Specification with lattice processes

Abstract. We describe tests for the correct speciffcation of a model when data is observed in a lattice. We then extend previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distribution of the test is not pivotal and it depends on the model under consideration. On consequence is that its critical values are di¢ cult, if at all possible, to obtain. So, to overcome the problem of its implementation, we propose to employ a martingale transformation, showing its validity in our context.