Explanation:
A is correct. The key characteristics observed in the plots indicate:
In time series analysis:
Why other options are incorrect:
B is incorrect: Only slow decay in the PACF would indicate that the model needs an MA component.
C is incorrect: The pattern described (slow ACF decay + sharp PACF cutoff) specifically indicates an AR model rather than an ARMA model.
D is incorrect: The time series is already covariance-stationary and there is no indication of deterministic seasonality, so no differencing is necessary.
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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 p 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 p.
D
The plots indicate that the model should incorporate an MA component after undergoing differencing for lag p.