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 Statement A is INCORRECT because: - 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 - The formula for EWMA is: σ²ₙ = λσ²ₙ₋₁ + (1-λ)u²ₙ₋₁, where λ is the decay factor - There is no long-run variance term in this equation For the other statements: - **B is CORRECT**: EWMA weights do decrease exponentially as observations become older - **C is CORRECT**: GARCH(1,1) includes a long-run average variance term (ω) with positive weight - **D is CORRECT**: GARCH(1,1) weights also decrease exponentially for older observations The key difference is that GARCH(1,1) includes a long-run variance component while EWMA does not.
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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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