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Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity

Author

Listed:
  • Stan Hurn

    (Economics, School of Social Sciences, University of Manchester, United Kingdom)

  • Ralf Becker

    (School of Economics and Finance, Queensland University of Technology, Brisbane, 4001)

Abstract

This paper considers an important practical problem in testing time-series data for nonlinearity in mean, namely, the distortion in the size of the test encountered if the the data are heteroskedastic. It is shown that using a heteroskedastic consistent auxiliary regression together with the wild bootstrap is an e®ective way of dealing with the problem. Simulation results indicate that signi¯cant improvements in empirical size are obtained, particularly in small samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecanpo:v39:y:2009:i:2:p:311-326
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    1. DAVIDSON, Russel & MACKINNON, James G., 1985. "Heteroskedastcity-robust tests in regressions directions," LIDAM Reprints CORE 678, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. Denise R. Osborn & Dong Heon Kim & Marianne Sensier, 2005. "Nonlinearity in the Fed's monetary policy rule," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 621-639.
    4. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    5. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
    6. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    9. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    10. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    11. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    12. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    13. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    14. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    16. Godfrey, Leslie G. & Orme, Chris D., 2004. "Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients," Economics Letters, Elsevier, vol. 82(2), pages 281-287, February.
    17. Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
    18. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    19. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    20. Timmermann, Allan & Elliott, Graham & Komunjer, Ivana, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
    21. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    22. Timo Teräsvirta & Chien‐Fu Lin & Clive W. J. Granger, 1993. "Power Of The Neural Network Linearity Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(2), pages 209-220, March.
    23. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    24. Bergstrom, P., 1999. "Bootstrap Methods and Applications in Econometrics -a Brief Survey," Papers 1999:2, Uppsala - Working Paper Series.
    25. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    26. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
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    Cited by:

    1. 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.
    2. Daiki Maki & Yasushi Ota, 2021. "Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1167-1182, April.
    3. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    4. Andrea Fracasso & Giuseppe Vittucci Marzetti, 2014. "International R&D Spillovers, Absorptive Capacity and Relative Backwardness: A Panel Smooth Transition Regression Model," International Economic Journal, Taylor & Francis Journals, vol. 28(1), pages 137-160, March.
    5. Jorge Belaire-Franch & Amado Peiró, 2015. "Asymmetry in the relationship between unemployment and the business cycle," Empirical Economics, Springer, vol. 48(2), pages 683-697, March.
    6. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    7. Giulio Cainelli & Andrea Fracasso & Giuseppe Vittucci Marzetti, 2015. "Spatial agglomeration and productivity in Italy: A panel smooth transition regression approach," Papers in Regional Science, Wiley Blackwell, vol. 94, pages 39-67, November.
    8. Ralf Becker & Denise R. Osborn, 2012. "Weighted Smooth Transition Regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 795-811, August.
    9. Daiki Maki & Yasushi Ota, 2019. "Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches," Papers 1907.12752, arXiv.org, revised Sep 2019.
    10. Fracasso, Andrea & Vittucci Marzetti, Giuseppe, 2015. "International trade and R&D spillovers," Journal of International Economics, Elsevier, vol. 96(1), pages 138-149.
    11. Birgit Strikholm & Timo Teräsvirta, 2006. "A sequential procedure for determining the number of regimes in a threshold autoregressive model," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 472-491, November.
    12. Nan Cai & Zongwu Cai & Ying Fang & Qiuhua Xu, 2015. "Forecasting major Asian exchange rates using a new semiparametric STAR model," Empirical Economics, Springer, vol. 48(1), pages 407-426, February.

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    More about this item

    Keywords

    nonlinearity in mean; heteroskedasticity; wild bootstrap; empirical size and power;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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