Statistical inference on specifying regression models for detecting dependence in autocorrelated series

The traditional regression model for dependence detection has been generalized by including the autocorrelated noise (ACN) or lagged dependent variable (LDV) to account for autocorrelation in time series. Existing studies on specifying the models with ACN or LDV are rare. We propose a statistical analysis framework of model specification and estimation, whose effectiveness is validated by simulations. As real-life cases we study the precipitation extreme dependence on temperature and temperature dependence on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>CO</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> and demonstrate how the traditional and misspecified models may overestimate dependence by up to three times. We provide a solid statistical basis for detecting dependence in autocorrelated series.