Calculation of the Asymptotic Covariance Matrix of the Generalized Exponential Autoregressive Model for the Least Absolute Deviations Method

Abstract

Over the past three decades, there has been significant attention paid to the development of high-level mathematical models and the investigation of their theoretical characteristics. One notable example is the generalized exponential autoregressive (Ozaki) model, which has been actively utilized in modeling medical, economic, and mechanical phenomena. This model serves as a standard for generating training data for artificial neural networks that can predict future values based on historical data of a given variable. In this paper, we present the calculation of the asymptotic covariance matrix used to estimate the smallest eigenvalues in the Ozaki model. We achieve this by decomposing the error function of the model using Taylor formula. A comparative analysis of the convergence rate of individual implementations of a model to its asymptotic behavior has been conducted for various distributions of the updating process: normal, skewed normal, Student t-distribution, Laplace, and logistic. The scientific contribution of this work lies in the determination of the asymptotic covariance matrix to estimate the smallest models within the Ozaki framework, and the practical relevance lies in applying the comparison results to selecting this model for engineering calculations

Please cite this article in English as:

Goryainov V.B., Masyagin M.M. Calculation of the asymptotic covariance matrix of the generalized exponential autoregressive model for the least absolute deviations method. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2025, no. 1 (118), pp. 4--29 (in Russ.). EDN: BEIMRT

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