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:
“The sanity of the average banquet speaker lasts about two and a half months; at the end of that time he begins to mutter to himself, and calls out in his sleep.”
—James Thurber (1894–1961)
“Autobiography is only to be trusted when it reveals something disgraceful. A man who gives a good account of himself is probably lying, since any life when viewed from the inside is simply a series of defeats.”
—George Orwell (1903–1950)
“The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
—Samuel Butler (1835–1902)