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.

• Signals and their models
• Signal detection
• Test statistics
• Corrections to the probability distribution
• Power of test statistics
• Time domain analysis
• Presentation and inspection of results
• Parameter estimation