complex (economic or financial) systems which can be crucial for their survival or extinction.Comment: 10 pages, 6 figures presented at APFA5, Torino, Italy, 29.06-01.07.200

Dynamic Orthogonal Subseries for High-Dimensional and Nonstationary Time Series

A multivariate time series could be partitioned either horizontally (over time) to induce local stationarity or vertically (over the variables) to reduce dimension and the high computational cost. Dimension reduction for a high-dimensional time series by linearly transforming it into several lower-dimensional subseries (vertical partition) where any two subseries are uncorrelated both temporally and cross-sectionally is of central importance in the modern age of big data. It reduces the challenging multivariate estimation problem with many parameters to that of a number of disjoint lower-dimensional problems with much fewer parameters. A notable example in the previous studies is the dynamic orthogonal components (DOC) utilizing nonlinear optimization which works well for stationary and low-dimensional time series data. First we reduce the computational burden of DOC by connecting it to the time series principal components analysis (TS-PCA) method in recent studies based on eigenanalysis of a positive-definite matrix. Next, we extend DOC to nonstationary processes which can be divided into several nearly homogeneous segments. Consistency and joint asymptotic normality of the estimates of the Givens angles parameterizing orthogonal matrices in each segment are established under some regularity conditions. Applications to multivariate volatility modeling in finance are illustrated using simulated and real datasets