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Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests

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Cited by:

  1. Ghysels, Eric & Babii, Andrii & Chen, Xi & Kumar, Rohit, 2020. "Binary Choice with Asymmetric Loss in a Data-Rich Environment: Theory and an Application to Racial Justice," CEPR Discussion Papers 15418, C.E.P.R. Discussion Papers.
  2. Jonathan B. Hill, 2004. "Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives," Econometric Society 2004 North American Summer Meetings 42, Econometric Society.
  3. Philip Kostov & Myles Patton & Seamus McErlean, 2008. "Nonparametric analysis of the influence of buyers' characteristics and personal relationships on agricultural land prices," Agribusiness, John Wiley & Sons, Ltd., vol. 24(2), pages 161-176.
  4. Yae Ji Jun & Jin Seo Cho, 2015. "Analyzing the Interrelationship of the Statistics for Testing Neglected Nonlinearity under the Null of Linearity," Working papers 2015rwp-78, Yonsei University, Yonsei Economics Research Institute.
  5. Zhuo Qiao & Keith Lam, 2011. "Granger causal relations among Greater China stock markets: a nonlinear perspective," Applied Financial Economics, Taylor & Francis Journals, vol. 21(19), pages 1437-1450.
  6. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
  7. Ng, Serena, 1996. "Looking for evidence of speculative stockholding in commodity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 123-143.
  8. Ibrahim Onour, "undated". "Financial Integration of North Africa Stock Markets," API-Working Paper Series 0908, Arab Planning Institute - Kuwait, Information Center.
  9. Andrew P. Blake & George Kapetanios, 2007. "Testing for Neglected Nonlinearity in Cointegrating Relationships," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 807-826, November.
  10. Stan Hurn & Ralf Becker, 2009. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Economic Analysis and Policy, Elsevier, vol. 39(2), pages 311-326, September.
  11. repec:lan:wpaper:4814 is not listed on IDEAS
  12. Gu, Rongbao & Shao, Yanmin, 2016. "How long the singular value decomposed entropy predicts the stock market? — Evidence from the Dow Jones Industrial Average Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 150-161.
  13. Shintani, Mototsugu, 2005. "Nonlinear Forecasting Analysis Using Diffusion Indexes: An Application to Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 517-538, June.
  14. Heather M. Anderson & Farshid Vahid, 2005. "Nonlinear Correlograms and Partial Autocorrelograms," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 957-982, December.
  15. Granger, Clive W.J. & Hyung, Namwon, 2006. "Introduction to m-m processes," Journal of Econometrics, Elsevier, vol. 130(1), pages 143-164, January.
  16. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
  17. Francisco Salas-Molina & Juan A. Rodr'iguez-Aguilar & Joan Serr`a & Montserrat Guillen & Francisco J. Martin, 2016. "Empirical analysis of daily cash flow time series and its implications for forecasting," Papers 1611.04941, arXiv.org, revised Jun 2017.
  18. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
  19. Aviral Kumar Tiwari & Adeolu O. Adewuyi & Olabanji B. Awodumi & David Roubaud, 2022. "Relationship between stock returns and inflation: New evidence from the US using wavelet and causality methods," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4515-4540, October.
  20. Norman J. Morin & John M. Roberts, 1999. "Is hysteresis important for U.S. unemployment?," Finance and Economics Discussion Series 1999-56, Board of Governors of the Federal Reserve System (U.S.).
  21. Martin Gassebner & Michael Lamla & Jan-Egbert Sturm, 2006. "Economic, demographic and political determinants of pollution reassessed," KOF Working papers 06-129, KOF Swiss Economic Institute, ETH Zurich.
  22. Rebeca Jiménez-Rodríguez, 2004. "Oil Price Shocks: Testing for Non-linearity," CSEF Working Papers 115, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  23. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
  24. Philip Rothman, "undated". "Higher-Order Residual Analysis for Simple Bilinear and Threshold Autoregressive Models with the TR Test," Working Papers 9813, East Carolina University, Department of Economics.
  25. Rebeca Jiménez-Rodríguez, 2002. "Oil Price Shock: A Nonlinear Approach," Working Papers. Serie EC 2002-32, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  26. Dash, Saumya Ranjan & Maitra, Debasish, 2019. "The relationship between emerging and developed market sentiment: A wavelet-based time-frequency analysis," Journal of Behavioral and Experimental Finance, Elsevier, vol. 22(C), pages 135-150.
  27. Carlo Altavilla & Paul De Grauwe, 2010. "Non-linearities in the relation between the exchange rate and its fundamentals," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(1), pages 1-21.
