Calculation of functional based on large dimension matrixes in maximal likelihood problems

Abstract

The problem of the likelihood function calculation is examined at parameter estimation of the stochastic process describing change of interest rates in the financial market. Such problem arises, when it is supposed, that process is not usual diffusion process, but possesses continuous derivatives. In this case the increments of process become correlated, and for the likelihood function evaluation it is necessary to invert a matrix of the high order equal to sample size. As is known the calculation of reciprocal matrixes of the high order either is impossible or results in essential mistakes of calculation. In paper the way to avoid this difficulty is offered.