Estimation for Autoregressive Time Series With a Root Near 1

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Testing for Shifts in Trend With an Integrated or Stationary Noise Component (2009, methodology): “To improve the finite-sample properties of the test, we also use a bias-corrected version of the OLS estimate of α (obtained from an autoregression based on the residuals from estimating the parameters of the trend function by OLS), as suggested by Roy and Fuller (2001).”
Estimating deterministic trends with an integrated or stationary noise component (2009, methodology): “…T−1X t=2 û2t + 1 T TX t=1 û2t ] −1(T − 3)−1 TX t=2 (ût − α̂W ût−1)2 9 and the associated t-ratio for testing that α = 1 is τ̂W = α̂W − 1 σ̂W The modification proposed by Roy and Fuller (2001) is similar in spirit to our superefficient estimate in that it also replaces estimates which are in a…”