Penganggaran Parameter bagi Model BL$(p,0,1,1)$ dengan Pendekatan Bayesian

Ibrahim Mohamed, Azami Zaharim, Mohd Sahar Yahya

Abstract



Model bilinear merupakan salah satu model tak linear bagi data siri masa dan diwakili oleh BL$(p,q,r,s)$. ARMA merupakan kes khas apabila $r$ dan $s$ mengambil nilai sifar. Model ini dipercayai sesuai digunakan ke atas data hidrologi dan meteorologi. Beberapa kaedah telah disarankan untuk menganggar kesemua parameter bagi model ini. Di dalam kertas kerja ini, kaedah bayesian digunakan untuk membuat penganggaran parameter. Walau bagaimanapun, ia memerlukan maklumat berkenaan dengan reja terdahulu. Oleh itu, kaedah kuasa dua ralat terkecil tak linear digunakan. Set data sunspot digunakan sebagai ilustrasi.

Katakunci: Bilinear; Bayesian; siri masa tak linear; Taburan prior tak tentu Jeffrey

Bilinear model is one of the nonlinear models for time series data, which is denoted by BL$(p, q, r, s)$. The ARMA model is a special case of Bilinear model when the value $r$ and $s$ are zero. This model is believed to suit best for hydrology and meteorology data. A few estimation methods have been suggested to estimate the parameters. In this paper, the bayesian approach is used. But the residual must be known first. For that the Least Square methods is chosen. The sunspot data is used as an illustration.

Keywords: Bilinear; Bayesian; nonlinear time series; Jeffreys' prior distribution

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DOI: https://doi.org/10.11113/matematika.v18.n.126

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