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Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors.

Umair Khalil1, Alamgir2, Amjad Ali3

  • 1Department of Statistics, Abdul wali Khan University Mardan, Mardan, Pakistan.

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Summary
This summary is machine-generated.

This study enhances the Kapetanios test for Exponential Smooth Transition Autoregressive (ESTAR) models, reducing size distortion under non-normal errors. It improves unit root testing for economic variables exhibiting nonlinear behavior.

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Area of Science:

  • Econometrics
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Exponential Smooth Transition Autoregressive (ESTAR) models capture nonlinear adjustments in economic variables, often appearing non-stationary linearly.
  • The Kapetanios test is commonly used for unit root testing against a stationary nonlinear alternative.
  • Existing tests assume normally distributed errors, which can lead to oversized statistics with heavy-tailed innovations.

Purpose of the Study:

  • To derive the size of the Kapetanios test statistic using heteroscedastic consistent covariance matrices (HCCME) for improved accuracy.
  • To investigate the properties of ESTAR model estimates with non-normal error distributions.
  • To compare nonlinear least squares with quantile regression in the presence of outliers.

Main Methods:

  • Derivation of Kapetanios test statistic size using HCCME.
  • Analysis of ESTAR model estimation properties under t-distributed errors.
  • Comparative analysis of nonlinear least squares and quantile regression.

Main Results:

  • Size distortion of the Kapetanios test is reduced when employing HCCME, especially for various sample sizes.
  • ESTAR model estimation properties are investigated for non-normal error distributions.
  • Quantile regression shows robust performance in the presence of outliers compared to nonlinear least squares.

Conclusions:

  • The use of HCCME offers a valuable alternative to conventional tests by reducing size distortion in unit root testing for ESTAR models.
  • ESTAR models and robust estimation techniques like quantile regression are crucial for analyzing economic data with non-normal error distributions and outliers.