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

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 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