ESTIMATION AND INFERENCE OF LINEAR TREND SLOPE RATIOS WITH AN APPLICATION TO GLOBAL TEMPERATURE DATA

摘要

We examine estimation and inference of the ratio of linear trend slopes between two time series. Our methodological results are motivated by recent empirical climate papers that estimate and test hypotheses about the relative warming rate in the lower-troposphere relative to surface warming, i.e. the amplification ratio. We analyze statistical properties of several estimators and test statistics that allow serial correlation. Relative merits of the estimators and test statistics depend on the magnitude of the trend slopes relative to the noise in the data. We make specific recommendations for practitioners. We revisit the empirical findings of Klotzbach et al. (2009, 2010) and obtain similar results using our recommended approach.