### Abstract

*p*) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The 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 auto-regression parameters and the innovation distribution.

Original language | English |
---|---|

Pages (from-to) | 467-485 |

Journal | Journal of the Royal Statistical Society, Series B |

Volume | 71 |

Issue number | 2 |

Publication status | Published - 2009 |

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**Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models.** / Drost, F.C.; van den Akker, R.; Werker, B.J.M.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models

AU - Drost, F.C.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Appeared earlier as CentER DP 2008-53

PY - 2009

Y1 - 2009

N2 - Integer-valued auto-regressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The 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 auto-regression parameters and the innovation distribution.

AB - Integer-valued auto-regressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The 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 auto-regression parameters and the innovation distribution.

M3 - Article

VL - 71

SP - 467

EP - 485

JO - Journal of the Royal Statistical Society, Series B

JF - Journal of the Royal Statistical Society, Series B

SN - 1369-7412

IS - 2

ER -