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This paper examines a first-order autoregressive model that incorporates student’s t-distributed errors. The estimation procedure is developed using the maximum likelihood method, with the solutions demonstrated using a simulation approach. As the estimating equations were not in a closed-form expression, we obtained the parameter estimates using the Newton–Raphson method. For a finite sample size, a parametric bootstrap procedure for the unit root test has been illustrated. To demonstrate the applications of the proposed model, a time series of quarterly GDP percentage changes are analyzed.

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Autoregressive Model with Student’s t-Errors

  • 会议论文

  • 发表日期：

    2026年

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  • Praveen Augustine,
  • Nimitha John

摘要

This paper examines a first-order autoregressive model that incorporates student’s t-distributed errors. The estimation procedure is developed using the maximum likelihood method, with the solutions demonstrated using a simulation approach. As the estimating equations were not in a closed-form expression, we obtained the parameter estimates using the Newton–Raphson method. For a finite sample size, a parametric bootstrap procedure for the unit root test has been illustrated. To demonstrate the applications of the proposed model, a time series of quarterly GDP percentage changes are analyzed.