The Estimation of Parameters in Linear Autoregressive Time Series

1. The problem is to estimate the values of the constants a in a linear
antoregressive series of type
(1) + al~l+k-l+ ... + qut = &t4h
glven a number 1%of coilsecutive terms of the series. The E'S are values
of a random variable and successive values may or may not, in general,
be dependent. In the major part of this paper I take them as independent.
Particular cases of (1) of importallre are the scheme generating a
Markoff chain
(2) aoUt+l + a1ut = E t + l
and Yule's equation
(3) ffoUt+2 + fflUt+l4 ff2Ut = E 1 ~ 2 .
In all cases I shall take a, --- 1 but it is useful to continue to write a,
in theoretical expressions.