Установление значимости коэффициентов квазилинейного уравнения n-факторной авторегрессии
Автор: Аботалеб М.С.А.
Журнал: Проблемы информатики @problem-info
Рубрика: Теоретическая и системная информатика
Статья в выпуске: 3 (64), 2024 года.
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В этой статье проводится анализ обобщенного метода наименьших отклонений (GLDM), применяемого при анализе временных рядов. Исследование посвящено установлению оптимального порядка модели и определению коэффициентов модели. Центральное место в этом анализе занимает программа оценки GLDM, которая определяет коэффициенты. Рассматривается адаптивность GLDM для анализа сложных процессов. Показано, что соответствующий порядок модели зависит не только от размера набора данных, но и от присущих характеристик данных, которые определяют сложность модели. Например, данные о температуре с ее значительными сезонными колебаниями и автокорреляцией требуют модели пятого порядка, тогда как скорость ветра и количество смертей от COVID-19 в России достаточно моделируются с помощью модели второго порядка. В документе также исследуются тонкости моделей более высокого порядка и предлагается специальная стратегия выбора модели, которая повышает точность и интерпретируемость прогнозов временных рядов.
Прогнозирование временных рядов, обобщенный метод наименьших отклонений, коэффициенты модели
Короткий адрес: https://sciup.org/143183461
IDR: 143183461 | УДК: 51-77 | DOI: 10.24412/2073-0667-2024-3-5-28
Establishing the significance of the coefficients of the quasi-linear equation of n-factor autoregression
This article conducts a thorough analysis of the Generalized Least Deviation Method (GLDM) applied to time series forecasting. The study concentrates on establishing the optimal model order and identifying conditions that lead to zero coefficients. Central to this analysis is the GLDM Estimator, which determines the coefficients {aj}"=^ by minimizing an objective function E(a), expressed as the sum of the arctangents of the absolute deviations from the time series data {y,}/=1 which belongs to R. The adaptability of GLDM to capture complex dataset interactions is examined, highlighting how it adjusts to different model orders. It is shown that the appropriate model order depends not only on the dataset size but also on the inherent data characteristics, which govern the model’s complexity. For example, the data for temperature, with its significant seasonal variations and autocorrelations, requires a fifth-order model, whereas wind speed and COVID-19 death counts in Russia are suitably modeled by a second-order framework. The paper also explores the subtleties of higher-order models and suggests a custom strategy for model selection that enhances the accuracy and interpretability of time series forecasting predictions.
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