8.1 Weak Stationarity and Cross-Correlation Matrices

Consider a k-dimensional time series Inline. The series Inline is weakly stationary if its first and second moments are time invariant. In particular, the mean vector and covariance matrix of a weakly stationary series are constant over time. Unless stated explicitly to the contrary, we assume that the return series of financial assets are weakly stationary.

For a weakly stationary time series Inline, we define its mean vector and covariance matrix as

8.1 8.1

where the expectation is taken element by element over the joint distribution of Inline

. The mean Inline is a k-dimensional vector consisting of the unconditional expectations of the components of Inline. The covariance matrix is a k × k matrix. The ith diagonal element of is the variance of rit, whereas the (i, j)th element ...

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