Abstract. In the paper is described and destabilized a process of near Earth asteroids (NEA) semi-major axes distributions analysis by investigation of corresponding series in a frequency domain. Such study allows getting a new knowledge about fine structure of orbits distributions and makes possible to find out new phenomena (e.g. presence of periodic components or some resonance structure) in these distributions. Versatile investigation of NEA's orbits distributions fine structure allows testing some theories and hypotheses according to which these distributions should have a certain structure. In order to reach the goal of investigation following subtasks have been solved: 1) orbits set transformation to a discrete signal (frequency histograms); 2) series trend estimation and removing; 3) frequency analysis. As a result of the investigation a presence of a harmonic component in distributions of NEA's semi-major axes has been found.

Abstract. This paper analyses methods of trend estimation focusing on a process of calculation of their effectiveness. Shown a procedure that helps to choose : "optimal" parameters of trend estimation methods for trends with known characteristics (steepness of increasing or decreasing of trends, a frequency of alternation of regions with positive and negative derivatives etc.). All calculation are shown for data that represents near Earth's asteroids (NEA) semi-major axes distributions. The method is based on running of multiple iterations (in order to provide static stability of results) of a procedure that was designed to find a test signal after adding investigated trend and noise. It allows to calculate a probability of a signal detection after trend removing with using trend estimation methods with different parameters.