Model Generalized Space-Time Autoregressive Moving Average (GSTARMA) Yang Melibatkan Variabel Eksogen Dengan Pendekatan Seemingly Unrelated Regression (SUR)

Akbar, Muhammad Sjahid (2022) Model Generalized Space-Time Autoregressive Moving Average (GSTARMA) Yang Melibatkan Variabel Eksogen Dengan Pendekatan Seemingly Unrelated Regression (SUR). Doctoral thesis, Institut Teknologi Sepuluh nopember.

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Abstract

Model GSTARMAX-SUR merupakan pengembangan model spatio temporal
dengan menambahkan variabel eksogen. Variabel eksogen pada model ini bersifat non
metrik seperti intervensi, variasi kalender, dan musiman. Jika terjadi korelasi error
model antar lokasi, maka metode estimasi parameter model GSTARMAX adalah SUR.
Sebagian besar data dicatat berdasarkan kalender Masehi. Di sisi lain beberapa
hari raya seperti Idul Fitri dan Galungan tidak ditetapkan berdasarkan kalender Masehi.
Oleh karena itu, tanggal hari raya Idul Fitri dan Galungan dapat bervariasi antara dua
bulan yang berdekatan dari tahun ke tahun. Kejadian seperti ini disebut sebagai variasi
kalender yang mempersulit identifikasi orde time model spatio temporal. Penelitian ini
bertujuan mengembangkan model spatio temporal ketika efek intervensi, variasi
kalender, dan musiman terjadi, dengan memasukkan efek-efek tersebut sebagai
variabel eksogen serta adanya korelasi error model antar lokasi. Originalitas penelitian
ini adalah menambahkan variabel eksogen non metrik pada model GSTARMA dan
estimasi parameter model dengan metode SUR, selanjutnya disebut GSTARMAX�SUR. Estimasi parameter model GSTARMAX-SUR terdiri dari dua tahap, yaitu tahap
pertama estimasi parameter model eksogen dan tahap kedua estimasi model
GSTARMA dengan error model eksogen sebagai respon dengan metode SUR.
Aplikasi model GSTARMAX-SUR pada peramalan data outflow currency di Bali,
Nusa Tenggara Barat, dan Nusa Tenggara Timur dengan efek intervensi, Idul Fitri dan
Galungan sebagai variasi kalender serta Nyepi dan liburan akhir tahun sebagai
musiman.
Hasil penelitian adalah pembangunan model GSTARMAX-SUR secara
teoretis meliputi dua tahap, yaitu: (1) memodelkan variabel eksogen dan (2)
membangun model GSTARMA dari error model eksogen. kajian praktis di-lengkapi
dengan aplikasi model GSTARMAX-SUR pada data outflow currency di tiga lokasi.
Hasil kajian aplikasi menujukkan peramalan outflow currency dengan model
GSTARMAX-SUR dapat mengikuti pola data aktual yang terdiri intervensi, variasi
kalender, musiman serta korelasi spasial antar lokasi. Model GSTARMAX-SUR dapat
meramalkan dengan baik data outflow currency di Bali dua bulan ke depan, Nusa
Tenggara Barat empat bulan kedepan, dan Nusa Tenggara Timur lima bulan ke depan
dengan root mean square error (RMSE) yang minimum.
=====================================================================================================
The GSTARMAX-SUR model is a Spatio-temporal model development by
adding exogenous variables. Exogenous variables in this model are non-metric such as
interven-tion, calendar variation, and seasonality. If there is a model error correlation
between loca-tions, then the parameter estimation method for the GSTARMAX model
is SUR.
Most of the data is recorded based on the Gregorian calendar, but some holidays
such as Eid al-Fitr and Galungan are calculated not based on the Gregorian calendar.
Therefore the dates of Eid and Galungan holidays can vary between two adjacent
months from year to year. Events like this are referred to as calendar variations which
make it diffi-cult to identify the order of time in the Spatio-temporal model. This study
aims to develop a Spatio-temporal model when the effects of intervention, calendar
variations, and seasona-lity occur, by including these effects as exogenous variables
and the existence of model error correlations between locations. The originality of this
research is to add non-metric exogenous variables to the GSTARMA model and
estimate the model parameters with SUR, hereinafter referred to as GSTARMAX�SUR. The parameter estimation of the GSTARMAX-SUR model consists of two
stages, the first stage is the estimation of the exogenous model parameters and the
second stage is the estimation of the GSTARMA model with the exogenous model
error as a response. Application of the GSTARMAX-SUR model for forecasting
outflow currency data in Bali, West Nusa Tenggara, and East Nusa Tenggara with
intervention effects, Eid al-Fitr, Galungan and Nyepi as calendar variations and year�end holidays as seasonal.
The result of this research is that the theoretical development of the
GSTARMAX-SUR model includes two stages, namely: (1) modeling exogenous
variables and (2) buil-ding a GSTARMA model from the error of the exogenous model.
The practical study is complemented by the application of the GSTARMAX-SUR
model on outflow currency data in three locations. The results of the application study
show that outflow currency fore-casting with the GSTARMAX-SUR model can follow
actual data patterns consisting of interventions, calendar variations, seasonality and
spatial correlation between locations. The GSTARMAX-SUR model can forecast well
the outflow currency data in Bali for the next two months, West Nusa Tenggara for the
next four months, and East Nusa Tenggara for the next five months with a minimum
root mean square error (RMSE).

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	GSTARMAX-SUR, Variabel Eksogen, Intervensi, Variasi Kalender, Outflow Currency, GSTARMAX-SUR, exogenous variable, intervention, Calendar Variation, Outflow Currency
Subjects:	H Social Sciences > HA Statistics > HA30.3 Time-series analysis
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Muhammad Sjahid Akbar
Date Deposited:	23 Feb 2022 10:02
Last Modified:	24 Feb 2022 01:03
URI:	http://repository.its.ac.id/id/eprint/94738

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