Construction of Copula Models

In this paper the device of models copula and opportunity of application is considered at the analysis of time series. For the purpose the copula definition and its properties, are discussed then different copulas families. The illustrative examples of modeling of distribution by various kinds copulas are described, using a package R

Weak Law Of Large Numbers For Arrays Of Random Elements In P-Uniformly Smooth Banach Spaces

We estabish a weak law of large numbers for weighted sums of the form К1 ^"_ aj ^Ущ ~ сщ X where {Vnj ,n>\, 1 < j <n} be array of random elements with values inpuniformly smooth Banach space, 0 < bn T QO, {an} and {cnj, n>\, 1 < j <n} are suitable sequences

Generalized hyperbolic processes autocovariance functions

Generalized hyperbolic processes are Levy processes which allow an almost perfect fit to financial data. Autocovariance functions of generalized hyperbolic processes such as the normal inverse Gaussian process, the variance gamma process and the hyperbolic process are deduced at this paper

Option pricing by Esscher transforms in the cases of normal inverse Gaussian and variance gamma processes

The class of Esscher transforms is an important tool for option pricing Gerber and Shiu (1994) showed that the Esscher transform is an efficient technique for valuing derivative securities if the log returns of the underlying securities are governed by certain stochastic processes with stationary and independent increments. Levy processes are the processes of such type. Special cases of the Levy processes such as the normal inverse Gaussian process and the variance gamma process are considered at this paper. Values of these processes parameters for the existence of Esscher transform are deduced. A new algorithm of a normal inverse Gaussian process and variance gamma process simulation is also presented in this paper. These algorithm is universal and simpler one compared with analogous algorithms

The mutual variogram estimate of the signal processes

The paper deals with the problem of a statistical analysis of time series connected with the estimation of mutual variogram, a measure of spatial correlation. G. Matheron has coined the term variogram, although earlier appearances of this function can be found in the scientific literature. We present the limiting expressions of the first two moments and the higher order cumulants of the classical mutual variogram estimate of the second-order-stationary stochastic process with discrete time. These expressions are then used to prove the theorem concerning the asymptotic distribution of the mutual variogram estimate

Asymptotic Properties of Moments Of Modified Periodogram Smoothed by Spectral Windows

Asymptotic properties of mathematical expectation of smoothed modified periodogram are investigated

Weak Law Of Large Numbers For Arrays Of Random Elements In P-Uniformly Smooth Banach Spaces

We estabish a weak law of large numbers for weighted sums of the form К1 ^"_ aj ^Ущ ~ сщ X where {Vnj ,n>\, 1 < j <n} be array of random elements with values inpuniformly smooth Banach space, 0 < bn T QO, {an} and {cnj, n>\, 1 < j <n} are suitable sequences

Estimation of the location parameter of a-stable distributions

In this paper a method of estimating location parameter \iofa- stable distribution for a e (0,2] is provided. Firstly, the estimates of parameters a and о with the characteristic function method (CF) are obtained, then the method of estimating of parameter ц based on the means of non-skewed transformations

Statistical analysis of parameter estimations of some time series models

This paper studies the M-estimation in a general conditionally heteroscedastic time series models. Sufficient conditions for strong consistency and asymptotic normality of the estimation are established

Construction of Copula Models

In this paper the device of models copula and opportunity of application is considered at the analysis of time series. For the purpose the copula definition and its properties, are discussed then different copulas families. The illustrative examples of modeling of distribution by various kinds copulas are described, using a package R