Descent аlong nodal straight lines in robust monitoring problems of dynamic regression models

Monitoring the state of dynamic systems requires rapid data processing in real time, however, traditional methods such as the least squares method are not always efficient in the presence of outliers and contaminated data. The goal of this work is to implement and evaluate the computational efficiency of dynamic dynamic descent along nodal straight lines algorithms based on the least absolute deviations method for continuous monitoring tasks of dynamic regression models. We proposed dynamic coordinate-wise and gradient descent descent along nodal lines algorithms to implement the least absolute deviations method, the weighted and the generalised least absolute deviations methods. The dynamic implementation significantly improves performance compared to the static one, bringing the analysis time closer to that of the least squares method. Approbation on stock price data showed high estimation accuracy even with non-optimal initial data, but the descent along nodal straight lines showed minor deviations from the exact solution in the presence of multicollinearity, which are decreased when we used nonlinear models. Due to high performance and robustness to outliers, the algorithms can effectively solve the problems of continuous monitoring of rapidly changing processes.