## ABSTRACT

This book is mainly concerned with the linear model
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where X = [x_{ti}
] is an n × k matrix of n observations on k independent or exogenous variables, Y = [y_{tj}
] is an n × m matrix of n observations on m jointly dependent or endogenous variables, and E = [ɛ_{tj}
] is an n × m matrix of random errors with zero means and specified variances and covariances, where t = 1, 2,…, n. To allow for a constant term, the first column of X may be specified to be a column of 1s. We shall in fact for the most part in Chapters 2-7 concentrate on the special univariate case m = 1, returning to the multivariate case in Chapter 8. The purpose of this chapter is to embed the above model in a multivariate model in which the rows x
_{t}. = (x
_{t1}, x
_{t2}, …, x
_{tk}) of X and y
_{t}. = (y
_{
t1}, y
_{
t2}, …, y
_{
tm
}) of Y are specified to have a joint distribution, and to consider the problem of the best predictor of y
_{
t
}. given x
_{
t
}. The linearity of the above model emerges as a practical aspect of optimal prediction.