| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | A | A |
| deepseekr1 | The Dickey-Fuller test statistic follows a non-standard distribution, which has more negative critical values compared to the standard normal distribution. For example, while the 5% critical value for a normal distribution is approximately -1.645, the Dickey-Fuller critical value is more negative (e.g., around -2.86). This means the left tail of the Dickey-Fuller distribution is more extreme. - **Option A** correctly states that the test statistics are "more negative" than those in the normal distribution's left tail. - **Option B** is incorrect, as it contradicts this key property. - **Option C** is false because the Dickey-Fuller distribution is not derived from an analytical formula but through simulations. - **Option D** is incorrect because critical values for lower significance levels (e.g., 5%) are more negative than those for higher levels (e.g., 10%). Answer: A |
A |
| gpto1 | A | A |
| GPT-4o | A. More negative than (i.e. bigger in absolute value than) those in the left hand tail of a normal distribution | A |
| llama3.1-70B-Instruct | A |
A |
| llama3.1-405B-Instruct | B. Less negative than (i.e. smaller in absolute value than) those in the left hand tail of a normal distribution |
A |
| DeepSeek-Coder-V2 | A | A |
| Qwen2-72B-Instruct | B. Less negative than (i.e. smaller in absolute value than) those in the left hand tail of a normal distribution | A |
| baichuan4 | D | A |
| doubao | C The Dickey-Fuller test statistic values are obtained from an analytical formula for the density of the Dickey-Fuller distribution. |
A |
| minimax | A. More negative than (i.e. bigger in absolute value than) those in the left hand tail of a normal distribution | A |
| kimi | D | A |
| wenxinyiyan | A Explanation: The Dickey-Fuller test is used to test for a unit root in a time series, which is often a concern in econometrics. The test statistic in the Dickey-Fuller test is typically compared to critical values from a specific distribution (not the normal distribution) to determine whether the null hypothesis of a unit root can be rejected. However, in the context of this question, we can make some general statements about the test statistic without referring to specific critical values or distributions. A. More negative than (i.e., bigger in absolute value than) those in the left-hand tail of a normal distribution This option suggests that the Dickey-Fuller test statistic, when significant, takes on values that are more negative (i.e., have a larger absolute value) than what you would expect in the left-hand tail of a normal distribution. This is generally true because the Dickey-Fuller test statistic is designed to detect a specific violation of the null hypothesis (the presence of a unit root), and when this violation is strong, the test statistic takes on extreme values. B. Less negative than (i.e., smaller in absolute value than) those in the left-hand tail of a normal distribution This option is the opposite of A and is not correct. C. Obtained from an analytical formula for the density of the Dickey-Fuller distribution While the Dickey-Fuller test statistic is indeed obtained from a specific formula, this option suggests that the values themselves are directly obtained from an analytical formula for the density of the Dickey-Fuller distribution, which is not the case. The test statistic is calculated from the data, and its distribution is used to determine critical values. D. More negative (i.e., bigger in absolute value) for a 10% size of test than a 5% test. This option suggests that the critical value of the Dickey-Fuller test statistic for a 10% significance level is more negative (i.e., has a larger absolute value) than the critical value for a 5% significance level. This is not necessarily true. In general, a smaller significance level (such as 5%) corresponds to a more extreme critical value (i.e., a value that is harder to exceed by chance), whether it's in the positive or negative direction. However, the specific direction (positive or negative) depends on the form of the Dickey-Fuller test and the hypothesis being tested. Given the options and the general nature of the Dickey-Fuller test, option A is the most appropriate answer. It correctly suggests that significant Dickey-Fuller test statistics tend to be more negative (i.e., have larger absolute values) than what you would expect from a normal distribution, reflecting the test's ability to detect specific violations of the null hypothesis. |
A |
| zhipu | A. More negative than (i.e. bigger in absolute value than) those in the left hand tail of a normal distribution The Dickey-Fuller test statistic values are designed to test for the presence of a unit root in a time series, and they are typically more negative (larger in absolute value) than the critical values from the left-hand tail of a normal distribution. This is because the null hypothesis of the Dickey-Fuller test (the presence of a unit root) implies a different distribution than the normal distribution. |
A |
| gpto1 | A | A |