GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models
Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provid...
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| Format: | Article |
| Language: | English |
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Universitas Muhammadiyah Mataram
2022-04-01
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| Series: | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| Subjects: | |
| Online Access: | http://journal.ummat.ac.id/index.php/jtam/article/view/7694 |
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| author | Didit Budi Nugroho Lam Peter Panjaitan Dini Kurniawati Zaini Kholil Bambang Susanto Leopoldus Ricky Sasongko |
| author_facet | Didit Budi Nugroho Lam Peter Panjaitan Dini Kurniawati Zaini Kholil Bambang Susanto Leopoldus Ricky Sasongko |
| author_sort | Didit Budi Nugroho |
| collection | DOAJ |
| description | Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation. |
| first_indexed | 2024-04-12T07:15:28Z |
| format | Article |
| id | doaj.art-e5b5e0c475f24ea080568385dd4690f2 |
| institution | Directory Open Access Journal |
| issn | 2597-7512 2614-1175 |
| language | English |
| last_indexed | 2024-04-12T07:15:28Z |
| publishDate | 2022-04-01 |
| publisher | Universitas Muhammadiyah Mataram |
| record_format | Article |
| series | JTAM (Jurnal Teori dan Aplikasi Matematika) |
| spelling | doaj.art-e5b5e0c475f24ea080568385dd4690f22022-12-22T03:42:29ZengUniversitas Muhammadiyah MataramJTAM (Jurnal Teori dan Aplikasi Matematika)2597-75122614-11752022-04-016244846010.31764/jtam.v6i2.76944192GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH ModelsDidit Budi Nugroho0Lam Peter Panjaitan1Dini Kurniawati2Zaini Kholil3Bambang Susanto4Leopoldus Ricky Sasongko5Department of Mathematics and Data Science, Universitas Kristen Satya WacanaDepartment of Mathematics and Data Science, Universitas Kristen Satya WacanaDepartment of Mathematics and Data Science, Universitas Kristen Satya WacanaDepartment of Mathematics and Data Science, Universitas Kristen Satya WacanaDepartment of Mathematics and Data Science, Universitas Kristen Satya WacanaDepartment of Mathematics and Data Science, Universitas Kristen Satya WacanaNumerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation.http://journal.ummat.ac.id/index.php/jtam/article/view/7694arwmexcel’s solvergarchgrg non-linearstudent-t |
| spellingShingle | Didit Budi Nugroho Lam Peter Panjaitan Dini Kurniawati Zaini Kholil Bambang Susanto Leopoldus Ricky Sasongko GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models JTAM (Jurnal Teori dan Aplikasi Matematika) arwm excel’s solver garch grg non-linear student-t |
| title | GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models |
| title_full | GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models |
| title_fullStr | GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models |
| title_full_unstemmed | GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models |
| title_short | GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models |
| title_sort | grg non linear and arwm methods for estimating the garch m gjr and log garch models |
| topic | arwm excel’s solver garch grg non-linear student-t |
| url | http://journal.ummat.ac.id/index.php/jtam/article/view/7694 |
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