Application example
Temporal series or chronological series

This chapter presents a simple, quantified illustration of a practical application of time series.

In statistical terms, this means detecting a value, or more generally a set of values, that is highly unlikely to occur in a time series. This type of problem is encountered in signal processing, for example in radar to detect a target against a background of clutter such as ground echoes. The aim is to show that, if the "background" is correlated, then an anomaly will be detected with a much smaller signal-to-noise ratio than on an uncorrelated background.

• Suppose we have a time series (X_t), the realization of an AR process (1), i.e. X_t = fX_{t – 1} + Z_t . It will be assumed here that (Z_t) is Gaussian to simplify the exposition, but often the reality of physics is different.

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