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ABSTRACT
Temporal series, also called chronological series, can be found in various domains of application: finance and econometrics, medicine and biology, earth and space sciences, signal processing, metrology, etc. This article describes the main types of temporal series and the techniques used in order to analyze them. These series and their properties are generally described via models or "summaries" the elements of which are obtained trhough an identification process. The way in which such models are used for higher-level operations is then studied. This article focuses on univariate series (a single quantity is observed over time) whilst presenting certain information on multivariate series and the applicable techniques. For didactic purposes, it is based on real series and simulated ones.
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Michel PRENAT: Innovation Policy Technical Director – Thales Optronique - Associate Professor – Université Paris Sud
INTRODUCTION
Time series are series of observations of one (or more) quantity(ies) over time. Depending on the case, they are referred to as uni-variate or multi-variate series. This article essentially develops techniques for uni-variate series, while making a foray into multi-variate series for particular problems. For uni-variate series, the observations belong to the set of real numbers . However, in cases where they are complex (for example, the signal observed at the output of a radar receiver), they are still considered uni-variate.
Observation times are discrete, but not necessarily evenly distributed. Some of the techniques described in this article, whose foundations assume this regular distribution, can easily be extended to the non-regular case, while others require more complex arrangements.
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KEYWORDS
covariance | prediction | identification | stationarity | conditional distribution
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