Positivity properties of the ARFIMA(0,d,0) specifications and credibility analysis of frequency risks

Jean Pinquet

Insurance: Mathematics and Economics, 2020, vol. 95, issue C, 159-165

Abstract: Allowing for the seniority of claims and of risk exposure in the prediction of frequency risks necessitates dynamic random effects in Poisson mixtures. Non-life insurance data show evidence of long memory in stationary random effects. This paper proves that the ARFIMA(0,d,0) mixtures of Poisson distributions ensure nonnegative credibilities per period in the affine prediction of frequency risks. This is true regardless of the risk exposure. This property is maintained if the random effect is the product of a time-invariant component (which provides the highest level of memory in the data) and of a component that follows an ARFIMA(0,d,0) specification. The proof uses approximations of the ARFIMA(0,d,0) time series by AR(p) time series, which result from truncations of the filtering equations that define the former ones. Every given ARFIMA(0,d,0) specification inherits the positivity properties of the truncations because the supremum of the spectral densities of these truncations is integrable on the frequency domain. These semiparametric specifications are easily estimated from longitudinal count data, with the generalized method of moments.

Keywords: ARFIMA(0,d,0) specifications; Poisson mixtures; Semiparametric analysis; Linear credibility; Spectral measure of stationary random effects (search for similar items in EconPapers)
JEL-codes: C02 C14 C18 C23 C35 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:95:y:2020:i:c:p:159-165

DOI: 10.1016/j.insmatheco.2020.10.001

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