I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is
$$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$
My goal is to get an estimate of $\sigma^2$.
I can observe S and K historically at times $t=1,2,..$, and know that the following approximately holds
$$ \lambda(t) \approx S(t)+K(t)$$
Does it make sense to simply take the sample variance of the time series $(S(t)+K(t))$, let's call it $\hat{\sigma}^2_S$, and say that a reasonable estimate of $\sigma^2$ is $2 \kappa\frac{\hat{\sigma}^2_S}{\theta}$?
It should be mentioned that the distribution of $\lambda$ is not pretty, but I have the mean and variance.