  28. Jennifer L. Castle & David F. Hendry, 2007. "A Low-Dimension Collinearity-Robust Test for Non-linearity," Economics Series Working Papers 326, University of Oxford, Department of Economics.
  29. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
  30. George Kapetanios, 2002. "Testing for Structural Breaks in Nonlinear Dynamic Models Using Artificial Neural Network Approximations," Working Papers 470, Queen Mary University of London, School of Economics and Finance.
  31. Andrew P. Blake & George Kapetanios, 2003. "Pure Significance Tests of the Unit Root Hypothesis Against Nonlinear Alternatives," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 253-267, May.
  32. Anders Bredahl Kock & Timo Teräsvirta, 2016. "Forecasting Macroeconomic Variables Using Neural Network Models and Three Automated Model Selection Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1753-1779, December.
  33. Arne Steinkraus, 2019. "Estimating Treatment Effects With Artificial Neural Nets – A Comparison to Synthetic Control Method," Economics Bulletin, AccessEcon, vol. 39(4), pages 2778-2791.
  34. de Mello Luiz & Moccero Diego & Mogliani Matteo, 2013. "Do Latin American Central Bankers Behave Non-Linearly? The Experiences of Brazil, Chile, Colombia and Mexico," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 141-165, April.
  35. Yuehjen E. Shao & Yi-Shan Tsai, 2018. "Electricity Sales Forecasting Using Hybrid Autoregressive Integrated Moving Average and Soft Computing Approaches in the Absence of Explanatory Variables," Energies, MDPI, vol. 11(7), pages 1-22, July.
  36. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
  37. Chihwa Kao & Yongmiao Hong, 2004. "Detecting Neglected Nonlinearity in Dynamic Panel Data with Time-Varying Conditional Heteroskedasticity," Econometric Society 2004 Far Eastern Meetings 753, Econometric Society.
  38. Georg Keilbar & Yanfen Zhang, 2021. "On cointegration and cryptocurrency dynamics," Digital Finance, Springer, vol. 3(1), pages 1-23, March.
  39. Artur Silva Lopes & Gabriel Florin Zsurkis, 2019. "Are linear models really unuseful to describe business cycle data?," Applied Economics, Taylor & Francis Journals, vol. 51(22), pages 2355-2376, May.
  40. Blake, Andrew P. & Kapetanios, George, 2000. "A radial basis function artificial neural network test for ARCH," Economics Letters, Elsevier, vol. 69(1), pages 15-23, October.
  41. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
  42. Andrés González & Kirstin Hubrich & Timo Teräsvirta, 2009. "Forecasting inflation with gradual regime shifts and exogenous information," CREATES Research Papers 2009-03, Department of Economics and Business Economics, Aarhus University.
  43. Corradi, Valentina & Swanson, Norman R., 2004. "Some recent developments in predictive accuracy testing with nested models and (generic) nonlinear alternatives," International Journal of Forecasting, Elsevier, vol. 20(2), pages 185-199.
  44. de Peretti Christian & Siani Carole, 2004. "Neural Tests for Conditional Heteroskedasticity in ARCH-M Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-24, September.
  45. repec:lan:wpaper:2454 is not listed on IDEAS
  46. Corradi, Valentina & Fernandez, Andres & Swanson, Norman R., 2009. "Information in the Revision Process of Real-Time Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 455-467.
  47. repec:lan:wpaper:2375 is not listed on IDEAS
  48. Pavlidis Efthymios G & Paya Ivan & Peel David A, 2010. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-40, May.
  49. Zacharias Psaradakis & Marián Vávra, 2019. "Portmanteau tests for linearity of stationary time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 248-262, February.
  50. Cipollini, A. & Kapetanios, G., 2008. "A stochastic variance factor model for large datasets and an application to S&P data," Economics Letters, Elsevier, vol. 100(1), pages 130-134, July.
  51. Kapetanios, G. & Tzavalis, E., 2010. "Modeling structural breaks in economic relationships using large shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 417-436, March.
  52. Granger, Clive W. J. & King, Maxwell L. & White, Halbert, 1995. "Comments on testing economic theories and the use of model selection criteria," Journal of Econometrics, Elsevier, vol. 67(1), pages 173-187, May.
  53. Hill Jonathan B., 2013. "Stochastically weighted average conditional moment tests of functional form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 121-139, April.
  54. Daniel Santín González & Rosa Romay López, 2003. "El control del gasto público por incapacidad temporal mediante redes neuronales," Hacienda Pública Española / Review of Public Economics, IEF, vol. 165(2), pages 53-78, June.
  55. Daniel Santin & Francisco Delgado & Aurelia Valino, 2004. "The measurement of technical efficiency: a neural network approach," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 627-635.
