I have an auto-correlation function of a non-stationary process given by: $$R_{yy}(t, \tau) = \frac{A}{(1-t/T_o)^{\frac{1}{\alpha}}}cos\frac{c\tau}{(1-t/T_o)^{\frac{1}{\alpha}}}, 0 < t < T_o \hspace{4pt} and -T_o < \tau < T_o.$$
I need to find the covariance matrix and this is all the information I have about the process.
Covariance matrix is defined by $$\mathbb{E}[(X_t - \mathbb{E}X_t)(X_{t+t_o} - \mathbb{E}X_{t+t_o})^T],$$ where t is the time index and $t_o$ is a shift after which the next sample was taken. This can be simplified to get $$\mathbb{E}[X_tX^{T}_{t+t_o}] - \mathbb{E}X_{t+t_o}\mathbb{E}X_t,$$ which can be further simplified to: $$R_{xx}(t, t+t_{o}) - \mathbb{E}X_{t+t_o}\mathbb{E}X_t.$$ The first term can be computed by plugging values into the first equation. Is there anyway to compute the second term?