Is there any way to calculate unconditional variance of $X_{t-1}^2$ i.e. (VAR($X_{t-1}^2$)), when X follows an AR(1) process, $X_t = \phi X_{t-1} + e_t$ with VAR(X) being $\sigma_v^2$ and the mean of the error term is E($e_t$)= 0?
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Not in general, because it depends on unspecified properties of the distribution of $e_t.$ Do you make a specific assumption about that distribution, such as being Gaussian for instance? – whuber Oct 07 '23 at 14:36
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No not as such but say If I assume a Gaussian distribution, then what would be its answer ? – Yadavindu Oct 07 '23 at 16:10
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Apply, for instance, the formula at https://stats.stackexchange.com/questions/628048. – whuber Oct 07 '23 at 16:14