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A multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic inno- vations sequence of independent random vectors is established. The bino- mial thinning operator replaces the scalar multiplication in the common time series models. The matricial form of the multivariate model and its basic statistical properties are de ned. Emphasis is placed upon models with periodic multivariate negative binomial innovations. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method a composite likelihood-based approach is adopted and compared with other traditional competitors.