Answer-first summary for fast verification
Answer: 0 < φ < 1 for MEV1 and φ < 0 for MEV2
## Explanation For AR(1) models, the behavior of the autocorrelation function (ACF) and partial autocorrelation function (PACF) provides important clues about the value of the AR parameter φ: ### MEV1 Analysis: - **ACF Pattern**: Gradually decays (decreases slowly toward zero) - **PACF Pattern**: Cuts off after lag 1 - **Interpretation**: A gradually decaying ACF with PACF cutting off after lag 1 is characteristic of an AR(1) process with **0 < φ < 1** ### MEV2 Analysis: - **ACF Pattern**: Oscillates between positive and negative values - **PACF Pattern**: Spikes at lag 1 then drops to zero - **Interpretation**: An oscillating ACF (alternating signs) with PACF cutting off after lag 1 is characteristic of an AR(1) process with **φ < 0** ### Key Principles: - **0 < φ < 1**: ACF decays exponentially toward zero (positive values) - **φ < 0**: ACF oscillates between positive and negative values - **PACF**: For AR(1) processes, PACF should have a single spike at lag 1 and be zero thereafter Therefore, the correct combination is **0 < φ < 1 for MEV1** and **φ < 0 for MEV2**, which corresponds to option C.
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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
[Graph showing ACF and PACF for MEV1 — ACF decays gradually, PACF cuts off after lag 1]
MEV2
[Graph showing ACF and PACF for MEV2 — ACF oscillates between positive and negative values, PACF spikes at lag 1 then drops to zero]
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