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A Non-parametric Bootstrap Simulation Study in ESTAR (1) Model

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Author Info

  • Liew Khim Sen

    (Universiti Putra Malaysia)

  • Ahmad Zubaidi Baharumshah

    (Universiti Putra Malaysia)

  • Choo Wei Chong

    (Universiti Putra Malaysia)

  • Habshah Midi

    (Universiti Putra Malaysia)

Abstract

Smooth Transition Autoregressive (STAR) model has been employed in a number of current studies dealing with non-linearities. The usefulness of this model has been documented in these studies. However, the population statistical properties of the parameters in this model remain unknown. This study attempts to investigate these properties through a non-parametric bootstrap simulation study. The exponential STAR model of order one, which is sufficient in providing us the necessary information on the linear and non-linear parameters as well as the speed of transition of the STAR model despite its simplicity, is employed in this study. This study also investigates the size effect of the bootstrapped estimators and their confidence intervals by varying the number of bootstrap replications. Results of this study show that their empirical distribution are asymmetrical in nature with the linear parameter being positively skewed and the non-linear and transition parameters being negatively skewed. Besides, we find that the normality theory over rejects the significance of the estimated transition parameter. Another interesting point worth mentioning is that the minimum number of replications needed for the bootstrap confidence interval to be a good approximate of the standard normal one is 500.

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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0307005.

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Date of creation: 23 Jul 2003
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Handle: RePEc:wpa:wuwpge:0307005

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Related research

Keywords: non-parametric bootstrap; ESTAR model; confidence intervals; statistical distribution;

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  1. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
  2. Ahmad Baharumshah & Venus Liew, 2006. "Forecasting Performance of Exponential Smooth Transition Autoregressive Exchange Rate Models," Open Economies Review, Springer, vol. 17(2), pages 235-251, April.
  3. Baum, Christopher F. & Barkoulas, John T. & Caglayan, Mustafa, 2001. "Nonlinear adjustment to purchasing power parity in the post-Bretton Woods era," Journal of International Money and Finance, Elsevier, vol. 20(3), pages 379-399, June.
  4. Liew Khim Sen & Ahmad Zubaidi Baharumshah, 2003. "How Well the Ringgit-Yen Rate Fits the Non-linear Smooth Transition Autoregressive and Linear Autoregressive Models," GE, Growth, Math methods 0307004, EconWPA.
  5. Taylor, Mark P. & Peel, David A., 2000. "Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals," Journal of International Money and Finance, Elsevier, vol. 19(1), pages 33-53, February.
  6. Sarantis, Nicholas, 1999. "Modeling non-linearities in real effective exchange rates," Journal of International Money and Finance, Elsevier, vol. 18(1), pages 27-45, January.
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