Stochastic unit root processes: Maximum likelihood estimation,and new Lagrange multiplier and likelihood ratio tests |
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| Affiliation: | 1. CERGAM EA 4225, Aix-Marseille University, Aix-Marseille Graduate School of Management-IAE, Aix-Marseille School of Economics, Aix-en-Provence, France;2. KEDGE BS, Marseille, France;3. THEMA, University of Cergy-Pontoise, 33 Bd du Port, 95011 Cergy-Pontoise, France;1. Université de Lorraine, 34 cours Léopold CS 25233, 54052 Nancy Cedex, France;2. BETA-CNRS, France;3. INRA, UMR356, France;4. AgroParisTech, Engref, LEF, France;5. Sciences Po Lyon, 14 avenue Berthelot, 69365 LYON Cedex 07, France;6. LET UMR CNRS 5593, France;7. IXXI — “Complex Systems Institute” — ENS Lyon, France;1. Department of Economics, Western Michigan University, 1903 West Michigan Ave., Kalamazoo, MI 49008, USA;2. Centre for Financial Econometrics, Deakin University, 221 Burwood Hwy., Melbourne, Victoria, 3125, Australia;1. University of Paris 1 Panthéon-Sorbonne, CES, France;2. ThEMA and Labex MME-DII, University of Cergy-Pontoise, 33 Bd du Port, 95011 Cergy-Pontoise, France |
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| Abstract: | We show in this study that the maximum likelihood estimators of stochastic unit root (STUR) processes are consistent and asymptotically normally distributed. We also present two new tests for STUR. We first propose a Lagrange multiplier test and show that it has a standard χ2 distribution asymptotically. We also propose a likelihood ratio test and show that it has an asymptotic distribution of 50–50 mixture of χ2 and a point mass at 0. As an empirical example, we test the existence of STUR in the Canadian real exchange rate and explore the implication of STUR on the validity of purchasing power parity. |
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