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Contrasting Bayesian and Frequentist Approaches to Autoregressions: the Role of the Initial Condition

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  • Marek Jarocinski
  • Albert Marcet

Abstract

The frequentist and the Bayesian approach to the estimation of autoregressions are often contrasted. Under standard assumptions, when the ordinary least squares (OLS) estimate is close to 1, a frequentist adjusts it upwards to counter the small sample bias, while a Bayesian who uses a at prior considers the OLS estimate to be the best point estimate. This contrast is surprising because a at prior is often interpreted as the Bayesian approach that is closest to the frequentist approach. We point out that the standard way that inference has been compared is misleading because frequentists and Bayesians tend to use different models, in particular, a different distribution of the initial condition. The contrast between the frequentist and the Bayesian at prior estimation of the autoregression disappears once we make the same assumption about the initial condition in both approaches.

Suggested Citation

  • Marek Jarocinski & Albert Marcet, 2014. "Contrasting Bayesian and Frequentist Approaches to Autoregressions: the Role of the Initial Condition," Working Papers 776, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:776
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    More about this item

    Keywords

    autoregression; initial condition; Bayesian estimation; small sample distribution; bias correction;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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