Central limit theorems for quadratic forms with time-domain conditions

We establish the central limit theorem for quadratic forms Σt, s=1N b(t - s)Pm, n (Xₜ, Xₛ) of the bivariate Appell polynomials Pm, n (Xₜ, Xₓ)) under time-domain conditions. These conditions relate the weights $b(t)$ and the covariances of the sequences (Pm, n (Xₜ, Xₛ)) and (Xₜ). The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.