13: Time-Series Analysis-LOS l习题精选 center, 2010, class, discuss

土豆妮

Session 3: Quantitative Methods: Quantitative
Methods for Valuation
Reading 13: Time-Series Analysis

LOS l: Explain autoregressive conditional heteroskedasticity (ARCH) and discuss how ARCH models can be applied to predict the variance of a time series.

 

 

 

Which of the following is least likely a consequence of a model containing ARCH(1) errors? The:

A) variance of the errors can be predicted.

B) model's specification can be corrected by adding an additional lag variable.

C) regression parameters will be incorrect.

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luqian55

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土豆妮

Suppose you estimate the following model of residuals from an autoregressive model:

ε_t² = 0.4 + 0.80ε_t-1² + μ_t, where ε = ε^{^}

If the residual at time t is 2.0, the forecasted variance for time t+1 is:

A) 3.6.

B) 3.2.

C) 2.0.

土豆妮

Suppose you estimate the following model of residuals from an autoregressive model:

ε_t² = 0.4 + 0.80ε_t-1² + μ_t, where ε = ε^{^}

If the residual at time t is 2.0, the forecasted variance for time t+1 is:

A) 3.6.

B) 3.2.

C) 2.0.

---

The variance at t=t+1 is 0.4 + [0.80 (4.0)] = 0.4 + 3.2. = 3.6.

土豆妮

Which of the following is least likely a consequence of a model containing ARCH(1) errors? The:

A) variance of the errors can be predicted.

B) model's specification can be corrected by adding an additional lag variable.

C) regression parameters will be incorrect.

---

The presence of autoregressive conditional heteroskedasticity (ARCH) indicates that the variance of the error terms is not constant. This is a violation of the regression assumptions upon which time series models are based. The addition of another lag variable to a model is not a means for correcting for ARCH (1) errors.

土豆妮

Suppose you estimate the following model of residuals from an autoregressive model:

ε_t² = 0.25 + 0.6ε²_t-1 + μ_t, where ε = ε^{^}

If the residual at time t is 0.9, the forecasted variance for time t+1 is:

A) 0.790.

B) 0.736.

C) 0.850.

土豆妮

Suppose you estimate the following model of residuals from an autoregressive model:

ε_t² = 0.25 + 0.6ε²_t-1 + μ_t, where ε = ε^{^}

If the residual at time t is 0.9, the forecasted variance for time t+1 is:

A) 0.790.

B) 0.736.

C) 0.850.

---

The variance at t=t+1 is 0.25 + [0.60 (0.81)] = 0.25 + 0.486 = 0.736.