  56. Chen, Jiafeng & Chen, Xiaohong & Tamer, Elie, 2023. "Efficient estimation of average derivatives in NPIV models: Simulation comparisons of neural network estimators," Journal of Econometrics, Elsevier, vol. 235(2), pages 1848-1875.
  57. Jiafeng Chen & Xiaohong Chen & Elie Tamer, 2021. "Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators," Cowles Foundation Discussion Papers 2319, Cowles Foundation for Research in Economics, Yale University.
  58. Tae-Hwy Lee & Zhou Xi & Ru Zhang, 2013. "Testing for Neglected Nonlinearity Using Regularized Artificial Neural Networks," Working Papers 201422, University of California at Riverside, Department of Economics, revised Apr 2012.
  59. Richard T. Baillie & George Kapetanios, 2006. "Nonlinear Models with Strongly Dependent Processes and Applications to Forward Premia and Real Exchange Rates," Working Papers 570, Queen Mary University of London, School of Economics and Finance.
  60. Martha Misas Arango & Enrique López Enciso & Pablo Querubín Borrero, 2002. "La inflación en Colombia: una aproximación desde las redes neuronales," Revista ESPE - Ensayos Sobre Política Económica, Banco de la República, vol. 20(41-42), pages 143-214, June.
  61. George Kapetanios & Andrew P. Blake, 2007. "Boosting Estimation of RBF Neural Networks for Dependent Data," Working Papers 588, Queen Mary University of London, School of Economics and Finance.
  62. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
  63. Benhmad, François, 2012. "Modeling nonlinear Granger causality between the oil price and U.S. dollar: A wavelet based approach," Economic Modelling, Elsevier, vol. 29(4), pages 1505-1514.
  64. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
  65. Lopes, Artur Silva & Zsurkis, Gabriel Florin, 2017. "Are linear models really unuseful to describe business cycle data?," Economics Discussion Papers 2017-5, Kiel Institute for the World Economy (IfW Kiel).
  66. Martha Misas A. & Enrique López E. & Carlos A. Arango A. & Juan Nicolás Hernández A., 2003. "La Demanda de Efectivo en Colombia: Una Caja Nagra a la Luz de las Redes Neuronales," Borradores de Economia 2963, Banco de la Republica.
  67. Saman, Corina, 2011. "Scenarios of the Romanian GDP Evolution With Neural Models," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 129-140, December.
  68. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
  69. Shintani, Mototsugu, 2008. "A dynamic factor approach to nonlinear stability analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2788-2808, September.
  70. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.
  71. Peguin-Feissolle, Anne, 1999. "A comparison of the power of some tests for conditional heteroscedasticity," Economics Letters, Elsevier, vol. 63(1), pages 5-17, April.
  72. George Kapetanios, 2002. "Testing for Structural Breaks in Nonlinear Dynamic Models Using Artificial Neural Network Approximations," Working Papers 470, Queen Mary University of London, School of Economics and Finance.
  73. George Kapetanios & Andrew P. Blake, 2007. "Testing the Martingale Difference Hypothesis Using Neural Network Approximations," Working Papers 601, Queen Mary University of London, School of Economics and Finance.
  74. Kuswanto, Heri & Sibbertsen, Philipp, 2009. "Testing for Long Memory Against ESTAR Nonlinearities," Hannover Economic Papers (HEP) dp-427, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  75. Bruno, Giancarlo, 2008. "Forecasting Using Functional Coefficients Autoregressive Models," MPRA Paper 42335, University Library of Munich, Germany.
  76. repec:lan:wpaper:2373 is not listed on IDEAS
  77. George Kapetanios & Tony Yates, 2014. "Evolving UK and US macroeconomic dynamics through the lens of a model of deterministic structural change," Empirical Economics, Springer, vol. 47(1), pages 305-345, August.
  78. T Tang, 2009. "Testing for Non-linearity in the Balancing Item of Balance of Payments Accounts: The Case of 20 Industrial Countries," Economic Issues Journal Articles, Economic Issues, vol. 14(2), pages 107-124, September.
  79. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
  80. Siani, Carole & de Peretti, Christian, 2007. "Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2442-2460, February.
  81. Robles-Fernandez M. Dolores & Nieto Luisa & Fernandez M. Angeles, 2004. "Nonlinear Intraday Dynamics in Eurostoxx50 Index Markets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-28, December.
  82. Zacharias Psaradakis & Martin Sola & Fabio Spagnolo, 2004. "On Markov error-correction models, with an application to stock prices and dividends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(1), pages 69-88.
  83. M. Hashem Pesaran & Larry W. Taylor, 1999. "Diagnostics for IV Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 255-281, May.
  84. Kapetanios George, 2003. "Bootstrap Neural Network Cointegration Tests Against Nonlinear Alternative Hypotheses," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-16, July.
