Financial Risk Manager Part 1
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A financial analyst wishes to conduct an ADF test on the log of 20-year real GDP from 1999 to 2019. The result of the tests is shown below:
| Deterministic | γ | δ₀ | δ₁ | Lags | 5% CV | 1% CV |
|---|---|---|---|---|---|---|
| None | -0.004 | 8 | -1.940 | -2.570 | ||
| (-1.555) | ||||||
| Constant | -0.008 | 0.010 | 4 | -2.860 | -3.445 | |
| (-1.422) | (1.025) | |||||
| Trend | -0.084 | 0.188 | 3 | -3.420 | -3.984 | |
| (-4.376) | (-4.110) |
The output of the ADF reports the results at the different number deterministic terms (first column), and the last three columns indicate the number of lags according to AIC and the 5% and 1% critical values that are appropriate to the underlying sample size and the deterministic terms. The quantities in the parenthesis (below the parameters) are the test-statistics. What deterministic term is most preferred for this model?
Exam-Like
Community
TTanishq
A
None
B
Constant
C
Trend
D
Cannot be determined from the given information
Explanation:
Explanation
In the Augmented Dickey-Fuller (ADF) test, we compare the test statistic (in parentheses) with the critical values to determine if we can reject the null hypothesis of a unit root.
Analysis of Each Deterministic Term:
-
None (No deterministic terms):
- Test statistic: -1.555
- 5% critical value: -1.940
- 1% critical value: -2.570
- Since -1.555 > -1.940, we cannot reject the null hypothesis at 5% significance level
-
Constant:
- Test statistic: -1.422
- 5% critical value: -2.860
- 1% critical value: -3.445
- Since -1.422 > -2.860, we cannot reject the null hypothesis at 5% significance level
-
Trend:
- Test statistic: -4.376
- 5% critical value: -3.420
- 1% critical value: -3.984
- Since -4.376 < -3.420 and -4.376 < -3.984, we reject the null hypothesis at both 5% and 1% significance levels
Conclusion:
The Trend deterministic term is most preferred because:
- It is the only specification where we can reject the null hypothesis of a unit root
- The test statistic (-4.376) is significantly below both the 5% and 1% critical values
- This suggests that the log of real GDP is stationary around a deterministic trend
For ADF tests, we typically prefer the specification that allows us to reject the null hypothesis of non-stationarity, as this indicates the series is stationary.
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