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This work is devoted to analysis and research of OLS-estimates properties when identifying parameters of distributed dynamic processes. The study showed that at a low level of observation errors (1% and lower), the use of direct OLS estimates to identify parameters of distributed dynamic processes gives satisfactory results. At the same time, the displacement value is always slightly higher than the value of the standard deviation of the parameter estimate, which does not allow to neglect the displacement, especially at a high and average level of observation errors. The method of obtaining so-called alternative OLS-estimates is also proposed, which allows to reduce multicollinearity in sample statistics and at any level of observation errors significantly reduce standard error of parameter estimation.

The problem of bias of OLS 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.

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