### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 39 |

Volume | 2008-53 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2008-53 |

### Fingerprint

### Keywords

- count data
- nonparametric maximum likelihood
- infinite-dimensional Z-estimator
- semiparametric efficiency

### Cite this

*Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)*. (CentER Discussion Paper; Vol. 2008-53). Tilburg: Econometrics.

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**Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23).** / Drost, F.C.; van den Akker, R.; Werker, B.J.M.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)

AU - Drost, F.C.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Revision of DP 2007-23, Subsequently published in Journal of the Royal Statistical Society, Series B, 2009 Pagination: 39

PY - 2008

Y1 - 2008

N2 - Integer-valued autoregressive (INAR) processes have been introduced to model nonnegative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of autoregression coefficients and a probability distribution on the nonnegative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. This paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the autoregression parameters and the innovation distribution.

AB - Integer-valued autoregressive (INAR) processes have been introduced to model nonnegative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of autoregression coefficients and a probability distribution on the nonnegative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. This paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the autoregression parameters and the innovation distribution.

KW - count data

KW - nonparametric maximum likelihood

KW - infinite-dimensional Z-estimator

KW - semiparametric efficiency

M3 - Discussion paper

VL - 2008-53

T3 - CentER Discussion Paper

BT - Efficient Estimation of Autoregression Parameters and Innovation Distributions forSemiparametric Integer-Valued AR(p) Models (Revision of DP 2007-23)

PB - Econometrics

CY - Tilburg

ER -