Model of Probabilistic Assessment of Trend stability at Financial market

The probabilistic model of assessing the state of the financial market, allowing to assess the probability of the trend reversal at the financial market was developed. A distinctive feature of the risk evaluation method, proposed in this paper, is that the time series of currency quotations are considered not as a set of individual points, but as a set of segments of stationarity, into which it is split by change-points. Finding of the change-points of the series allows to divide the series into the segments with similar statistical properties that corresponds to one of the main paradigms of the technical analysis – the division of the time series into segments with a constant trend. For the solution of the problem of the series splitting, two methods are used, such as the graphical method for finding the inflection points of the diagram, aimed at finding the reversal points a posteriori, and the CUSUM algorithm, relating to the methods of sequential detection of change-points. Splitting the diagram into segments using the change-points generates the random vector, comprising the segment duration in time and the difference between the prices at the beginning and the end of the segment. For the estimation of the probability density function of the vector, B-splines, constructed on a rectangular grid with the restoration of the intermediate points, were used. Based on the basic principles of financial market functioning, the assumptions were accepted, allowing to calculate the probability of the next change-point during the time interval in the future at each step of observation