On the question of modelling time series trends

The paper presents the analysis of modern methods of modelling time series trends. In economy and other spheres of scientific and practical activity we see objects of our interest developing over time. In order to model these objects, econometric methods and presentation of initial and resulting data in the form of time series are usually used. At present there is a great number of methods of time series modelling. Many of the methods, developed for solving specific problems, are not universal. Very often researchers use dynamic decomposition of time series into several components. Commonly a trend component, a cyclical component and a random component are singled out. In this paper the first method (method of weighted tangents - MWT) involves decomposition into the trend and cyclical components. The second method does not involve decomposition containing a cyclical component. Instead, the method of phase trends (MPT) uses the concept of "phases", which can be found in the initial form of time series. Application of the phase trends method allows for performing a piecewise approximation of time series. Modern methods are not aimed at work with short time series as some part of statistical data is lost in the preliminary smoothing. The MWT can be applied for short time series in case there is at least one cycle. Many methods do not consider development of time series over time (evolution). That is why the authors suggest using the MPT, which in many cases gives results that are not inferior in quality compared to complicated modern methods.