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Estimating Parameters in Autoregressive Models with Asymmetric Innovations

Author

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  • Wing-Keung Wong

    (National University of Singapore)

  • Guorui Bian

    (East China Normal University, China)

Abstract

Tiku et al (1999) considered the estimation in a regression model with autocorrelated error in which the underlying distribution be a shift-scaled Student’s t distribution, developed the modified maximum likelihood (MML) estimators of the parameters and showed that the proposed estimators had closed forms and were remarkably efficient and robust. In this paper, we extend the results to the case, where the underlying distribution is a generalized logistic distribution. The generalized logistic distribution family represents very wide skew distributions ranging from highly right skewed to highly left skewed. Analogously, we develop the MML estimators since the ML (maximum likelihood) estimators are intractable for the generalized logistic data. We then study the asymptotic properties of the proposed estimators and conduct simulation to the study.

Suggested Citation

  • Wing-Keung Wong & Guorui Bian, 2004. "Estimating Parameters in Autoregressive Models with Asymmetric Innovations," Departmental Working Papers wp0408, National University of Singapore, Department of Economics.
  • Handle: RePEc:nus:nusewp:wp0408
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    References listed on IDEAS

    as
    1. Wing-keung Wong & Raymond Chan, 2004. "On the estimation of cost of capital and its reliability," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 365-372.
    2. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    3. Wong, Wing-Keung & Li, Chi-Kwong, 1999. "A note on convex stochastic dominance," Economics Letters, Elsevier, vol. 62(3), pages 293-300, March.
    4. Weiss, Andrew A., 1990. "Least absolute error estimation in the presence of serial correlation," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 127-158.
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    Cited by:

    1. Akkaya, Aysen D. & Tiku, Moti L., 2008. "Estimating parameters in autoregressive models with asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2916-2916, December.
    2. GUORUI BIAN & MICHAEL McALEER & WING-KEUNG WONG, 2013. "Robust Estimation And Forecasting Of The Capital Asset Pricing Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-18.
    3. Bondon, Pascal, 2009. "Estimation of autoregressive models with epsilon-skew-normal innovations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1761-1776, September.
    4. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    5. Wing-Keung Wong & Meher Manzur & Boon-Kiat Chew, 2003. "How rewarding is technical analysis? Evidence from Singapore stock market," Applied Financial Economics, Taylor & Francis Journals, vol. 13(7), pages 543-551.
    6. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Management Information, Decision Sciences, and Financial Economics : a connection," Econometric Institute Research Papers 2018-004/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    8. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    9. Wing-Keung Wong & Aman Agarwal & Jun Du, 2005. "Financial Integration for India Stock Market, a Fractional Cointegration Approach," Departmental Working Papers wp0501, National University of Singapore, Department of Economics.
    10. Hirose, Hideo, 2007. "The mixed trunsored model with applications to SARS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 443-453.
    11. Wong, Wing-Keung & Du, Jun & Chong, Terence Tai-Leung, 2005. "Do the technical indicators reward chartists? A study on the stock markets of China, Hong Kong and Taiwan," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 0(Number 2), pages 1-23.
    12. Wing-Keung Wong & Boon-Kiat Chew & Douglas Sikorsk, 2001. "Can the Forecasts Generated from E/P Ratio and Bond Yield be Used to Beat Stock Markets?," Multinational Finance Journal, Multinational Finance Journal, vol. 5(1), pages 59-86, March.
    13. repec:gam:jjrfmx:v:11:y:2018:i:1:p:15-:d:137130 is not listed on IDEAS
    14. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    15. Wing-Keung Wong & Robert B. Miller & Keshab Shrestha, 2002. "Maximum Likelihood Estimation of ARMA Model with Error Processes for Replicated Observations," Departmental Working Papers wp0217, National University of Singapore, Department of Economics.
    16. Wong Keung-Wing & Habibullah Khan & Jun Du, 2006. "Money, Interest Rate and Stock Prices: New Evidence from Singapore and The United States," Departmental Working Papers wp0601, National University of Singapore, Department of Economics.
    17. Shuangzhe Liu & Chris Heyde & Wing-Keung Wong, 2011. "Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models," Statistical Papers, Springer, vol. 52(3), pages 621-632, August.
    18. Wing-Keung Wong & Guorui Bian, 2005. "Robust Estimation of Multiple Regression Model with asymmetric innovations and Its Applicability on Asset Pricing Model," Departmental Working Papers wp0508, National University of Singapore, Department of Economics.
    19. Wing-Keung Wong & Guorui Bian, 2005. "Robust Estimation of Multiple Regression Model with Non-normal Error: Symmetric Distribution," Monash Economics Working Papers 09/05, Monash University, Department of Economics.
    20. Bai, Zhidong & Wang, Keyan & Wong, Wing-Keung, 2011. "The mean-variance ratio test--A complement to the coefficient of variation test and the Sharpe ratio test," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1078-1085, August.
    21. Eric S. Fung & Kin Lam & Tak-Kuen Siu & Wing-Keung Wong, 2011. "A Pseudo-Bayesian Model for Stock Returns In Financial Crises," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 1-31, December.

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