THE PROPERTIES OF KULLBACK–LEIBLER DIVERGENCE FOR THE UNIT ROOT HYPOTHESIS
研究了模型设定对检测经济时间序列单位根能力的影响，用Kullback-Leibler散度替代渐近功效来量化这种影响，并证明其可最小化，揭示了近似线性趋势和负单位根移动平均创新会降低单位根推断工具的有效性。
The fundamental contributions made by Paul Newbold have highlighted how crucial it is to detect when economic time series have unit roots. This paper explores the effects that model specification has on our ability to do that. Asymptotic power, a natural choice to quantify these effects, does not accurately predict finite-sample power. Instead, here the Kullback–Leibler divergence between the unit root null and any alternative is used and its numeric and analytic properties detailed. Numerically it behaves in a similar way to finite-sample power. However, because it is analytically available we are able to prove that it is a minimizable function of the degree of trending in any included deterministic component and of the correlation of the underlying innovations. It is explicitly confirmed, therefore, that it is approximately linear trends and negative unit root moving average innovations that minimize the efficacy of unit root inferential tools. Applied to the Nelson and Plosser macroeconomic series the effect that different types of trends included in the model have on unit root inference is clearly revealed.