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?