Integer-valued autoregressive (INAR) time series form a very useful class of processes suitable to model time series of counts. In the common formulation of Du and Li (1991, JTSA), INAR models of order p share the autocorrelation structure with classical autoregressive time series. This fact allows to estimate the INAR coefficients, e.g., by Yule-Walker estimators. However, contrary to the AR c...

We propose an integrated scheme for estimating the mobility state and model parameters of a user based on a first-order autoregressive model of mobility that accurately captures the characteristics of realistic user movements in wireless networks. Estimation of the mobility parameters is performed by applying the Yule-Walker equations to the training data. Estimation of the mobility state, whic...

In this paper, a new estimation method is introduced for the quantile spectrum, which uses parametric form of autoregressive (AR) spectrum coupled with nonparametric smoothing. The begins periodograms are constructed by trigonometric regression at different levels, to represent serial dependence time series various quantiles. At each level, we approximate function in an ordinary AR spectrum. mo...

Solving linear system of equations Ax = b enters into many scientific applications. In this paper, we consider a special kind of linear systems, the matrix A is an equivariant matrix with respect to a finite group of permutations. Examples of this kind are special Toeplitz matrices, circulant matrices, and others. The equivariance property of A may be used to reduce the cost of computation for ...

In this paper, we propose a method for the detection of irregularities in time series, based on linear prediction. We demonstrate how we can estimate the linear predictor by solving the Yule Walker equations, and how we can combine several predictors in a simple mixture model. In several tests, we compare our model to a Gaussian mixture and a hidden Markov model approach. We successfully apply ...

Several pieces of research have spotlighted the importance count data modelling and its applications in real-world phenomena. In light this, a novel two-parameter compound-Poisson distribution is developed this paper. Its mathematical functionalities are investigated. The two unknown parameters estimated using both maximum likelihood Bayesian approaches. We also offer parametric regression mode...