The problem of detecting a major change point in a stochastic process is often of interest in applications, in particular when the effects of modifications of some external variables, on the process itself, must be identified. We here propose a modification of the classical Pearson \(\chi ^2\) test to detect the presence of such major change point in the transition probabilities of an inhomogeneous discrete time Markov Chain, taking values in a finite space. The test can be applied also in presence of big identically distributed samples of the Markov Chain under study, which might not be necessarily independent. The test is based on the maximum likelihood estimate of the size of the ’right’ experimental unit, i.e. the units that must be aggregated to filter out the small scale variability of the transition probabilities. We here apply our test both to simulated data and to a real dataset, to study the impact, on farmland uses, of the new Common Agricultural Policy, which entered into force in EU in 2015.

在应用程序中，通常需要检测随机过程中的主要变化点的问题，特别是当必须确定某些外部变量的修改对过程本身的影响时。我们在这里提出对经典Pearson \（\ chi ^ 2 \）的修改检验在有限空间中取非均质离散时间马尔可夫链的转移概率中是否存在这种主要变化点。该测试也可以在研究中的马尔可夫链的大量相同分布的样本中应用，这些样本不一定是独立的。该测试基于“正确”实验单元的大小的最大似然估计，即，必须合计以滤除过渡概率的小规模变化的单元。我们在此将测试应用于模拟数据和真实数据集，以研究新的《通用农业政策》对农田使用的影响，该政策于2015年在欧盟生效。