Time Series Models
An example of a linear time series model is an autoregressive moving average model. Here the model for values {Xt} in a time series can be written in the form
where again the quantities εt are random variables representing innovations which are new random effects that appear at a certain time but also affect values of X at later times. In this instance the use of the term "linear model" refers to the structure of the above relationship in representing Xt as a linear function of past values of the same time series and of current and past values of the innovations. This particular aspect of the structure means that it is relative simple to derive relations for the mean and covariance properties of the time series. Note that here the "linear" part of the term "linear model" is not referring to the coefficients φi and θi, as it would be in the case of a regression model, which looks structurally similar.
Read more about this topic: Linear Model
Famous quotes containing the words time, series and/or models:
“They know time comes, not only you and I,
But the whose world shall whiten, here or there;”
—James Elroy Flecker (1884–1919)
“Depression moods lead, almost invariably, to accidents. But, when they occur, our mood changes again, since the accident shows we can draw the world in our wake, and that we still retain some degree of power even when our spirits are low. A series of accidents creates a positively light-hearted state, out of consideration for this strange power.”
—Jean Baudrillard (b. 1929)
“The greatest and truest models for all orators ... is Demosthenes. One who has not studied deeply and constantly all the great speeches of the great Athenian, is not prepared to speak in public. Only as the constant companion of Demosthenes, Burke, Fox, Canning and Webster, can we hope to become orators.”
—Woodrow Wilson (1856–1924)