CFA Level II ExamQuantitative MethodsMedium
An investment firm uses a time-series model to forecast daily stock returns. The firm's analyst notices that large forecast errors tend to be followed by large forecast errors, and small errors by small errors, irrespective of the sign of the error. Which of the following models would be most appropriate to capture this characteristic?
- AAutoregressive (AR) model
- BGeneralized Autoregressive Conditional Heteroskedasticity (GARCH) model
- CAutoregressive Conditional Heteroskedasticity (ARCH) model
- DMoving Average (MA) model
Show answer & explanationAnswer & explanation
Correct answer: C. Autoregressive Conditional Heteroskedasticity (ARCH) model
The described pattern of forecast errors (large errors followed by large errors, small by small, irrespective of sign) is characteristic of volatility clustering, which is captured by Autoregressive Conditional Heteroskedasticity (ARCH) models. GARCH models are a generalization of ARCH, also fitting this pattern, but ARCH is the fundamental model for this specific observation.
Why the other options are wrong
- A. AR models capture serial correlation in the mean of a time series, not the variance of its errors.
- B. GARCH models are an extension of ARCH models and also capture volatility clustering, but ARCH is the foundational model for this specific phenomenon presented.
- D. MA models capture serial correlation in the error terms affecting the mean, not the conditional variance of errors.
ARCH Models (Autoregressive Conditional Heteroskedasticity)
A class of statistical models used to model time-series data with changing variance (heteroskedasticity) where the variance of the current error term is a function of the squares of the previous error terms.
- Captures volatility clustering.
- The conditional variance depends on past squared errors.
- Used extensively in financial time series analysis.
Memory trick: Errors cluster like stormy weather.