Explanation:
C is correct. Both macroeconomic variables clearly exhibit contrasting ACF and PACF:
For an ACF which decays towards zero, 0 < φ < 1, which matches the pattern observed for MEV1. For an ACF which oscillates between positive and negative values, φ < 0, which matches the pattern observed for MEV2.
A, B and D are incorrect. They can be eliminated by recognizing the differences explained above.
Learning Objective: Define and describe the properties of autoregressive moving average (ARMA) processes. Describe sample autocorrelation and partial autocorrelation.
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-59. A quantitative risk analyst at a large financial institution is reviewing the existing model for estimating expected credit loss (ECL) reserves. Upon thoroughly examining the model, the analyst discovers that two key macroeconomic variables, MEV1 & MEV2, need an updated forecast. Before deciding which time series model to apply, the analyst uses statistical software to graph the autocorrelation function (ACF) and partial autocorrelation function (PACF) for each macroeconomic variable and generates the following graphs:
MEV1
(ACF gradually decays; PACF tends to zero after the 3rd observation)
MEV2
(ACF oscillates between positive and negative values; PACF is –0.9 at the first lag and then zero for all other lags)
Based on the graphs above, and supposing that the analyst chose to estimate an AR(1) model, what are the most likely values of the AR parameter (φ) in each case?
A
φ < 0 for MEV1 and φ < 0 for MEV2
B
φ < 0 for MEV1 and 0 < φ < 1 for MEV2
C
0 < φ < 1 for MEV1 and φ < 0 for MEV2
D
0 < φ < 1 for MEV1 and 0 < φ < 1 for MEV2
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