Dickey-Fuller Test for an Extended MA Model
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초록
The AR(1) model X_t=ρX_(t-1)+ϵ_t with iid error ϵ_t has been used extensively for the inference of the stochastic process X_t where its key parameter ρ plays an essential role. In particular, the Dickey-Fuller test (DF test) has been extensively used for testing random walk model (or ρ=1) in the literatures. However, it is well known that the DF test is subject to serious size distortion when errors are correlated. This study proposes the use of an extended MA(∞) model X_t=∑_(i=0)^∞ b_i ϵ_(t-i) for a more precise inference of X_t by the DF test. We develop and investigate a new persistency parameter b_∞=lim_(j→∞) b_j from the extended MA(∞) model. It is shown that the DF test serves well for testing the MA(∞) model with the new persistency parameter b_∞. Our approach critically addresses the size distortion issues in the literatures.
Abstract
The AR(1) model X_t=ρX_(t-1)+ϵ_t with iid error ϵ_t has been used extensively for the inference of the stochastic process X_t where its key parameter ρ plays an essential role. In particular, the Dickey-Fuller test (DF test) has been extensively used for testing random walk model (or ρ=1) in the literatures. However, it is well known that the DF test is subject to serious size distortion when errors are correlated. This study proposes the use of an extended MA(∞) model X_t=∑_(i=0)^∞ b_i ϵ_(t-i) for a more precise inference of X_t by the DF test. We develop and investigate a new persistency parameter b_∞=lim_(j→∞) b_j from the extended MA(∞) model. It is shown that the DF test serves well for testing the MA(∞) model with the new persistency parameter b_∞. Our approach critically addresses the size distortion issues in the literatures.
참고문헌 (10)
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