Piet M.T. Broersen - Automatic Autocorrelation and Spectral Analysis (Repost)

The subject of this book is the description of the main properties of univariate
stationary stochastic signals. A univariate signal is a single observed variable that
varies as a function of time or position. Stochastic (or random) loosely means that
the measured signal looks different every time an experiment is repeated. However,
the process that generates the signal is still the same. Stationary indicates that the
statistical properties of the signal are constant in time. The properties of a
stochastic signal are fully described by the joint probability density function of the
observations. This density would give all information about the signal, if it could
be estimated from the observations. Unfortunately, that is generally not possible
without very much additional knowledge about the process that generated the
observations. General characteristics that can always be estimated are the power
spectral density that describes the frequency content of a signal and the autocovariance
function that indicates how fast a signal can change in time. Estimation
of spectrum or autocovariance is the main purpose of time series identification.
This knowledge is sufficient for an exact description of the joint probability density
function of normally distributed observations. For observations with other
densities, it is also useful information.