Application of Multivariate Statistical Analysis for the Detection of Structural Changes in the Series of Monitoring Data

Antonovsky, M.Y., Buchstaber, V.M., & Veksler, L.S. (1991). Application of Multivariate Statistical Analysis for the Detection of Structural Changes in the Series of Monitoring Data. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-91-037

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Abstract

A new approach to the study of time series by the projection pursuit methods is described. The ideas are illustrated on the time series of the monitoring of the environment and climate: (a) on time series of anomalies of global mean annual temperature -- the main climatological parameter; (b) on time series of atmospheric CO2 concentrations -- the main greenhouse gases; (c) on time series of vegetation index (NDVI) -- the main global characteristic of biota activity on the satellite data.

With the aid of the shift operator for time signal, we construct a curve in n-dimensional Euclidian space (shift operator and integer n are the parameters of method). So an analysis of a time series is reduced to the analysis of the most informative projections [for example, by the criterion of factor analysis or spectral analysis (discrete Fourie analysis)] of the corresponding n-dimensional curve. We show that the comparison of such projections for model-test time series with the projection of the time series under investigation gives an effective way of finding the structural changes of the monitoring time series. For example, the case of the Hansen-Lebedeff time series of anomalies of the global mean annual temperature (see Rends 'go), shows that the structure of the series in the interval from 1920 until 1950 essentially differs from the structure on the intervals 1880-1920 and 1950-1987. For the series of CO2 on the Mauna Loa and Barrow monitoring stations, we obtained dynamics of the amplitudes of the year and semi-year cycles. We give the construction of a nonparametric estimation of a model of the initial time series using k-dimensional projection of n-dimensional curve. As a consequence, for example, we found the main components of the CO2 time series and obtained the models of the yearly behaviors of NDVI time series which permit one to carry out statistically stable classification of ecosystems by ecotypes and to describe dynamics of the separate ecosystems.

Thus it is proposed a tool for the creation of the statistical description of the current state of the given monitoring series in the form of geometrical image. These geometrical images permit us to analyze the anomalies in the monitoring series in the terms of deviation of these images. As it follows from the examples given below such a method of the analysis of monitoring data is an effective method. Between the theoretical let us stress the following: we show how the methods of the analysis of the time series widely used in statistical treatment of monitoring data could also be used in our approach as the tools of the projections pursuit for comparing the images of the curves of the signal under investigation with the curves of the corresponding signals; it is shown that the proposed approach permits us to join in a united method the achievement of the theory of operators of a generalized shift and exploratory analysis on the basis of the projection pursuit.

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