Table of Contents
CFA Level 2 – Quantitative Analysis, Session 3 – Reading 13 – LOS m
(Practice Questions, Sample Questions)
LOS m: Explain autoregressive conditional heteroskedasticity (ARCH), and discuss how ARCH models can be applied to predict the variance of a time series.
1. 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.
Explanation: B) 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.
2. Suppose you estimate the following model of residuals from an autoregressive model:
εt2 = 0.25 + 0.6ε2t-1 + μt, where ε = ε^
If the residual at time t is 0.9, the forecasted variance for time t+1 is:
A) 0.736.
B) 0.790.
C) 0.850.
Explanation: A) The variance at t=t+1 is 0.25 + [0.60 (0.81)] = 0.25 + 0.486 = 0.736.
3. Suppose you estimate the following model of residuals from an autoregressive model:
εt2 = 0.4 + 0.80εt-12 + μt, where ε = ε^
If the residual at time t is 2.0, the forecasted variance for time t+1 is:
A) 3.2.
B) 2.0.
C) 3.6.
Explanation: C) The variance at t=t+1 is 0.4 + [0.80 (4.0)] = 0.4 + 3.2. = 3.6.
