Pemodelan Skew Normal Pada Seemingly Unrelated Regression (SUR) Dengan Pendekatan Bayesian

Santosa, Agus Budhi (2018) Pemodelan Skew Normal Pada Seemingly Unrelated Regression (SUR) Dengan Pendekatan Bayesian. Doctoral thesis, Institut Teknologi Sepuluh Nopember Surabaya,.

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Abstract

Seemingly unrelated regression (SUR) adalah model ekonometrika yang banyak digunakan dalam menyelesaikan beberapa persamaan regresi dimana masing-masing persamaan memiliki parameter sendiri dan nampak bahwa tiap persamaan tidak berhubungan (seemingly unrelated). Namun demikian, antar persamaan-persamaan tersebut terjadi kaitan satu sama lain yaitu dengan adanya korelasi antar error dalam persamaan yang berbeda. Namun pembahasan dan penelitian model SUR masih banyak terbatas pada asumsi error yang berdistribusi Normal, padahal kenyataannya distribusi error bisa tidak simetri atau miring dan bahkan bisa juga berbentuk fat tails atau thin tails dibandingkan distribusi Normal. Salah satu distribusi yang secara adaptif mampu menangkap pola kemiringan datanya adalah distribusi Skew Normal. Metode Bayesian yang menggunakan teorema Bayes sebagai dasar dalam inferensial statistik, sering digunakan dalam menyelesaikan model-model yang sangat kompleks. Pendekatan metode Bayesian memandang parameter sebagai variabel random yang memiliki distribusi sehingga hasil estimasinya menjadi lebih efisien. Penelitian ini bertujuan untuk melakukan pemodelan SUR dengan asumsi Normal error dan Skew Normal error menggunakan pendekatan Bayesian yang diterapkan pada data Produk Domestik Regional Bruto (PDRB) Jawa Timur. Untuk menentukan kebaikan diantara dua model tersebut digunakan tiga ukuran kebaikan model yaitu Root of Mean Square Error (RMSE), Mean Absolute Error (MAE) dan Mean Absolute Percentage Error (MAPE). Hasil estimasi parameter dengan pendekatan Bayesian menunjukkan bahwa model SUR Skew Normal lebih sesuai untuk pemodelan PDRB Jawa Timur daripada menggunakan model Bayesian SUR dengan Normal error. Hal Ini didasarkan pada nilai RMSE, MAE dan MAPE model Bayesian SUR Skew Normal yang lebih kecil. ========================================================= Seemingly unrelated regression (SUR) was an econometric model that was widely used in solving multiple regression equations where each equation has its own parameters and it appears that each equation was seemingly unrelated. However, the inter-equations were related to each other with the correlation between errors in different equations. However, the discussion and research of the SUR model is still limited to the assumption of Normal distributed error, whereas the fact that the error distribution can not be symmetrical or skewed and can even be fat tails or thin tails compared to Normal distribution. One distribution that is adaptively capable of capturing the data skew pattern is the Skew Normal distribution. Bayesian methods that used Bayes's theorem as a basis for inferential statistics were often used in solving very complex models. The Bayesian method approach looks at the parameter as a random variable that has a distribution so that its estimation results become more efficient. This study aims to SUR model with the assumption of Normal error and Skew Normal error using Bayesian approach applied to Gross Regional Domestic Product (GRDP) of East Java. To determine the goodness between the two models was used three model goodness measure that was Root of Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). The result of parameter estimation with Bayesian approach shows that SUR Skew Normal model was more suitable for East Java GRDP modeling rather than using Normal error model. This was based on the smaller RMSE, MAE and MAPE value.

Item Type: Thesis (Doctoral)
Additional Information: RDSt 519.542 San p
Uncontrolled Keywords: Seemingly Unrelated Regression, Skew Normal, Bayesian, Produk Domestik Regional Bruto.
Subjects: H Social Sciences > HA Statistics > HA31.7 Estimation
H Social Sciences > HB Economic Theory > Economic forecasting--Mathematical models.
Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory.
Divisions: Faculty of Mathematics, Computation, and Data Science > Statistics
Depositing User: Santosa Agus Budhi
Date Deposited: 07 Oct 2020 04:39
Last Modified: 07 Oct 2020 04:39
URI: https://repository.its.ac.id/id/eprint/59544

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