The following graph represents the ACF of variable Y:

Which of the following statements is correct about the best time series model of variable Y?

Question

The following graph represents the ACF of variable Y:

Which of the following statements is correct about the best time series model of variable Y?

BlackTom AI · Accepted Answer

To interpret the ACF graph for Y, I’ll evaluate what the pattern says about potential time-series structures.
Option 1: The best model for Y is an MA(1). The ACF shows a large spike at lag 1 with subsequent lags largely within the significance bounds and not showing a clear pattern of persistence. This is characteristic of an MA(1) process, where only the first lag is significantly different from zero and higher-order lags are essentially white noise.
Option 2: The best model for Y is an AR(2). If an AR(2) were the right structure, we would expect two or more consecutive lags to display significant autocorrelations (often a decaying pattern across lags 1 and 2, or a more persistent shape). The graph does not show multiple consecutive large spikes beyond lag 1, so AR(2) is unlikely.
Option 3: The best model for Y is an MA(2). For MA(2), significant autocorrelations would typically appear at lags 1 and 2 (and potentially diminish afterward). Here, lag 2 is not markedly significant, and there isn’t a second prominent spike near lag 2, making MA(2) an improbable choice.
Option 4: The best model for Y is an AR(1). An AR(1) would generally produce a slowly decaying ACF across several lags rather than a single strong spike at lag 1. Since the ACF does not exhibit a clear monotonic decay from lag 1 onward, AR(1) does not fit well.
In summary, the strong, isolated spike at lag 1 with no clear, sustained pattern in higher lags aligns best with an MA(1) process, while the other structures would typically show multiple significant lags or a decaying pattern that is not evident here.

The following graph represents the ACF of variable Y: Which of the following statements is correct about the best time series model of variable Y?单项选择题

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