HYPOTHESIS TESTING FOR MARKOVIAN MODELS WITH RANDOM TIME OBSERVATIONS

Flavia Barsotti (1) , Anne Philippe (2) , Paul Rochet (2)

1 Risk Methodologies, Group Financial Risks, Group Risk Management, UniCredit S.p.A
2 LMJL - Laboratoire de Mathématiques Jean Leray

The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals τ k , assumed to be iid with unknown distribution µ. Two test procedures are investigated. The first one is devoted to testing if the transition matrix P of the Markov chain X satisfies specific affine constraints, covering a wide range of situations such as symmetry or sparsity. The second procedure is a goodness-of-fit test on the distribution µ, which reveals to be consistent under mild assumptions even though the time gaps are not observed. The theoretical results are supported by a Monte Carlo simulation study to show the performance and robustness of the proposed methodologies on specific numerical examples.

Mots clés: Asymptotic Tests of Statistical Hypotheses; Markov Chain; Random Sampling

Domaines: Statistiques [math.ST]

Flavia Barsotti, Anne Philippe, Paul Rochet. HYPOTHESIS TESTING FOR MARKOVIAN MODELS WITH RANDOM TIME OBSERVATIONS. 2015. ⟨hal-01151675⟩