Estimasi Parameter pada Model Poisson Generalized Autoregressive Moving Average (GARMA) dengan Algoritma IRLS Studi Kasus: Peramalan Jumlah Kecelakaan di Jalan Tol Surabaya-Gempol

Agil Desti Fauzia, Laksmi Prita Wardhani
Submission Date: 2018-08-07 15:07:59
Accepted Date: 2019-05-31 12:37:16

Abstract


Peramalan adalah pengolahan data masa lalu untuk mendapatkan estimasi data masa depan. Data yang digunakan pada penelitian ini adalah data count. Pada kasus data count metode peramalan pada umumnya seperti ARIMA kurang tepat digunakan. Benjamin, dkk. mengembangkan sebuah model peramalan yaitu Generalized Autoregessive Moving Average (GARMA) dengan menggunakan fungsi penghubung (link function) dengan data diasumsikan mengikuti Distribusi Poisson sehingga disebut juga Poisson GARMA (p,q). Pada model tersebut terdapat beberapa parameter yang tidak diketahui. Parameter yang dimaksud diestimasi menggunakan metode Maximum Likelihood Estimation (MLE) dengan optimasi Algoritma Iteratively Reweighted Least Squares (IRLS). Model Poisson GARMA ini diterapkan pada data jumlah kejadian kecelakaan di jalan tol Surabaya-Gempol ruas Waru-Sidoarjo. Hasil yang didapat yaitu model khusus Poisson GARMA (1,1) dengan 3 parameter yaitu parameter konstanta (β_0), Autoregressive (ϕ), dan Moving Average (θ). Kriteria pemilihan model terbaik menggunakan AIC.

Keywords


Data count; Distribusi Poisson; Fungsi Link; Poisson GARMA (p, q); Algoritma IRLS

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