Auto-regression
A regressive dependence of the values of 
of a given random sequence 
on the preceding values of 
. A linear auto-regression scheme of order 
is defined by a linear regression equation between 
and 
, 
, i.e.
 | (*) |
where 
are constants and the random variables 
are identically distributed with average zero, variance 
and are uncorrelated (sometimes they are assumed to be independent). An auto-regression scheme is a useful stochastic model for the description of certain time series (the concept of a linear auto-regression scheme was first introduced by G. Yule in 1921) in order to analyze time series describing a system which is oscillating under the effect of internal forces and random external shocks. The auto-regression scheme (*) may be regarded as a stochastic process of a special type: an auto-regressive process.
Auto-regression. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Auto-regression&oldid=52903