  85. Psaradakis, Zacharias & Vávra, Marián, 2014. "On testing for nonlinearity in multivariate time series," Economics Letters, Elsevier, vol. 125(1), pages 1-4.
  86. Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, University Library of Munich, Germany.
  87. Khurshid Kiani, 2005. "Detecting Business Cycle Asymmetries Using Artificial Neural Networks and Time Series Models," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 65-89, August.
  88. Jan-Egbert Sturm & Jakob de Haan, 2001. "Inflation in Developing Countries: Does Central Bank Independence Matter?," CESifo Working Paper Series 511, CESifo.
  89. Martha Misas Arango & Enrique López Enciso & Pablo Querubín Borrero, 2002. "La inflación en Colombia: una aproximación desde las redes neuronales," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, vol. 20(41-42), pages 143-214, June.
  90. Bruce Curry, 2007. "Parameter redundancy in neural networks: an application of Chebyshev polynomials," Computational Management Science, Springer, vol. 4(3), pages 227-242, July.
  91. Marcelo Fernandes & Marco Aurélio Dos Santos Rocha, 0. "Are price limits on futures markets that cool? Evidence from the Brazilian Mercantile and Futures Exchange," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(2), pages 219-242.
  92. Clive W. Granger & Timo Terasvirta & Heather M. Anderson, 1993. "Modeling Nonlinearity over the Business Cycle," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 311-326, National Bureau of Economic Research, Inc.
  93. Clive W. J. Granger, 1993. "Strategies for Modelling Nonlinear Time‐Series Relationships," The Economic Record, The Economic Society of Australia, vol. 69(3), pages 233-238, September.
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  95. Baillie, Richard T. & Kapetanios, George, 2008. "Nonlinear models for strongly dependent processes with financial applications," Journal of Econometrics, Elsevier, vol. 147(1), pages 60-71, November.
  96. George Kapetanios & Andrew P. Blake, 2007. "Boosting Estimation of RBF Neural Networks for Dependent Data," Working Papers 588, Queen Mary University of London, School of Economics and Finance.
  97. Ralf Becker & Walter Enders & A. Stan Hurn, 2001. "Testing for Time Dependence in Parameters," Research Paper Series 58, Quantitative Finance Research Centre, University of Technology, Sydney.
  98. Psaradakis Zacharias & Spagnolo Nicola, 2002. "Power Properties of Nonlinearity Tests for Time Series with Markov Regimes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-16, November.
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  100. Chuffart Thomas & Flachaire Emmanuel & Péguin-Feissolle Anne, 2018. "Testing for misspecification in the short-run component of GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-17, December.
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  102. Baillie, Richard T. & Kapetanios, George, 2007. "Testing for Neglected Nonlinearity in Long-Memory Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 447-461, October.
  103. Adrian Pagan & Hashem Pesaran, 2007. "Econometric Analysis of Structural Systems with Permanent and Transitory Shocks. Working paper #7," NCER Working Paper Series 7, National Centre for Econometric Research.
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  120. José Luis Torres, 2006. "Modelos Para La Inflación Básica de Bienes Transables y No Transables en Colombia," Borradores de Economia 365, Banco de la Republica de Colombia.
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  125. Pesaran, M Hashem & Taylor, Larry W, 1999. "Diagnostics for IV Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 255-281, May.
  126. Bildirici, Melike & Alp, Aykaç, 2008. "The Relationship Between Wages and Productivity: TAR Unit Root and TAR Cointegration Approach," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 5(1), pages 93-110.
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  128. Yang, Jian & Cabrera, Juan & Wang, Tao, 2010. "Nonlinearity, data-snooping, and stock index ETF return predictability," European Journal of Operational Research, Elsevier, vol. 200(2), pages 498-507, January.
  129. Bai, Xiwen, 2021. "Tanker freight rates and economic policy uncertainty: A wavelet-based copula approach," Energy, Elsevier, vol. 235(C).
  130. Baillie, Richard T. & Kapetanios, George, 2007. "Testing for Neglected Nonlinearity in Long-Memory Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 447-461, October.
  131. Psaradakis Zacharias, 2000. "p-Value Adjustments for Multiple Tests for Nonlinearity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(3), pages 1-8, October.
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  133. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, vol. 158(2), pages 231-245, October.
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  135. Breitung, Jorg, 2001. "Rank Tests for Nonlinear Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 331-340, July.
  136. Hsu, Shih-Hsun & Kuan, Chung-Ming, 2014. "Constructing smooth tests without estimating the eigenpairs of the limiting process," Journal of Econometrics, Elsevier, vol. 178(P1), pages 71-79.
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