Improving the Quality of Estimates of the Parametric Identification Problem Using the Conservative Condition in Models of Distributed Dynamic Processes

Abstract

Today the apparatus for modelling non-stationary time series is most in demand in various areas of human activity: meteorology, sociology, medicine, financial market research, and a number of others. The general scientific problem of modelling such series is associated with solving the problem of identification, namely, obtaining such model parameters that would provide a high degree of accuracy and adequacy of the model. However, the problem of bias of least square method (LSM) estimates arises when solving the problem of parametric identification of distributed dynamic processes. There are various possible solutions to this problem. If the time series is trend-stationary, then these may be "ostationation" methods, which are generally difficult to apply. It is possible to use dimensionality reduction methods, but in this case we will still get biased estimates. In our previous works, it was shown that the problem of biased estimates can be solved using the conservativeness condition. The aim of this work was to investigate the possibility of using the conservativeness condition to improve the quality of estimates of the parametric identification problem, as well as to compare these results with the solution of the problem, in the case of applying a filter to it, as well as ridge regression.