Sains Malaysiana 52(3)(2023): 1011-1021

http://doi.org/10.17576/jsm-2023-5203-23

Hybrid Lee-Carter Model with Adaptive Network of Fuzzy Inference System and Wavelet Functions

(Model Hibrid Lee-Carter dengan Rangkaian Adaptif Sistem Inferens Kabur dan Fungsi Gelombang Kecil)

JAMIL J. JABER¹ NURUL AITYQAH YAACOB ^2,3,* & SADAM ALWADI¹

¹Department of Finance, Faculty of Business, The University of Jordan /Aqaba branch, Aqaba, Jordan

 ²Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

³Mathematical Sciences Studies, College of Computing, Informatics and Media,

Universiti Teknologi MARA Cawangan Negeri Sembilan, Kampus Kuala Pilah, 72000 Kuala Pilah, Negeri Sembilan, Malaysia

Received: 9 May 2022/Accepted: 24 January 2023

Abstract

Mortality studies are essential in determining the health status and demographic composition of a population. The Lee–Carter (LC) modelling framework is extended to incorporate the macroeconomic variables that affect mortality, especially in forecasting. This paper makes several major contributions. First, a new model (LC-WT-ANFIS) employing the adaptive network-based fuzzy inference system (ANFIS) was proposed in conjunction with a nonlinear spectral model of maximum overlapping discrete wavelet transform (MODWT) that includes five mathematical functions, namely, Haar, Daubechies (d4), least square (la8), best localization (bl14), and Coiflet (c6) to enhance the forecasting accuracy of the LC model. Annual mortality data was collected from five countries (Australia, England, France, Japan, and the USA) from 1950 to 2016. Second, we selected gross domestic product (GDP), unemployment rate (UR), and inflation rate (IF) as input values according to correlation and multiple regressions. The input variables in this study were obtained from the World Bank and Datastream. The output variable was collected from the mortality rates in Human Mortality Database. Finally, the LC model’s projected log of death rates was compared with wavelet filters and the traditional LC model. The performance of the proposed model (LC-WT-ANFIS) was evaluated based on mean absolute percentage error (MAPE) and mean error (ME). Results showed that the LC-WT-ANFIS model performed better than the traditional model. Therefore, the proposed forecasting model is capable of projecting mortality rates.

Keywords: ANFIS; forecast; macroeconomic; mortality; Lee–Carter model; wavelet

Abstrak

Kajian kematian adalah penting dalam menentukan status kesihatan dan komposisi demografi populasi. Rangka kerja pemodelan Lee–Carter (LC) diperluaskan untuk menggabungkan pemboleh ubah makroekonomi yang mempengaruhi kematian, terutamanya dalam peramalan. Sumbangan utama kertas ini adalah seperti berikut. Pertama, model baharu (LC-WT-ANFIS) yang menggunakan sistem inferens kabur berasaskan rangkaian adaptif (ANFIS) telah dicadangkan bersama dengan model spektrum tak linear bagi transformasi gelombang kecil diskret bertindih maksimum (MODWT) yang merangkumi lima fungsi matematik, iaitu, Haar, Daubechies (d4), least square (la8), best localization (bl14) dan Coiflet (c6) untuk meningkatkan ketepatan ramalan model LC. Data kematian tahunan telah dikumpulkan dari lima negara (Australia, England, Perancis, Jepun dan Amerika Syarikat) dari tahun 1950 hingga 2016. Kedua, keluaran dalam negara kasar (GDP), kadar pengangguran (UR) dan kadar inflasi (IF) dipilih sebagai nilai input mengikut korelasi dan regresi berganda. Pemboleh ubah input bagi kajian ini diperoleh dari World Bank dan Datastream, manakala pemboleh ubah output dikumpulkan daripada kadar kematian dalam Human Mortality Database. Akhir sekali, unjuran log kadar kematian model LC dibandingkan dengan penapis gelombang kecil dan model tradisional LC. Prestasi model yang dicadangkan (LC-WT-ANFIS) dinilai dari segi ralat peratusan mutlak min (MAPE) dan ralat min (ME). Keputusan kajian menunjukkan bahawa prestasi LC-WT-ANFIS adalah lebih baik daripada model tradisi. Oleh itu, model ramalan yang dicadangkan mampu mengunjurkan kadar kematian.

Kata kunci: ANFIS; gelombang kecil; kematian; makroekonomi; model Lee–Carter; ramalan

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^*Corresponding author; email: aityqah@uitm.edu.my