ABSTRACT
In Chapters 1 and 2 we have seen examples of high-dimensional time series data. The most common assumptions made in modelling such data is stationarity.
Let {Xt,p : t = 0,±1,±2, . . .} be p-dimensional random vectors with E(Xt,p) = 0 for all t. It is called weak or covariance stationary if and only if, for all u ≥ 0, the p× p matrix
Γu,p = E(Xt,pX ∗ t+u,p) (3.1)
does not depend on t and is a function of only u. The matrix Γu,p is called the (population) autocovariance matrix of order u. Note that Γ0,p is the covariance matrix of Xt,p.
