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Least Squares and IVX Limit Theory in Systems of Predictive Regressions with GARCH innovations

Author

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  • Tassos Magdalinos

    (University of Southampton, UK; Rimini Centre for Economic Analysis)

Abstract

The paper examines the effect of conditional heteroskedasticity to least squares inference in stochastic regression models. We show that a regressor signal of exact order O^e_p(n^{1+\alpha}) for arbitrary \alpha > 0 is sufficient to eliminate stationary GARCH effects from the limit distributions of least squares based estimators and self-normalised test statistics. The above order dominates the O e p (n) signal of stationary regressors but is dominated by the O e p (n 2 ) signal of I(1) regressors, thereby showing that least squares invariance to GARCH effects is not an exclusively I(1) phenomenon but extends to processes with persistence degree arbitrarily close to stationarity. The theory validates standard inference for self normalised test statistics based on: (i) the OLS estimator when \alpha \in (0,1); (ii) the IVX estimator (Phillips and Magdalinos, 2009; Kostakis, Magdalinos and Stamatogiannis 2015a) when \alpha > 0, when the innovation sequence of the system is a stationary vec-GARCH process. An adjusted version of the IVX testing procedure is shown to also accommodate stationary regressors and produce standard chi-squared inference under conditional heteroskedasticity in the innovations across the full range \alpha \qeq 0.

Suggested Citation

  • Tassos Magdalinos, 2018. "Least Squares and IVX Limit Theory in Systems of Predictive Regressions with GARCH innovations," Working Paper series 18-24, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:18-24
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    References listed on IDEAS

    as
    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(2), pages 482-526, April.
    3. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Alexandros Kostakis & Tassos Magdalinos & Michalis P. Stamatogiannis, 2015. "Robust Econometric Inference for Stock Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1506-1553.
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    More about this item

    Keywords

    Central limit theory; Conditional Heteroskedasticity; Mixed Normality; Wald test;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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