Informatica

We present a new method for solving the change-point detection problem for ARMA systems which are assumed to have a slow and non-decaying drift after the change occurs. The proposed technique is inspired by the stochastic complexity theory, which gives a basis of comparison of different models with different change-point times. Some partial results on the analysis of the estimator are stated. A simulation is included which shows that the approach exhibits surprisingly good detection capabilities.

The idea of predicting the case, when the considered long-term ARMA model, fitted to the observed time series tends to become unstable because of deep changes in the structural stability of data, is developed in this paper. The aim is to predict a possible unstable regime of the process {Xt,t∈T}τ-steps in advance before it will express itself by a high level crossing or large variance of an output variable Xt. The problem is solved here for locally stationary AR(p) sequences {Xt,t∈T}, whose estimated parameters can reach critical sets located at the boundary of the stability area. An alarm function and an alarm set are fitted here to predict catastrophic failures in systems output τ units in advance for given τ>0 and a confidence level γ. The probability of false alarm is derived explicitly for AR(1) depending on τ,γ and N – the number of the last observations of {Xt}.

The dynamic programming method for estimation of many change-points in univariate autoregressive (AR) sequences with known AR parameters between change-points is investigated. A problem how to use this method for long autoregressive sequences is solved and a constructive solution is given. A simulation experiment illustrates the advantages of the solution obtained.

The paper defines the decomposition problem of a mixture of time series into homogeneous components. First part deals with a solution based on Bayesian approach in the case of independent observations, the other part is devoted to a solution of on-line decomposition for a time series consisting of weakly stationary components.

The paper defines the decomposition problem of a mixture of time series into homogeneous components. First part deals with a solution based on Bayesian approach in the case of independent observations, the other part is devoted to a solution of on-line decomposition for a time series consisting of weakly stationary components.

An essentially new method for sequential detection of many abrupt or slow changes in several unknown states of dynamic systems is presented. This method is based on the sequential nonlinear mapping into two-dimensional vectors of many-dimensional vectors which describe the present system states. The expressions for sequential nonlinear mapping are obtained. The mapping preserves the inner structure of distances between the vectors. Examples are given.

A practical method for segmentation and estimation of model parameters of processes is proposed in this paper. A pseudo-stationary random process with instantly changing properties is divided into stationary segments. Every segment is described by an autoregressive model. A maximum likehood method is used for segmentation of the random process and estimation of unknown model parameters. An example with simulated data is presented.

In the previous paper (Pupeikis, 1990) the problem of model order determination in the presence of outliers in observations has been considered by means of introducing robust analogues of the sample covariance and cross-covariance functions instead of the respective classical function meanings used in the determinant ratio test. The aim of the given paper is the development of statistical hypothesis-testing procedures for determination of the model order of dynamic objects, described by linear difference equations. The results of numerical simulations by computer (Table 1) show the efficiency of the proposed statistical procedures for determining the model order by input-output data in the presence of outliers in observations.

We consider a class of identification algorithms for distributed parameter systems. Utilizing stochastic optimization techniques, sequences of estimators are constructed by minimizing appropriate functionals. The main effort is to develop weak and strong invariance principles for the underlying algorithms. By means of weak convergence methods, a functional central limit theorem is established. Using the Skorohod imbedding, a strong invariance principle is obtained. These invariance principles provide very precise rates of convergence results for parameter estimates, yielding important information for experimental design.