Statistical analysis of high-order Markov dependencies

The paper deals with parsimonious models of integer valued time series. Such models are special cases of high-order Markov chain with a small number of parameters. Two new parsimonious models are presented. The first is Markov chain of order s with r partial connections, and the second model is called Markov chain of conditional order. Theoretical results on probabilistic properties and statistical inferences for these models are given

ВЕКТОРНАЯ ЦЕПЬ МАРКОВА С ЧАСТИЧНЫМИ СВЯЗЯМИ И СТАТИСТИЧЕСКИЕ ВЫВОДЫ О ЕЕ ПАРАМЕТРАХ

A new mathematical model of discrete time series is proposed. It is called homogenous vector Markov chain of the order s with partial connections. The conditional probability distribution for this model is determined only by a few components of previous vector states. Probabilistic properties of the model are given: ergodicity conditions and conditions under which the stationary probability distribution is uniform. Consistent statistical estimators for model parameters are constructed.Предложена новая малопараметрическая модель дискретных временных рядов – однородная векторная цепь Маркова s-го порядка с частичными связями, для которой условное распределение вероятностей определяется лишь некоторыми компонентами предыдущих векторов-состояний. Установлены вероятностные свойства модели:  критерий эргодичности, условия, при которых стационарное распределение  вероятностей является равномерным. Построены состоятельные статистические оценки параметров модели

On statistical estimation for markov chain of conditional order

The paper deals with Markov chain of conditional order, which is a special case of a high-order Markov chain with a small number of parameters. Estimator for the order is constructed and its consistency is proved. Numerical results of comparison of different Markov models via Bayesian information criterion are presented

Identification of Markov Chains of Conditional Order

A new special case of high-order Markov chains with a small number of parameters – Markov chain of conditional order – is considered. Statistical estimators for parameters of the model by observed time series are constructed; their asymptotic properties are analyzed. Results of computer experiments are presented

On statistical estimation for markov chain of conditional order

The paper deals with Markov chain of conditional order, which is a special case of a high-order Markov chain with a small number of parameters. Estimator for the order is constructed and its consistency is proved. Numerical results of comparison of different Markov models via Bayesian information criterion are presented

On statistical analysis of Markov chains with conditional memory depth

A new mathematical model of the s-order Markov chain with conditional memory depth is proposed. Maximum likelihood estimators of parameters are constnicted and their properties are analyzed. A statistical test on parameter values is constructed. Numerical results are presented

On One Generalization of Markov Chain with Partial Connections

SECTION 3 PROBABILISTIC AND STATISTICAL ANALYSIS OF DISCRETE DAT