This thesis presents a study of a state space model for positive data where the observed process is conditionally independent given a latent process gamma Markov process. The observed process conditioned to the latent process has gamma distribution. The model facilitates the inclusion of as many covariates through the latent process as of the observed process.The obtained model is log-linear and the estimate of the regression parameters is made through Kalman estimating functions. The dispersion parameters are obtained via the adjusted Pearson estimation. Some simulation studies and an application are developed to the data of the series of rainfall of Fortaleza, Ceará, where they are incorporate stylized facts of the series (tendency, sazonalidade or cycles) are include as well as the effect of explanatory variables (temperature of the level of the sea, pressure, sunspots).