Sains Malaysiana 49(5)(2020): 1153-1164

http://dx.doi.org/10.17576/jsm-2020-4905-21

Two Stages Fitting Techniques using Generalized Lambda Distribution: Application on Malaysian Financial Return

(Teknik Penyuaian Dua Peringkat menggunakan Taburan Generalisasi Lambda: Aplikasinya ke atas Pulangan Kewangan Malaysia)

MUHAMMAD FADHIL MARSANI^1,2* & ANI SHABRI¹

¹Department of Mathematics, Universiti Teknologi Malaysia, 81310, Johor Darul Takzim, Malaysia

²School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Minden, Pulau Pinang, Malaysia

Received: 24 June 2019/Accepted: 24 January 2020

ABSTRACT

The underline distribution assumption used in the analysis of share market returns is crucial in risk management. An important aspect related to stock return modelling is to obtain accurate prediction. This paper presents an innovative fitting method called two stages (TS) method for modelling daily stock returns. The proposed approach by first establishing trend in the series, and then separately performing L-moment estimation on the generalized lambda distribution (GLD) parameter. The performance of the TS-GLD models had been evaluated using Monte Carlo simulation and Malaysian Kuala Lumpur Composite Index (KLCI) returns from year 2001 to 2015. Based on k-sample Anderson darling goodness of fit test, the two stages GLD model in location parameter (GLD.1) performed well in all studied cases. The GLD.1 model benefits risk management by providing effective distribution fitting.

Keywords: Fat-tailed distributions; generalized lambda distribution; L-moment; risk management; stock returns

ABSTRAK

Andaian taburan yang digunakan dalam analisis pulangan pasaran saham adalah penting dalam pengurusan risiko. Isu utama dalam memodelkan pulangan saham adalah untuk mendapatkan anggaran yang tepat. Kajian ini membentangkan kaedah penyuaian inovatif iaitu kaedah dua peringkat (TS) dalam memodelkan pulangan saham harian. Pendekatan ini dijalankan dengan cara mengenal pasti bentuk trend di dalam siri, kemudian melaksanakan anggaran L-momen pada parameter taburan generalisasi lambda (GLD). Prestasi model TS-GLD dinilai dengan menggunakan kaedah simulasi Monte Carlo dan data sebenar iaitu Indeks Komposit Kuala Lumpur Malaysia (KLCI) dari tahun 2001 hingga 2015. Berdasarkan ujian kebagusan k-sample Anderson darling, model dua peringkat (TS) GLD bagi parameter lokasi (GLD.1) menunjukkan prestasi yang lebih baik untuk semua kes yang dikaji. Model GLD.1 bermanfaat dalam pengurusan risiko dengan memberikan penyuaian taburan yang lebih baik.

Kata kunci: L-momen; pengurusan risiko; pulangan saham; taburan berekor tebal; taburan generalisasi lambda

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*Corresponding author; email: fadhilmarsani@gmail.com