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Unformatted text preview: Autocontours: Dynamic Specification Testing * Gloria GonzalezRivera Zeynep Senyuz Emre Yoldas First version: January 2007 This version: October 2009 Abstract We propose a new battery of dynamic specification tests for the joint hypothesis of i.i.d.ness and density function based on the fundamental properties of independent ran dom variables with identical distributions. We introduce a device the autocontour whose shape is very sensitive to departures from the null in either direction, thus providing su perior power. The tests are parametric with asymptotic t and chisquared limiting dis tributions and standard convergence rates. They do not require a transformation of the original data or an assessment of goodnessoffit ala Kolmogorov, explicitly account for parameter uncertainty, and have superior finite sample properties. An application to ACD models for trade durations shows that the difficulty with the assumed densities lies on the probability assigned to very small durations. Keywords : Probability Contour Plot, Specification Test, Parameter Uncertainty, Boot strap. JEL Classification : C12, C15, C16, C22. * We would like to thank the participants in the 2006 NBER/NSF Time Series Conference in Montreal, the 2006 International Symposium in Forecasting in Santander (Spain), the 2007 FarEastern Meetings of the Econometric Society in Taipei, the 2007 (EC)2 Conference in Faro (Portugal), and the 2008 Symposium of the SNDE in San Francisco for their comments and insights. Special thanks to Aman Ullah, TaeHwy Lee, and Christian Bontemps. We are also grateful to the editor, Arthur Lewbel, associate editor and two anonymous referees, whose constructive comments have greatly improved this manuscript. The usual caveat applies. Financial support from the UCR Academic Senate grants and the University Scholar award are greatly appreciated. Department of Economics, University of California, Riverside, CA 92521. Email: gloria.gonzalez@ucr.edu (Corresponding author). Department of Economics, Whittemore School of Business and Economics, University of New Hampshire, Durham, NH 03824. Email: zeynep.senyuz@unh.edu Department of Economics, Bentley University, Waltham, MA 02452. Email: eyoldas@bentley.edu 1 Introduction We propose a new battery of tests for dynamic specification that rely on the fundamental properties of independent random variables with identical distributions. We focus on models in which all the dependence is contained in the first and second moments such that for a process { y t } we have y t = t ( 01 , = t 1 ) + t ( 02 , = t 1 ) t where t ( . ) is the conditional mean and 2 t ( . ) is the conditional variance, both functions of an information set = t 1 , = ( 01 , 02 ) is a parameter vector, and t is an innovation that is i.i.d. The innovation, is characterized by a parametric p.d.f., say f ( t ). In this context, we formulate a collection of statistics for the joint hypothesis of i.i.d.ness and density functional form of the innovation as specificationjoint hypothesis of i....
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