CFA Level II ExamQuantitative MethodsMedium
An investment firm uses a time-series model to forecast daily stock returns. The firm's analyst observes that the forecast errors exhibit a pattern where positive errors are frequently followed by positive errors, and negative errors by negative errors, indicating conditional heteroskedasticity. Which of the following models would be most appropriate to address this issue?
- AARCH(q)
- BARIMA(p, d, q)
- CSARIMA(p, d, q)(P, D, Q)s
- DVAR(p)
Show answer & explanationAnswer & explanation
Correct answer: A. ARCH(q)
The observed pattern of forecast errors (positive errors followed by positive, negative by negative) suggests clustering of volatility, which is a symptom of conditional heteroskedasticity. ARCH (Autoregressive Conditional Heteroskedasticity) models are specifically designed to capture and model this time-varying volatility.
Why the other options are wrong
- B. ARIMA models are used to model the mean of a time series and account for autocorrelation in the mean, not conditional heteroskedasticity in the variance.
- C. SARIMA models extend ARIMA to seasonal data, focusing on the mean structure and autocorrelation, not conditional heteroskedasticity.
- D. VAR models are used for multivariate time series, where multiple variables are interdependent, and primarily focus on modeling the mean relationships, not conditional heteroskedasticity.
ARCH Models (Autoregressive Conditional Heteroskedasticity)
ARCH models are a class of statistical models used to model financial time series that exhibit time-varying volatility, specifically conditional heteroskedasticity, where the variance of the error term depends on the squared past error terms.
- Developed by Robert Engle in 1982.
- Captures volatility clustering in financial data.
- Generalized to GARCH models (Generalized Autoregressive Conditional Heteroskedasticity).
Memory trick: ARCH models capture the swings of market volatility.