Explanation

Let's analyze each statement:

Statement A: INCORRECT

• In the EWMA (Exponentially Weighted Moving Average) model, there is NO weight assigned to the long-run average variance. The EWMA model only uses recent observations with exponentially decaying weights, but it does not include a long-run variance component. The model is: σ²ₜ = λσ²ₜ₋₁ + (1-λ)r²ₜ₋₁, where λ is the decay factor.

Statement B: CORRECT

• In EWMA, weights do decrease exponentially as observations become older. The weight for observation t-k is proportional to (1-λ)λᵏ.

Statement C: CORRECT

• In GARCH(1,1), the model is: σ²ₜ = ω + αr²ₜ₋₁ + βσ²ₜ₋₁, where ω = γVᴸ (γ is the weight for long-run variance Vᴸ). Since ω > 0, there is indeed a positive weight assigned to the long-run average variance.

Statement D: CORRECT

• In GARCH(1,1), the weights for observations do decrease exponentially as they become older, similar to EWMA but with different decay structure.

Therefore, Statement A is the incorrect one because EWMA does not assign any weight to the long-run average variance, unlike GARCH models which do include this component.