A model which possesses both spatial and time dependence is the Markov chain Markov field (see X. Guyon, 1995). Here inference about the parameter for spatio-temporal interaction of a special case of a Markov chain Markov field model is considered. A statistic which is minimal sufficient for the interaction parameter and its asympotic distribution are derived. A condition for stationarity of the sufficient statistic process and the stationary distribution are given. Likelihood based inference such as estimation, hypothesis testing and monitoring are briefly examined.