## Introduction 

The quantitative assessment of dietary exposure to certain contaminants is of high priority to the Food and Agricultural Organization and the World Health Organization (FAO/WHO). For exam- ple, excessive exposure to methylmercury, a contaminant mainly found in fish and other seafood (mollusks and shellfish) may have neurotoxic effects such as neuronal loss, ataxia, visual disturbance, impaired hearing, and paralysis (WHO, 1990). Quantitative risk assessments for such chronic risk require the comparison between a tolerable dose of the contaminant called Provisional Tolerable Weekly Intake (PTWI) and the population’s usual intake. The usual intake distribution is gener- ally estimated from independent individual food consumption surveys (generally not exceeding 7 days) and food contamination data. Several models have been developed to estimate the distribu- tion of usual dietary intake from short-term measurements (see for example, Nusser et al. , 1996; Hoffmann et al. , 2002). The proportion of consumers whose usual weekly intake exceeds the PTWI can then be viewed as a risk indicator (see for example, Tressou et al. , 2004). This kind of risk assessment does not account for the underlying dynamic process, i.e. for the fact that the contami- nant is ingested over time and naturally eliminated at a certain rate by the human body. Moreover, longer term measurements of consumption are available through household budget surveys (HBS). 

In this paper, we propose to use HBS data to quantify individual long term exposure to a contaminant. This data provides long time series of household food acquisitions which are first used in a decomposition model, similar to the one proposed by Chesher (1997, 1998) in the nutrition field, in order to obtain time series of individual intakes. Then, the pharmacokinetic properties of the contaminant are integrated into an autoregressive model in which the current body burden is defined as a fraction of the previous one plus the current intake. 

From a toxicological point of view, this approach is, to our knowledge, novel and hence requires the definition of an ad-hoc long term safe dose as proposed in the next section. We refer to this autoregressive model as Kinetic Dietary Exposure Model (KDEM). 

From a statistical point of view, such autoregressive models are well known in general time series analysis (see for example, Hamilton, 1994) and most of the paper is devoted to the description of the decomposition model. This statistical model aims at estimating individual quantities from total 

