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Bias-adjusted estimation in the ARX(1) model

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  • Broda, Simon
  • Carstensen, Kai
  • Paolella, Marc S.

Abstract

A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median‐unbiased estimator, but uses the mode as a measure of central tendency. The mean‐adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large‐scale simulation studies for assessing their small‐sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space.
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Suggested Citation

  • Broda, Simon & Carstensen, Kai & Paolella, Marc S., 2007. "Bias-adjusted estimation in the ARX(1) model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3355-3367, April.
    • Handle: RePEc:eee:csdana:v:51:y:2007:i:7:p:3355-3367
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    1. Broda, S. & Paolella, M.S., 2009. "Evaluating the density of ratios of noncentral quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1264-1270, February.
    2. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    3. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    4. Jorge Arevalillo, 2014. "Higher-order approximations to the quantile of the distribution for a class of statistics in the first-order autoregression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 291-310, June.
    5. van Giersbergen, Noud P.A., 2016. "The ability to correct the bias in the stable AD(1,1) model with a feedback effect," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 186-204.

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