Mathematics and Statistics Vol. 11(6), pp. 883 - 894
DOI: 10.13189/ms.2023.110603
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Identifying and Estimating Seasonal Moving Average Models by Mathematical Programming


Rasha A. Farghali , Hemat M. Abd-Elgaber *, Essam A. Ahmed
Department of Applied Statistics, Faculty of Commerce and Business Administration, Helwan University, Egypt

ABSTRACT

In this paper, a novel method is presented for simultaneously identifying and estimating Seasonal Moving Average (SMA) models, which are considered a special case of Seasonal Autoregressive Integrated Moving Average (SARIMA) models introduced by Box and Jenkins. To accomplish this, we utilize a mixed-integer nonlinear programming (MINLP) model, which falls within the class of optimization problems involving integer and continuous decision variables, as well as non-linear objective functions and/or constraints. The advantage of employing MINLP lies in its ability to provide a more flexible representation of real-world problems. The aim of employing the MINLP is to identify and estimate the appropriate SMA model, specifically determining whether it is Multiplicative or Non-multiplicative. To evaluate the effectiveness of the proposed MINLP approach, we conducted both a simulation study and real-world applications. In the simulation study, we generate 1000 time series datasets from each of the twelve SMA models, which comprised six multiplicative SMA models and six non-multiplicative SMA models, with different orders. Additionally, we examine the effectiveness of MINLP through two real-world applications: Carbon Dioxide Levels data and College Enrollment data. The results obtained from both the simulation study and real-world applications consistently demonstrate the effectiveness of MINLP in accurately identifying the appropriate SMA model. These findings support the applicability and reliability of the proposed method in practical scenarios. Overall, our research contributes to the field of time series analysis by providing a new approach for identifying and estimating SMA models using MINLP, paving the way for improved forecasting and decision-making in various domains.

KEYWORDS
Multiplicative Seasonal Moving Average Model, Non-multiplicative Seasonal Moving Average Model, Mixed Integer Non-linear Programming Model

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Rasha A. Farghali , Hemat M. Abd-Elgaber , Essam A. Ahmed , "Identifying and Estimating Seasonal Moving Average Models by Mathematical Programming," Mathematics and Statistics, Vol. 11, No. 6, pp. 883 - 894, 2023. DOI: 10.13189/ms.2023.110603.

(b). APA Format:
Rasha A. Farghali , Hemat M. Abd-Elgaber , Essam A. Ahmed (2023). Identifying and Estimating Seasonal Moving Average Models by Mathematical Programming. Mathematics and Statistics, 11(6), 883 - 894. DOI: 10.13189/ms.2023.110603.