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Applying the linear covariance operator to both sides of the equation $y_t = X y_{t-1} + Y e_t$ yields
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$$
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\mathrm{Cov}(y_t) = X ⋅ \mathrm{Cov}(y_{t-1}) ⋅ X^* + Y ⋅ \mathrm{Cov}(e_t) ⋅ Y^*
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\\mathrm{Cov}(y_t) = X ⋅ \\mathrm{Cov}(y_{t-1}) ⋅ X^* + Y ⋅ \\mathrm{Cov}(e_t) ⋅ Y^*
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$$
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By stationarity of $y_t$, $\mathrm{Cov}(y_t) = \mathrm{Cov}(y_{t-1}) := \Gamma$, so
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By stationarity of $y_t$, $\\mathrm{Cov}(y_t) = \\mathrm{Cov}(y_{t-1}) := Γ$, so
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$$
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Γ = X Γ X^* + Γ₀
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$$
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By applying the [Vec-operator](https://en.wikipedia.org/wiki/Vectorization_(mathematics)#Compatibility_with_Kronecker_products), we get the following equation:
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