In this paper we give a solution for the problem of identifying and predicting latent components integer-valued time series with skewed Skellam marginal distribution. At beginning, expressions identification prediction are derived. These us possibility revealing values two hidden, immeasurable which affect marginals. Yule-Walker estimators unknown parameters obtained. Also, quality lag-one is t...

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which ...

We compute the Newton step for the characteristic polynomial and for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix as the reciprocal of the trace of an appropriate matrix. We show that, after the Yule–Walker equations are solved, this trace can be computed in O(n) additional arithmetic operations, which is in contrast to existing methods, which rel...

In this paper we investigate bootstrap techniques applied to the estimation of the thinning parameters in INAR(p) models. We propose a new bootstrap approach based on sieve bootstrap. The approach is then applied to the Yule-Walker estimator of the thinning parameters. Monte Carlo experiments are carried out to valuate the performance of bootstrap estimator and the superiority of our proposal i...

First, we would like to congratulate Prof. McMurry and Prof. Politis for their thought-provoking paper on the optimal linear prediction based on full time series sample (hereafter, referred as [MP15]). [MP15] considered the one-step optimal linear predictor X∗ n+1 = ∑n i=1 φi(n)Xn+1−i of a univariate time series X1, . . . , Xn in the ` 2 sense which is given by the solution of the Yule-Walker e...

We discuss and analyze generalized linear dynamic factor models. These models have been developed recently and they are used to model high dimensional time series in order to overcome the “curse of dimensionality”. The basic idea in factor models is to seperate “comovement” between the variables (caused by a relatively small number of factors) from individual (idiosyncratic) variation. Here fac...

Data generation is straightforward if the parameters of a time series model define the prescribed spectral density or covariance function. Otherwise, a time series model has to be determined. An arbitrary prescribed spectral density will be approximated by a finite number of equidistant samples in the frequency domain. This approximation becomes accurate by taking more and more samples. Those s...

Many time series exhibit non-stationary behavior, i.e. either their mean or covariances are functions of time. The so-called modulated autoregressive process, an AR process where the variance is allowed to be a function of time, is a model that allows certain forms of non-stationarity to be modeled in a convenient way. For instance, this model has been used for seismic events such as earthquake...