• Bernoulli
  • Volume 8, Number 2 (2002), 255-274.

Estimation of the innovation quantile density function of an AR(p) process based on autoregression quantiles

Faouzi El Bantli and Marc Hallin

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In this paper, we propose two types of estimator (one of histogram type, the other a kernel estimate) of the quantile density (or sparsity) function α\mapsto [f(F-1(α ))]-1 associated with the innovation density f of an autoregressive model of order p. Our estimators are based on autoregression quantiles. Contrary to more classical estimators based on estimated residuals, they are autoregression-invariant and scale-equivariant. Their asymptotic behaviour is derived from a uniform Bahadur representation for autoregression quantiles - a result of independent interest. Simulations are carried out to illustrate their performance.

Article information

Bernoulli, Volume 8, Number 2 (2002), 255-274.

First available in Project Euclid: 9 March 2004

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autoregression autoregression quantiles Bahadur-Kiefer representation histogram estimator kernel estimator quantile density function sparsity function


El Bantli, Faouzi; Hallin, Marc. Estimation of the innovation quantile density function of an AR( p ) process based on autoregression quantiles. Bernoulli 8 (2002), no. 2, 255--274.

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