Application of Generalized Space Time Autoregressive Model on Farmer Exchange Rate Data in Three Provinces of The Sumatera Island

Fadhilatul Nida Aryani; Sri Sulistijowati Handajani; Etik Zukhronah

doi:10.19184/jid.v21i2.17226

Fadhilatul Nida Aryani Program Studi Statistika, Fakultas Matematika dan IlmuPengetahuan Alam, Universitas Sebelas Maret, Surakarta
Sri Sulistijowati Handajani Program Studi Statistika, Fakultas Matematika dan IlmuPengetahuan Alam, Universitas Sebelas Maret, Surakarta
Etik Zukhronah Program Studi Statistika, Fakultas Matematika dan IlmuPengetahuan Alam, Universitas Sebelas Maret, Surakarta

DOI: https://doi.org/10.19184/jid.v21i2.17226

Abstract

The agricultural sector has a big role in the development of the Gross Regional Domestic Product (GDP). Therefore the agricultural sector is very important. Besides the agricultural sector, the farmer's welfare also needs to be considered because the agricultural sector will be good if the welfare of farmers is good also. In measuring the level of farmers' welfare, the method used is the farmer's exchange rate. The farmer's exchange rate has a location relationship and a previous time relationship. The Generalized Space-Time Autoregressive (GSTAR) model is a good method of forecasting data that contains time series and location relationships by assuming that the data has heterogeneous characteristics. The purpose of this study is to model the farmer exchange rate data with GSTAR using normalization of cross-correlations weighting and inverse distance in three provinces namely West Sumatra, Bengkulu and Jambi Provinces. Based on data analysis, the best GSTAR model obtained by using the best weighting with the model is GSTAR (1₁) − I(1) using normalization of cross-correlations because the assumption of normal white noise and multivariate are fulfilled with an RMSE value of 1.097775. The best GSTAR model explains that the exchange rate of West Sumatra farmers is only the previous time, Bengkulu farmers' exchange rate is the previous time and is the exchange rates of farmers of West Sumatra and Jambi, whereas for the exchange rate of farmers of Jambi is the exchange rates of farmers of Bengkulu and West Sumatra and influenced by previous times.
Keywords: GSTAR, RMSE, farmers exchange rate, normalization of cross-correlations, inverse distance.

References

Anggraeni, D. 2013. Aplikasi Generalized Space Time Autoregressive (GSTAR) pada Pemodelan Volume Kendaraan Masuk Tol Semarang. Jurnal Media Statistik. Vol. 6(2): 71-80.

Badan Perencanaan Pembangunan Nasional. 2012. Distribusi Persentase PDRB Menurut Provinsi dan Lapangan Usaha Wilayah Sumatera. Badan Perencanaan Pembangunan Nasional. Jakarta.

Badan Pusat Statistik Provinsi Bengkulu. 2017. Nilai Tukar Petani Tahun 2014-2018. Badan Pusat Statistik Bengkulu. Bengkulu.

Badan Pusat Statistik Jakarta Pusat. 2018. Statistik Pertanian Indonesia 2018. Badan Pusat Statistik. Jakarta.

Badan Pusat Statistik Provinsi Jambi. 2006. Jambi Dalam Angka. Jambi.

Badan Pusat Statistik Provinsi Jambi. 2017. Nilai Tukar Petani Tahun 2014-2018. Badan Pusat Statistik Jambi. Jambi.

Badan Pusat Statistik Provinsi Sumatera Barat. 2016. Sumatera Barat dalam Angka Tahun 2016. Badan Pusat Statistik Sumatera Barat. Padang.

Badan Pusat Statistik Provinsi Sumatra Barat. 2017. Nilai Tukar Petani Tahun 2014-2018. Badan Pusat Statistik Sumatera Barat. Padang.

Borovkova, S., Lopuhaä, H.P., and Ruchjana, B.N.2002. Generalized STAR Model with Experimental Weight. Proceedings of the 17th International Workshop on Statistical Modeling, 139-147.

Darwanto, D.H. 2005. Ketahanan Pangan Berbasis Produksi Dan Kesejahteraan Petani. Ilmu Pertanian. 12(2): 152–64.

DeGroot, M., and Schervish, M. 2012. Probability and Statistics, 4th edition. Addison-Wesley. Boston MA, US.

Faizah, L.A. dan Setiawan. 2013. Pemodelan Inflasi Di Kota Semarang, Yogyakarta dan Surakarta dengan Pendekatan GSTAR. Jurnal Sains dan Seni Pomits. 2(2).

Gurajati, D.2006. Ekonometrika Dasar. Erlangga. Jakarta.

Karlina, H.W., Cahyandari, R., Awalludin, A.S. 2014. Aplikasi Model GSTAR Pada Data Jumlah TKI di Jawa Barat Dengan Pemilihan Lokasi Berdasarkan Kluster DBSCAN. Jurnal Matematika Integratif, 10(1): 37-48.

Mansoer, AS. 2016. Pemodelan Seasonal Generalized Space Time Autoregressive pada Data Produksi Padi (Studi Kasus Demak, Boyolali, dan Grobogan). Skripsi. Tidak diterbitkan. Fakultas Sains dan Matematika. Universitas Diponegoro. Semarang.

Montgomery, DC., Jennings, CL., and Kulahci, M. 2015. Introduction to Time Series Analysis and Forecasting: Second Edition. John Wiley and Sons Inc. Canada.

Pfeifer PE, Deutsch SJ. 1980. A Three-Stage Iterative Procedure for Space Time Modeling. Technometrics. 22(1):35-47.

Ruchjana, BN, .2002. Pemodelan Bobot lokasi yang optimal pada model Generalisasi S-TAR, Forum Statistika dan Komputasi. Bogor.

Sipayung, F. 2018. Peramalan Harga Cabai Merah Keriting di Jawa Tengah menggunakan Model Generalized Space Time Autoregressive (Studi Kasus Semarang, Cilacap, Pekalongan dan Purwokerto). Skripsi. Tidak Diterbitkan. Fakultas Sains dan Matematika. Universitas Diponegoro. Semarang.

Suhartono dan Atok, R.M. 2006. Pemilihan Bobot Lokasi yang Optimal pada Model GSTAR. Universitas Negeri Semarang. Semarang.

Suhartono dan Wutsqa, D.U. 2007. Perbandingan Model VAR dan STAR pada Peramalan Produksi Teh di Jawa Barat.

Tsay, RS. 2002. Analysis of Financial Runtun Waktu: Financial Econometric. University of Chicago:John Wiley and Sons, New Jersey.

Wei, WWS. 2006. Time Series Analysis Univariate and Multivariate Methods. Second Edition. Pearson Education, Inc. USA.

Wutsqa, D.U., Suhartono, & Sujito, B. 2010. Generalized Space Time Autoregressive Modeling. Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics dan its Apllication.