Pengembangan Model Threshold Spatial Vector Autoregressive Dengan Variabel Eksogen (TSpVARX)

Sohibien, Gama Putra Danu (2024) Pengembangan Model Threshold Spatial Vector Autoregressive Dengan Variabel Eksogen (TSpVARX). Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Beberapa aspek yang perlu diperhatikan dalam memodelkan data time series khususnya data ekonomi, yaitu: keterkaitan antar variabel time series, pengaruh variabel eksogen, keterkaitan antar wilayah, dan hubungan tidak linear antar variabel time series. Beberapa model time series sudah dikembangkan, antara lain: Generalized Space Time Autoregressive dengan variabel eksogen (GSTARX), Threshold Vector Autoregressive (TVAR), dan Spatial Vector Autoregressive with Calender Variation. Model-model tersebut belum dapat mengakomodasi empat aspek secara bersamaan. Selain itu, metode pendugaan parameter juga menarik diperhatikan. Statistik uji koefisien model yang diduga dengan metode MLE tidak valid jika asumsi error berdistribusi normal terlanggar. Metode Quasi Maximum Likelihood Estimation (QMLE) dapat digunakan untuk memperkuat inferensia statistik jika asumsi error terlanggar. Pada penelitian ini dilakukan pengembangkan model Threshold Spatial VAR dengan variabel eksogen metrik yang dapat mengakomodasi empat aspek yang dijelaskan sebelumnya. Penelitian ini bertujuan untuk membentuk model TSpVARX, mencari penduga dan statistik uji koefisien model TSpVARX dengan metode QMLE, melakukan kajian simulasi untuk mengetahui kinerja model TSpVARX dengan QMLE, dan mengaplikasikan model TSpVARX pada peramalan inflasi dan outflow uang kartal di kota Yogyakarta, Solo, dan Semarang. Hasil penelitian adalah (1) model TSpVARX dibentuk dengan menambahkan variabel eksogen metrik pada SpVAR sehingga menjadi SpVARX dan membentuk SpVARX pada rezim-rezim berbeda dengan pembagian rezim berdasarkan variabel dan nilai threshold terpilih, (2) penduga koefisien model TSpVARX pada rezim ke-g yang diperoleh dengan QMLE bersifat konsisten serta berdistribusi asimtotik normal multivariat dan standar error penduga koefisien model TSpVARX yang digunakan pada uji hipotesis signifikansi parameter diperoleh dari matriks kovarians sandwich, (3) berdasarkan kajian simulasi kinerja peramalan, model TSpVARX lebih baik dibandingkan SpVARX dan standar error penduga QMLE lebih baik dibanding MLE dalam menggambarkan variabilitas penduga koefisien model, (4) terdapat ketidaklinearan hubungan antara inflasi dan outflow uang kartal terhadap variabel predetermined; terdapat hubungan timbal balik antara inflasi dan outflow uang kartal; terdapat keterkaitan inflasi dan outflow uang kartal Semarang, Solo, dan Yogyakarta; dan model terpilih untuk peramalan, adalah TSpVARX tiga rezim dengan penambahan variabel subset 12, variabel dummy kenaikan, dan penurunan harga BBM.
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Some aspects need to be considered in modeling time series data, especially economic data: the relationship between time series variables, the influence of exogenous variables, the relationship between regions, and non-linear relationships between time series variables. Some time series models have been developed, including Generalized Space-Time Autoregressive with exogenous variables (GSTARX), Threshold Vector Autoregressive (TVAR), and Spatial Vector Autoregressive with Calendar Variation. These models cannot yet accommodate four aspects simultaneously. In addition, the model coefficient estimation method is also interesting to note. Test statistics of model coefficient estimated by the MLE method are invalid if the assumption of normally distributed errors is violated. Quasi Maximum Likelihood Estimation (QMLE) methods can reinforce statistical inference if error assumptions are violated. This study develops a Threshold Spatial VAR model with exogenous metric variables that can accommodate the four aspects described earlier. This study aims to form a TSpVARX model, find estimators and test statistics of model coefficients for the TSpVARX model with the QMLE method, conduct simulation studies to determine the performance of the TSpVARX model with QMLE and apply the TSpVARX model to forecast inflation and cash outflow in the Yogyakarta, Solo, and Semarang. The results of the study are (1) the TSpVARX model is formed by adding exogenous metric variables to SpVAR so that it becomes SpVARX and formed SpVARX in different regimes with regime divisions based on the selected variables and threshold values, (2) the parameters coefficient estimator of TSpVARX model in the g-th regime obtained with QMLE is consistent as well as multivariate normal asymptotic distributed and the parameter estimator standard error of the TSpVARX used in the hypothesis test of the model coefficient is obtained from the sandwich covariance matrix, (3) based on the simulation study, the forecasting performance of the TSpVARX model is better than SpVARX and the model estimator standard error of QMLE is better than MLE in describing the variability of the model coefficient estimator, (4) there is an nonlinearity relationship between inflation and cash outflow to the predetermined variable; there is a reciprocal relationship between inflation and cash outflow; there is a linkage between inflation and cash outflow of Semarang, Solo, and Yogyakarta; and the selected model for forecasting is the three-regime TSpVARX with the addition of subset variable 12, the dummy variable of fuel price increase and decrease.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	Threshold, SpVARX, QMLE, Inflasi, Outflow, Spatiotemporal; Threshold, SpVARX, QMLE, Inflation, Outflow, Spatiotemporal
Subjects:	Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Gama Putra Danu Sohibien
Date Deposited:	12 Feb 2024 05:55
Last Modified:	12 Feb 2024 05:55
URI:	http://repository.its.ac.id/id/eprint/106932

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