Is the following equation right? $E\left(\left(\sum_{k=1}^{n}\alpha_{k}X_{k}\right)^{2}\right)=n^{2H}E(X_{0}^2)\sum_{k_{1},k_{2}=1}^{n}\alpha_{k_{1}}\alpha_{k_{2}}$?Where $(X_{k})$ is the fractional Gaussian Noise with Hurst Index $H\in(0,1)$?
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