Answer-first summary for fast verification
Answer: In the exponentially weighted moving average (EWMA) model, some positive weight is assigned to the long-run average variance.
## 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.
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Which of the following four statements on models for estimating volatility is INCORRECT?
A
In the exponentially weighted moving average (EWMA) model, some positive weight is assigned to the long-run average variance.
B
In the EWMA model, the weights assigned to observations decrease exponentially as the observations become older.
C
In the GARCH (1,1) model, a positive weight is estimated for the long-run average variance.
D
In the GARCH (1,1) model, the weights estimated for observations decrease exponentially as the observations become older.
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