可以再具体解释下吗？正负号怎么取值？哪个颜色是ACF，是怎么区分的啊？

问题如下：

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

MEV2

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?

选项：

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

解释：

Explanation: C is correct. Both macroeconomic variables clearly exhibit contrasting ACF and PACF:

• MEV1 ACF gradually decays while MEV2 ACF is oscillating between positive and negative values.
• MEV1 PACF tends to zero after the 3^rd observation while for MEV2, the PACF is −0.9 at the first lag and then zero for all other lags.

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]