Sains Malaysiana 50(4)(2021): 1101-1111

http://doi.org/10.17576/jsm-2021-5004-20

Coherent Mortality Model in A State-Space Approach

(Model Kemortalan Koheren dalam Pendekatan Keadaan-Ruang)

SITI ROHANI MOHD NOR*, FADHILAH YUSOF & SITI MARIAM NORRULASHIKIN

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor Darul Takzim, Malaysia

Received: 27 January 2020/Accepted: 9 September 2020

ABSTRACT

Mortality improvements that have recently become apparent in most developing countries have significantly shaped queries on forecast divergent between populations in recent years. Therefore, to ensure a more coherent way of forecasting, previous researchers have proposed multi-population mortality model in the form of independent estimation procedures. However, similar to single-population mortality model, such independent approaches might lead to inaccurate prediction interval. As a result of this inaccurate mortality forecasts, the life expectancies and the life annuities that the mortality model aims to generate is underestimated. In this study, we propose another new extension of the multi-population mortality model in a joint estimation approach by recasting the model into a state-space framework. A combination of augmented Li-Lee and O’Hare-Li methods are employed, before we transform the proposed model into a state-space formulation. In addition, this study incorporates the quadratic age effect parameter to the proposed model to better capture the younger ages mortality. We apply the method to gender and age-specific data for Malaysia. The results show that our latter framework brings a significant contribution to the multi-population mortality model due to the incorporation of joint-estimate and quadratic age effect parameters into the model’s structure. Consequently, the proposed model improves the mortality forecast accuracy.

Keywords: Coherent mortality model; multi-population; state-space

ABSTRAK

Kadar kematian yang semakin menurun di kebanyakan negara membangun telah menimbulkan beberapa persoalan penting terhadap perbezaan jurang ramalan antara populasi bagi tahun-tahun kebelakangan ini. Oleh itu, untuk memastikan hasil ramalan yang lebih koheren, penyelidik sebelum ini telah mengemukakan model kemortalan berbilang penduduk dalam bentuk prosedur anggaran yang dibuat secara berasingan antara populasi. Walau bagaimanapun, sebagaimana model kemortalan penduduk tunggal, pendekatan berasingan mungkin menyebabkan ramalan yang tidak tepat. Akibat ramalan kemortalan yang tidak tepat ini, jangkaan hayat dan anuiti hayat yang dihasilkan oleh model kemortalanakan menjadi lebih rendah daripada yang sepatutnya. Dalam kajian ini, kami mencadangkan satu lagi model kemortalan yang mengintegrasikan maklumat antara populasi dengan cara menggabungkan model tersebut dalam rangka keadaan-ruang. Gabungan kaedah Li-Lee dan O'Hare-Li digunakan dan kemudian kami mengubah model yang dicadangkan ke dalam formulasi keadaan-ruang. Di samping itu, kajian ini menggabungkan parameter kesan usia kuadratik kepada model yang dicadangkan untuk menganggar kematian yang berlaku pada usia muda dengan lebih baik. Kami menggunakan kaedah tersebut ke atas data jantina dan data khusus umur bagi Malaysia. Keputusan menunjukkan bahawa rangka kerja ini membawa sumbangan penting kepada model kemortalan pelbagai penduduk kerana menggabungkan parameter kesan umur dan kuadratik parameter ke dalam struktur model. Hasilnya, model yang dicadangkan dapat meningkatkan lagi ketepatan ramalan kematian.

Kata kunci: Keadaan-ruang; kepelbagaian penduduk; model kemortalan koheren

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*Corresponding author; email: sitirohani@utm.my