Premium
Efficient estimation of auto‐regression parameters and innovation distributions for semiparametric integer‐valued AR( p ) models
Author(s) -
Drost Feike C.,
Akker Ramon van den,
Werker Bas J. M.
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00687.x
Subject(s) - semiparametric regression , mathematics , estimator , semiparametric model , parametric statistics , integer (computer science) , autoregressive model , econometrics , distribution (mathematics) , regression analysis , statistics , computer science , mathematical analysis , programming language
Summary. 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.