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Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

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  • Pesaran, M. Hashem

Abstract

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

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  • Pesaran, M. Hashem, 1987. "Global and Partial Non-Nested Hypotheses and Asymptotic Local Power," Econometric Theory, Cambridge University Press, vol. 3(01), pages 69-97, February.
  • Handle: RePEc:cup:etheor:v:3:y:1987:i:01:p:69-97_00
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    1. Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis.
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    3. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    4. Magnus, J.R. & Neudecker, H., 1980. "The elimination matrix : Some lemmas and applications," Other publications TiSEM 0e3315d3-846c-4bc5-928e-f, Tilburg University, School of Economics and Management.
    5. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    6. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    7. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier.
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    Cited by:

    1. Pieroni, Luca & Ricciarelli, Matteo, 2008. "Modelling dynamic storage function in commodity markets: Theory and evidence," Economic Modelling, Elsevier, vol. 25(5), pages 1080-1092, September.
    2. Neil R. Ericsson, 1987. "Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses," International Finance Discussion Papers 317, Board of Governors of the Federal Reserve System (U.S.).
    3. Xu, T.T., 2012. "The role of credit in international business cycles," Cambridge Working Papers in Economics 1202, Faculty of Economics, University of Cambridge.
    4. Heinz König & Michael Lechner, 1994. "Some Recent Developments in Microeconometrics - A Survey," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(III), pages 299-331, September.
    5. McAleer, Michael, 1995. "The significance of testing empirical non-nested models," Journal of Econometrics, Elsevier, vol. 67(1), pages 149-171, May.
    6. McAleer, Michael, 1994. " Sherlock Holmes and the Search for Truth: A Diagnostic Tale," Journal of Economic Surveys, Wiley Blackwell, vol. 8(4), pages 317-370, December.
    7. Pons Novell, Jordi, 1997. "Selección de modelos no anidados. Un estudio de Monte Carlo," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 7, pages 131-139, Junio.

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