Testing joint hypotheses when one of the alternatives is one-sided
We propose a class of statistics where the direction of one of the alternatives is incorporated. We modify a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive exact explicit distributions, then prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.
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- Maddala, G S & Wu, Shaowen, 1999. " A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 631-52, Special I.
- Dufour, Jean-Marie, 1989.
"Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions,"
Econometric Society, vol. 57(2), pages 335-55, March.
- Dufour, J.-M., 1986. "Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions," CORE Discussion Papers 1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
- Heijmans, R.D.H. & Magnus, J.R., 1986. "Consistent maximum-likelihood estimation with dependent observations : the general (non-normal) case and the normal case," Other publications TiSEM 9b460ea9-57c5-4d5b-934f-c, Tilburg University, School of Economics and Management.
- Silvapulle, Mervyn J., 1991. "On Limited Dependent Variable Models: Maximum Likelihood Estimation and Test of One-sided Hypothesis," Econometric Theory, Cambridge University Press, vol. 7(03), pages 385-395, September.
- Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
- McCabe,B.P.M. & Tremayne,A.R., 1995. "Testing a Time-Series for Difference Stationarity," Cambridge Working Papers in Economics 9420, Faculty of Economics, University of Cambridge.
- Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- Andrews, Donald W. K., 1998.
"Hypothesis testing with a restricted parameter space,"
Journal of Econometrics,
Elsevier, vol. 84(1), pages 155-199, May.
- Donald W.K. Andrews, 1994. "Hypothesis Testing with a Restricted Parameter Space," Cowles Foundation Discussion Papers 1060R, Cowles Foundation for Research in Economics, Yale University.
- Abadir, Karim M., 1995.
"The Limiting Distribution of the t Ratio Under a Unit Root,"
Cambridge University Press, vol. 11(04), pages 775-793, August.
- Abadir, K.M., 1992. "The Limiting Distribution of the T Ratio Under a Unit Root," Papers 1992-2, American Cairo - Economics and Political Sciences.
- Heijmans, Risto D. H. & Magnus, Jan R., 1986. "Consistent maximum-likelihood estimation with dependent observations : The general (non-normal) case and the normal case," Journal of Econometrics, Elsevier, vol. 32(2), pages 253-285, July.
- Perron, P, 1988.
"The Great Crash, The Oil Price Shock And The Unit Root Hypothesis,"
338, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
- Taylor, A.M.R. & Smith, R.J., 1999.
"Tests of the Seasonal Unit Root Hypothesis Against Heteroscedastic Seasonal Integration,"
99-13, Department of Economics, University of Birmingham.
- Taylor, A M Robert & Smith, Richard J, 2001. "Tests of the Seasonal Unit-Root Hypothesis against Heteroscedastic Seasonal Integration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 192-207, April.
- Abadir, Karim, 1995.
"An Introduction to Hypergeometric Functions for Economists,"
9510, Exeter University, Department of Economics.
- Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
- Dagenais, M.G. & Dufour, J.M., 1987.
"Invariance, Nonlinear Models and Asymptotic Tests,"
Cahiers de recherche
8738, Universite de Montreal, Departement de sciences economiques.
- Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November.
- Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
- Rogers, Alan J., 1986. "Modified lagrange multiplier tests for problems with one-sided alternatives," Journal of Econometrics, Elsevier, vol. 31(3), pages 341-361, April.
- Larsson, Rolf, 1995. "The Asymptotic Distributions Of Some Test Statistics in Near-Integrated AR Processes," Econometric Theory, Cambridge University Press, vol. 11(02), pages 306-330, February.
- Abadir, Karim M., 1993. "On the Asymptotic Power of Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 9(02), pages 189-221, April.
- Wang, Yining & McDermott, Michael P., 1998. "A Conditional Test for a Non-negative Mean Vector Based on a Hotelling'sT2-Type Statistic," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 64-70, July.
- Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
- Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
- Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "On the Exact Moments of Asymptotic Distributions in an Unstable AR(1) with Dependent Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(1), pages 71-88, February.
- Heijmans, R.D.H. & Magnus, J.R., 1986. "On the first-order efficiency and asymptotic normality of maximum likelihood estimators obtained from dependent observations," Other publications TiSEM b2fc9176-e950-4580-90e6-5, Tilburg University, School of Economics and Management.
- Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
- Tae-Hwan Kim & Paul Newbold, 2001. "Unit root tests based on inequality-restricted estimators," Applied Economics Letters, Taylor & Francis Journals, vol. 8(12), pages 793-797.
- Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-22, September.
- Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-46, October.
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