Question

Augmented Dickey-Fuller Test for stationarity was performed on a certain series (both at level, that is original series, and at first difference). The output from R are given below: Augmented Dickey-Fuller Test data: at level (original) Dickey-Fuller = -0.99253, Lag order = 4, p-value = 0.9324 Augmented Dickey-Fuller Test data: first difference Dickey-Fuller = -3.3902, Lag order = 4, p-value = 0.06496
i. State the null and the alternative hypotheses for both at level and first difference;
ii. Interpret the results of this test. Is stationarity achieved? If not recommend an appropriate step to achieve stationarity.

Answer 1

SOLUTION:-

(i)

For at level:

H₀ : Y_t is random walk

H₁ : Y_t is stationary process.

For first difference:

H₀ : Y_t is random walk

H₁ : Y_t is stationary process

(ii)

Interpret:-

For at level:

P-value is 0.9324 > 0.05 we fail to reject the null hypothesis. This means data is random walk.

For at level:

P-value is 0.064 > 0.5 This means data is random walk.

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