Un semplice test preliminare di markovianità

A test of the Markov hypothesis (of arbitrary order) on an observed discrete stochastic process is often necessary before advancing further in the analysis. For this, however, a common goodness-of-fit test cannot be applied if a specific alternative is not specified, due to difficulties with its asymptotic distribution and to its computational intensity. In this paper a test based on the marginal (w. r. to time) distributions of the process is proposed. Specifically, a Wald-type test is developed after computing the general variance-covariance matrix for observed frequencies in any two different times t1 and t2, obtained from a Markov chain of arbitrary order m. Similarities with the literature on goodness-of-fit tests for complex samples are also investigated, since the marginal (w. r. to time) distributions of the process can be seen as generated by a cluster sampling scheme. Such at test has also to be performed before the application of the multivariate Markov chain models considered in Scagni (1993).