Basic principles of time series analysis

The practical problems in the analysis of time series concern

1.

the detection of a signal against noise,

2.

the estimation of the parameters characterizing the signal, and

3.

the presentation of the results.

Presentation and/or evaluation of the results involves a function of the time series called statistics. Detection of a signal, e.g. a period, and evaluation of its properties, e.g. error and significance, then usually mean finding and characterizing a related signal in the associated statistics which is normally based on some model of the signal.