Exploring the Identification of Autoregression Model by General Least Deviation Method

We are considering a novel method for analyzing time series data that relies on quasi-linear recurrence relations. Unlike neural networks, this approach allows for directly formulating high-quality quasi-linear difference equations that accurately represent the studied process. Techniques for determining the parameters of a single equation have been devised and validated. This work discusses and tests a technique for identifying the parameters of a quasi-linear recurrence equation. This approach is employed to tackle the issue of regression analysis including observable variables that are mutually dependent. It enables the utilization of the Generalized Least Deviations Method (GLDM). This model was utilized in a computational experiment to determine the parameters of quasi-linear differential equations that describe the spread of Covid-19 infection. The model underwent testing on three distinct types of processes: (1) monotonous (predicting cumulative cases); (2) oscillatory (predicting daily cases). The specified parameters allow the model to generate long-term predictions.