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Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form

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  • Yongmiao Hong
  • Yoon-Jin Lee
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    Abstract

    Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be infinite. Both linear and nonlinear conditional mean specifications are covered. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroscedasticity and higher order time-varying moments of unknown form. They check a large number of lags, but naturally discount higher order lags, which is consistent with the stylized fact that economic behaviours are more affected by the recent past events than by the remote past events. No specific estimation method is required, and the tests have the appealing "nuisance parameter free" property that parameter estimation uncertainty has no impact on the limit distribution of the tests. A simulation study shows that it is important to take into account the impact of conditional heteroscedasticity; failure to do so will cause overrejection of a correct conditional mean model. In a horse race competition on testing linearity in mean, our tests have omnibus and robust power against a variety of alternatives relative to some existing tests. In an application, we find that after removing significant but possibly spurious autocorrelations due to nonsynchronous trading, there still exists significant predictable nonlinearity in mean for S&P 500 and NASDAQ daily returns. Copyright 2005, Wiley-Blackwell.

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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2005.00341.x
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    Bibliographic Info

    Article provided by Oxford University Press in its journal The Review of Economic Studies.

    Volume (Year): 72 (2005)
    Issue (Month): 2 ()
    Pages: 499-541

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    Handle: RePEc:oup:restud:v:72:y:2005:i:2:p:499-541

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    Cited by:
    1. Hong, Yongmiao & Lin, Hai & Wu, Chunchi, 2012. "Are corporate bond market returns predictable?," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2216-2232.
    2. Zhang, Bing, 2013. "Are the crude oil markets becoming more efficient over time? New evidence from a generalized spectral test," Energy Economics, Elsevier, vol. 40(C), pages 875-881.
    3. Peter C.B. Phillips & Sainan Jin, 2013. "Testing the Martingale Hypothesis," Cowles Foundation Discussion Papers 1912, Cowles Foundation for Research in Economics, Yale University.
    4. repec:wyi:journl:002156 is not listed on IDEAS
    5. Lee, Yoon-Jin, 2014. "Testing a linear dynamic panel data model against nonlinear alternatives," Journal of Econometrics, Elsevier, vol. 178(P1), pages 146-166.
    6. Kian-Ping Lim & Weiwei Luo & Jae H. Kim, 2013. "Are US stock index returns predictable? Evidence from automatic autocorrelation-based tests," Applied Economics, Taylor & Francis Journals, vol. 45(8), pages 953-962, March.
    7. Jarrow, Robert & Kwok, Simon, 2013. "Specification Tests of Calibrated Option Pricing Models," Working Papers 2013-08, University of Sydney, School of Economics.
    8. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2012. "Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1607-1626.
    9. repec:wyi:journl:002120 is not listed on IDEAS
    10. Guay, Alain & Guerre, Emmanuel & Lazarová, Štěpána, 2013. "Robust adaptive rate-optimal testing for the white noise hypothesis," Journal of Econometrics, Elsevier, vol. 176(2), pages 134-145.
    11. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.

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