Consider the original dataset consisting of m variables, where
one is the ground solar radiation time series yt (t ¼ 1, ., N), and
others are meteorological variables Xt, which is a N (m 1)
matrix. In this paper, Xt
(i) is the ith (i ¼ 1, ., m 1) column of the
matrix Xt and represents a time series of the ith meteorological
variable. X(i)(t) represents the value of Xt
(i) at the time t.
In this paper the following normalized time series of solar
radiation is used as the input and output of the predict models.
yt ¼ f ðytÞ (1)
where f($) is the normalization function to be defined in Section
3.3; yt is the normalized values of the original time series yt.
Similarly, XðiÞ
t can be normalized to X
ðiÞ
t .
2.1. The AR model
The AR model expresses a time series as a linear function of its
past values. The order of the AR model indicates how many past
values are used. An AR model, AR(m$D), with an order of m$D can
be written as