Biljana Č. Popović

The uniform autoregressive process of the second order (UAR(2))

We introduce a stationary uniform autoregressive process of second order. Spectral density, autocovariance and autocorrelation functions are derived. The unknown parameters of this model are estimated by the conditional least squares.

The Split-SV model

A modification of one of the most popular stochastic model in describing financial indexes dynamics is introduced. For describing a nonlinear behavior of volatility, a threshold noise indicator in the autoregressive time series of stochastic volatility is used. Toward this end, the model named the Split-SV model is introduced and its basic stochastic properties are investigated. Furthermore, the Empirical Characteristic Function (ECF) method is used for obtaining the parameter estimations of the model and a numerical simulation of the obtained estimates is given as well. Finally, the Split-SV model is applied for fitting the empirical data: the daily returns of the exchange rates of GBP and USD per euro.

Memory effect and time correlations in breakdown initiation of DC glow discharge in argon and synthetic air

The memory effect and correlations of the statistical and formative time delay in argon and synthetic air DC glow discharge at low pressure were studied. The memory coefficients and ratios and Pearsons and Spearmans correlation coefficients were determined, ranging from about unity at low relaxation times and vanishing at the saturation region of the memory curves (determined by the background ionization). It was shown that the statistical ts and the formative time delay tf are correlated variables and the positive correlation between them was confirmed experimentally and theoretically.

From binomial distribution of electron occurrence to Gauss and Gauss-exponential distribution of the statistical time delay: Analytical transition and simulations

Starting from the binomial distribution for the electron occurrence in the interelectrode space, the Gaussian and mixed Gauss-exponential distribution for the statistical time delay are theoretically derived based on physical grounds. The analytical transition from discrete (number) representation to continuous (time) representation is accompanied by the Monte Carlo simulation of the statistical time delay distributions.

A bivariate uniform autoregressive process

We define the bivariate first order stationary autoregressive process {(Xn,Yn)} with uniform marginal distribution where {Xn} and {Yn} are the two stationary sequences with uniformU(0, 1) marginal distributions. We also estimate the unknown parameters of the model.

Distributions of the formative time delay in argon and synthetic air at low pressure

The determination of the formative time delay of electric breakdown is a complex problem due to its stochastic nature. Several methods based on the extreme values are used in the literature. However, there is the limit of applicability of this method due to low preionization level, since the breakdown initiation would not be immediate. In this paper, we propose a new methodology for the determination of the distribution of the formative time delay and discuss its application. The proposed method is applied for determination of formative time delay distribution in argon and synthetic air at low pressure and results are compared to theoretical predictions.

The likelihood functions of some autoregressive time series

We consider the application of some generalized time series in statistics. The likelihood functions of some autoregressive time series with non-Gaussian marginal distributions are defined by means of Diracs and Heavisides functions. Specially, we discuss the autoregressive time series with exponential marginals.