Explanation:
A is correct. If the ACF decays slowly while the PACF has a sharp cutoff at lags, then an AR model is likely to fit the data better than an MA or ARMA. In general, slow decay in the sample ACF indicates that the model needs an AR component, and slow decay in the sample PACF indicates that the model should have an MA component.
B is incorrect. Only a slow decay in the PACF would indicate that the model needs an MA component.
C is incorrect. As explained above, if the ACF decays slowly while the PACF has a sharp cutoff at lags, then an AR model is likely to fit the data better than an MA or ARMA.
D is incorrect. The time series is already covariance-stationary and there is no indication of deterministic seasonality, so no differencing is necessary.
Learning Objective: Describe the application of AR, MA, and ARMA processes.
Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2023, Chapter 10, Stationary Time Series [QA-10].
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Q-41. A quantitative risk manager at a hedge fund is using an autoregressive moving average (ARMA) process to model the default premium of corporate bond portfolios held by the fund and constructs several covariance-stationary ARMA models with varying lag lengths. The manager conducts a graphical analysis of the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots to identify candidate models. In this analysis, the manager notes that there is a slow decay in the ACF plot, but the PACF plot indicates a sharp cutoff at lags. In determining whether an autoregressive (AR) or a moving average (MA) component is needed in the model, which of the following would be correct for the manager to conclude?
A
The plots indicate that the model should include an AR component.
B
The plots indicate that the model should include an MA component.
C
The plots indicate that the model should include both an AR and an MA component with lag length .
D
The plots indicate that the model should incorporate an MA component after undergoing differencing for lag .
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