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              <p>We consider an observed subcritical Galton Watson process $\{Y_n,\ n\in  \mathbb{Z} \}$ with correlated stationary immigration process $\{\epsilon_n,\ n\in  \mathbb{Z}  \}$. Two situations are presented. The first one is when $\mbox{Cov}(\epsilon_0,\epsilon_k)=0$ for $k$ larger than some $k_0$: a consistent estimator for the reproduction and mean immigration rates is given, and a central limit theorem is proved. The second one is when $\{\epsilon_n,\ n\in  \mathbb{Z}  \}$ has general correlation structure: under mixing assumptions, we exhibit an estimator for the the logarithm of the reproduction rate and we prove that it converges in quadratic mean with explicit speed. In addition, when the mixing coefficients decrease fast enough, we provide and prove a two terms expansion for the estimator. Numerical illustrations are provided.</p>
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              <p>Nous considérons un processus observé de Galton Watson $\{Y_n,\ n\in  \mathbb{Z} \}$ avec immigration modélisé par un processus corrélé $\{\epsilon_n,\ n\in \mathbb{Z} \}$. Nous présentons des résultats d’estimation du taux de reproduction et l’espérance de l’immigration dans deux situations. La première est lorsque $\mbox{Cov}(\epsilon_0,\epsilon_k)=0$  pour $k$ supérieur à un certain $k_0$ : nous fournissons un estimateur et prouvons un résultat de normalité asymptotique. Dans un deuxième temps, nous considérons le cas où $\{\epsilon_n,\ n\in  \mathbb{Z}  \}$ a une structure de corrélation générale. Sous des hypothèses de mélange, nous déterminons un estimateur pour le taux de reproduction et nous montrons sa convergence en moyenne quadratique avec vitesse explicite. Lorsque le coefficient de mélange décroit suffisamment vite, un développement d’ordre 2 pour cet estimateur est établi.</p>
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