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A first-order autoregressive model designed for integer-valued data, incorporating time-dependent periodic parameters is proposed. This framework employs a signed thinning operator and is driven by a periodic sequence of innovations. The proposed model accommodates integer values, allowing both the series and its autocorrelation function to take negative values. Some properties of the model are established. This model follows a periodic structure and relies on the extended Poisson distribution for its innovation process. Parameters are estimated using conditional least squares and conditional maximum likelihood methods. A simulation study is carried out to evaluate the effectiveness of the estimation techniques. The periodic model is then applied to analyze an environmental dataset related to fire activity in Portugal.