Consider the first-order autoregressive model Xt = ρXt-1 + "єt,= 1,..,T with X0 = 0 and...

Consider the first-order autoregressive model

X_t = ρX_t-₁ + "є_t,= 1,..,T

with X₀ = 0 and {є_t} ~ i.i.d.(0, σ ²).

Explain what is the Dickey-Fuller test in the context of this model. In particular, your answer should include the null and alternative hypotheses, the definitions of both the coe¢cient test and the t test version of the Dickey-Fuller test and how the critical values are obtained.
Consistency is a desirable property of statistical test. Explain the definition of a consistent test and why it’s desirable. Show the coe¢cient Dickey-Fuller test (not the t-test version of the Dickey-Fuller test) is consistent.
Consider the first-order autoregressive model
X_t = ρX_t-₁ + "є_t,= 1,..,T

with X₀ = 0 and {є_t} ~ i.i.d.(0, σ ²).
1. Explain what is the Dickey-Fuller test in the context of this model. In particular, your answer should include the null and alternative hypotheses, the definitions of both the coe¢cient test and the t test version of the Dickey-Fuller test and how the critical values are obtained.
2. Consistency is a desirable property of statistical test. Explain the definition of a consistent test and why it’s desirable. Show the coe¢cient Dickey-Fuller test (not the t-test version of the Dickey-Fuller test) is consistent.

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Expert Solution

Rahul Sunny answered 5 months ago

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