Identification of the Ramsay logistic curve by total least squares

Logistics curves are widely used in various fields of economics, technology, biology, chemistry. Estimating the parameters of logistic trends from the results of observations of the dynamic process in the economic system, with the aim of reliable analysis of economic indicators and predicting their future behavior, is one of the main tasks in the economy. One of the logistic models is the Ramsay function. The advantage of this function is the ability to use a linear difference equation to estimate its parameters. At the same time, non-linear data transformations are not required as for the logistics functions of Ferhulst or Gompertz. Modifications of a two-stage estimation algorithm based on the total least squares method and the extended instrumental variables method are proposed for estimating the parameters of the Ramsey curve.Tests have shown that the accuracy of parameter estimation using the proposed modifications is higher than the accuracy of the estimate obtained using the ordinary least squares method (LS).

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