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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. 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.
    2. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Timmermann, Allan & Elliott, Graham & Komunjer, Ivana, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
    10. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
    16. Bergstrom, P., 1999. "Bootstrap Methods and Applications in Econometrics -a Brief Survey," Papers 1999:2, Uppsala - Working Paper Series.
    17. 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.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    20. 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.
    21. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    22. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    23. 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.
    24. 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.
    25. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics.
    26. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Fracasso, Andrea & Vittucci Marzetti, Giuseppe, 2015. "International trade and R&D spillovers," Journal of International Economics, Elsevier, vol. 96(1), pages 138-149.
    3. 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.
    4. 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.
    5. 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.
    6. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    7. 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.
    8. 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.
    9. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    10. 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.
    11. 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.
    12. 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.

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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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