Statistical Properties of Threshold Models

This article focuses the attention on the Self Exciting Threshold Autoregressive Moving Average model (SETARMA) proposed in Tong (1983 Tong , H. ( 1983 ). Threshold Models in Nonlinear Time Series Analysis . London : Springer-Verlag .[Crossref] , [Google Scholar]). The stochastic structure of the model is discussed and different specifications are presented. Starting from one of them, we give sufficient conditions for the weak stationarity of the model that are discussed and critically compared to other results given in literature. In particular, after showing that the SETARMA model belongs to the class of the Random Coefficients Autoregressive models, widely discussed in Nicholls and Quinn (1982 Nicholls , D. F. , Quinn , B. G. (1982). Random Coefficients Autoregressive Models. An Introduction . New York : Springer-Verlag.[Crossref] , [Google Scholar]), we give some issues on the weak stationarity of its stochastic structure that are more general than those given in the existing literature and appear not affected by the moving average component.     

Generalized Laplacian Distributions and Autoregressive Processes

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.     

A New Approach for Testing Periodicity

This article describes testing for periodicity in the presence of FD processes. We propose two approaches for testing the periodicity based on Fisher's test. The first one is performed using the periodogram which has been divided into different parts. The second one is based on the discrete wavelet transform. Properties of the tests are illustrated by means of Monte Carlo simulations.     

On the Multivariate Two-Sample Problem Using Strong Approximations of Empirical Copula Processes

In this article, we establish optimal rates for the strong approximation of empirical copula processes in ?² by sequences of Gaussian processes. These results are applied to investigate Cramér–von Mises-type statistics.     

The Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes

We study locally self-similar processes (LSSPs) in Silverman’s sense. By deriving the minimum mean-square optimal kernel within Cohen’s class counterpart of time–frequency representations, we obtain an optimal estimation for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of estimators is completely characterized in terms of kernels, so the optimal kernel minimizes the mean-square error of the estimation. We obtain the SIWS estimation for two cases: global and local, where in the local case, the kernel is allowed to vary with time and frequency. We also introduce two generalizations of LSSPs: the locally self-similar chirp process and the multicomponent LSSP, and obtain their optimal kernels. Finally, the performance and accuracy of the estimation is studied via simulation.     

A Bayesian semi-parametric approach to the ordinal calibration problem

ABSTRACT

We introduce a semi-parametric Bayesian approach based on skewed Dirichlet processes priors for location parameters in the ordinal calibration problem. This approach allows the modeling of asymmetrical error distributions. Conditional posterior distributions are implemented, thus allowing the use of Markov chains Monte Carlo to generate the posterior distributions. The methodology is applied to both simulated and real data.     

A detection algorithm for the first jump time in sample trajectories of jump-diffusions driven by α-stable white noise

Abstract

The purpose of this paper is to develop a detection algorithm for the first jump point in sampling trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by α-stable white noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilize computer simulation algorithm in MATLAB to visualize the sampling trajectories of the jump-diffusions for various combinations of parameters arising in the modeling structure of stochastic differential equations.     

Bayesian inferences and forecasts with moving averages processes

This paper will develop Bayesian inferential and forecasting techniques which can be used with any moving average process. By employing the conditional likelihood function, at-approximation to the predictive distribution and the marginal posterior distribution of the moving average parameters is developed. Several examples demonstrate posterior and predictive inferences.