In this paper, we introduce a new combined integer-valued moving average model of order 2 with poisson innovation, denoted by PCINMA(2). We consider some properties of this process, such as expectation, variance, autocovariance function. Stationary and ergodicity are obtained. We estimate the unknown parameters by using Yule-Walker estimation, and use simulation to assess the performance of Yul...

The extension of stationary process autocorrelation coefficient sequence is a classical problem in the field of spectral estimation. In this note, we treat this extension problem for the periodically correlated processes by using the partial autocorrelation function. We show that the theory of the non-stationary processes can be adapted to the periodically correlated processes. The partial auto...

Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule...

Let {Xk, k ∈ Z} be an autoregressive process of order q. Various estimators for the order q and the parameters q = (θ1, . . . , θq) are known; the order is usually determined with Akaike’s criterion or related modifications, whereas Yule–Walker, Burger or maximum likelihood estimators are used for the parameters q . In this paper, we establish simultaneous confidence bands for the Yule–Walker e...

This thesis introduces time-frequency-autoregressive-moving-average (TFARMA) models for underspread nonstationary stochastic processes (i.e., nonstationary processes with rapidly decaying TF correlations). TFARMAmodels are parsimonious as well as physically intuitive and meaningful because they are formulated in terms of time shifts (delays) and Doppler frequency shifts. They are a subclass of ...

In this note we introduce a new inferential method for STAR (spatio-temporal autoregression) models. Due to the complexity of such models the maximum likelihood estimation is difficult to undertake when several nearest neighbours are included in the model, see Ali (1979). Moreover, only approximate likelihoods are available in practice because of the observations lying on the edges of the spati...

In this paper, we introduce a new threshold model with poisson innovation: Threshold Integer-Valued Moving Average model (TINMA). We derive the numerical characteristics of TINMA(1) model. Stationary and ergodicity are also obtained. The methods of estimation under analysis is Yule-Walker. Some simulation results illustrate the performance of the proposed method.

Abstract The periodic behavior of real data can be manifested in the time series or its characteristics. One characteristics that often manifests is sample autocovariance function. In this case, periodically correlated (PC) considered. main models exhibits PC property autoregressive (PARMA) model considered as generalization classical moving average (ARMA) process. However, when one considers d...

Modern treatments of actuarial risk decision problems increasingly involve heavy tailed data and distributions. Here we consider the setting of time series and the problem of fitting an autogressive model with heavy tailed innovations. Assuming only finite first moments, we introduce a linear system of equations similar to the least squares approach but using Gini covariances instead of the usu...