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Heteroscedasticity and Autocorrelation Efficient (HAE) Estimation and Pivots for Jointly Evolving Series

  • Hrishikesh D. Vinod

    (Fordham University, Department of Economics)

A new two-way map between time domain and numerical magnitudes or values domain (v-dom) provides a new solution to heteroscedasticity. Since sorted logs of squared fitted residuals are monotonic in the v-dom, we obtain a parsimonious fit there. Two theorems prove consistency, asymptotic normality, efficiency and specification-robustness, supplemented by a simulation. Since Dufour's (1997) impossibility theorems show how confidence intervals from Wald-type tests can have zero coverage, I suggest Godambe pivot functions (GPF) with good finite sample coverage and distribution-free robustness. I use the Frisch-Waugh theorem and the scalar GPF to construct new confidence intervals for regression parameters and apply Vinod's (2004, 2006) maximum entropy bootstrap. I use Irving Fisher's model for interest rates and Keynesian consumption function for illustration.

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Paper provided by Fordham University, Department of Economics in its series Fordham Economics Discussion Paper Series with number dp2008-15.

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Date of creation: 2008
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Handle: RePEc:frd:wpaper:dp2008-15
Contact details of provider: Web page: http://www.fordham.edu/economics/
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  1. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  2. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July.
  3. Cribari-Neto, Francisco, 2004. "Asymptotic inference under heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 215-233, March.
  4. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar.
  5. Vinod, H. D., 1985. "Exact maximum likelihood regression estimation with ARMA (n, n - 1) errors," Economics Letters, Elsevier, vol. 17(4), pages 355-358.
  6. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  7. Godfrey, L.G., 2006. "Tests for regression models with heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2715-2733, June.
  8. Noriega, Antonio E. & Ventosa Santaulària, Daniel, 2005. "Spurious regression under broken trend stationarity," MPRA Paper 58768, University Library of Munich, Germany.
  9. Vinod, Hrishikesh D., 2006. "Maximum entropy ensembles for time series inference in economics," Journal of Asian Economics, Elsevier, vol. 17(6), pages 955-978, December.
  10. B. D. McCullough & H. D. Vinod, 2003. "Verifying the Solution from a Nonlinear Solver: A Case Study," American Economic Review, American Economic Association, vol. 93(3), pages 873-892, June.
  11. Vinod, H. D., 1998. "FELLOW'S CORNER Foundations of statistical inference based on numerical roots of robust pivot functions," Journal of Econometrics, Elsevier, vol. 86(2), pages 387-396, June.
  12. Vinod, H. D., 2004. "Ranking mutual funds using unconventional utility theory and stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 353-377, June.
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