Abstract
A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.
Highlights
In many areas, such as the actuarial field used in the application section of this paper, little attention has been paid to the possibility of including several dependence assumptions in the regression models to fit the data at hand
These models can be applied to the ratemaking problem of pricing an automobile insurance contract with two types of coverage, considering the serial correlation between the observations of the same policyholder over time and the correlation between claims from different coverage types, as shown in [2], where a bivariate integer-valued autoregressive process of order 1, BINAR(1), is fitted to the data using a bivariate Poisson distribution to allow for cross correlation
We developed a model to account for time and cross dependence for a case of longitudinal multivariate count data
Summary
In many areas, such as the actuarial field used in the application section of this paper, little attention has been paid to the possibility of including several dependence assumptions in the regression models to fit the data at hand. We make use of multivariate discrete distributions defined using the Sarmanov family to address the cross correlation. Based on (3), we can define a multivariate integer-valued autoregressive process of order 1 (MINAR(1)) as in [10]: Yt = A ◦ Yt−1 + Rt, t ∈ Z,. The numerical difficulty of the maximum likelihood approach, increase intensely with a dimensional increase [10] and the assumption of a cross-correlated innovation process. [11] consider a simplified MINAR(1) model where a unique source of dependence between the univariate series is assumed They assume {Rt} follow jointly a discrete multivariate distribution while A is a m × m diagonal matrix with independent elements αi = [A]ii, i = 1, .
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