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Find the M x M empirical covariance matrix C from the outer product matrix B with itself:
Regarding the best structure of the covariance matrix for random effects (G), lower values of -2LMV, AIC, BIC, and residuals were observed for the UN matrix in random quadratic regression models with intercepts (model 3), followed by the cubic model without intercept (model 6) (Table 1).
In the proposed iterative ML detection (IMLD) scheme, the instantaneous covariance matrix of the noise and CSI errors is estimated by considering the probabilities of multiple transmit candidate symbol vectors, whereas the published methods [10, 11] use the bound or the long-term statistical information of CSI errors.
The relationship between the residual and the innovation vectors, as well as the covariance matrix, can be expressed as (Yang, 2001):
Next, the covariance matrix C needs to be diagonalizable.
The investor plans to take a position in four risky assets where the expected return vector, r, and covariance matrix, S, are the following:
We start from the observation that we can always decompose a covariance matrix [[OMEGA].
The risk-free rate of return on the risk-free asset is r, an n x 1 vector of the expected excess rates of return is R - r, and the n x n non-singular covariance matrix of risky assets' rates of return is [OMEGA].
Hence, we need to decompose the time-varying covariance matrix in such a way to guarantee this property.
Similarly, the LM test for ARCH effects performed on the standardized residuals, indicate that the BEKK model is successful in modeling the time varying aspect of a covariance matrix.