Please use this identifier to cite or link to this item: https://repository.uksw.edu//handle/123456789/23198
Title: Model Regresi untuk Return Aset dengan Volatilitas Mengikuti Model GARCH(1,1) Berdistribusi Epsilon-Skew Normal dan Student-T
Other Titles: Regression Models for Return of Asset with Volatility Follows The GARCH(1,1) Model with Epsilon-Skew Normal and Student-T Distribution
Authors: Anggraeni, Kristia
Keywords: ARWM;GARCH(1,1);GRG Non-Linier;regresi
Issue Date: 2020
Abstract: Studi ini mendiskusikan dua perluasan dari model GARCH(1,1), yaitu AR(1)-GARCH(1,1) dan MA(1)-GARCH(1,1), yang diperoleh dengan cara menambahkan Autoregression tingkat 1 atau Moving Average tingkat 1 pada persamaan return. Untuk kasus ini, error dari return diasumsikan berdistribusi Normal, Skew Normal (SN), Epsilon Skew Normal (ESN), dan Student-t. Analisis terhadap model didasarkan pada pencocokan model untuk return dari indeks saham FTSE100 periode harian dari Januari 2000 sampai Desember 2017 dan indeks saham TOPIX periode harian dari Januari 2000 sampai Desember 2014. Model yang dipelajari diestimasi menggunakan metode GRG (Generalized Reduced Gradient) Non Linear yang tersedia di Solver Excel dan juga metode Adaptive Random Walk Metropolis (ARWM) yang diimplementasikan pada program Scilab. Hasil estimasi dari kedua alat bantu tersebut menunjukkan nilai-nilai yang hampir sama, mengindikasikan bahwa Solver Excel mempunyai kemampuan yang handal dalam mengestimasi parameter model. Uji rasio log-likelihood dan AIC (Akaike Information Criterion) menunjukkan bahwa model dengan distribusi ESN lebih unggul dibandingkan dengan model-model berdistribusi tipe normal lainnya untuk setiap kasus model dan data pengamatan, bahkan ini bisa mengungguli distribusi Student-t pada suatu model dan data pengamatan. Lebih lanjut, model-model dengan penambahan proses regresi di persamaan return menyediakan pencocokan yang lebih baik daripada model dasar, dimana pencocokan terbaik untuk kedua data pengamatan diberikan oleh model AR(1)-GARCH(1,1) berdistribusi Student-t.
This study discusses two extensions of GARCH(1,1), i.e. AR(1)-GARCH(1,1) and MA(1)-GARCH(1,1), by incorporating either first-order Autoregression or first-order Moving Average into the return eqation. In this case, the series of return errors is assumed either Normally, Normal Skew, Epsilon Skew Normal, or Student-t distributed. The data analysis is based on fitting the models to the FTSE100 stock index for the daily period from January 2000 to December 2017 and the TOPIX stock index for the daily period from January 2000 to December 2014. The considered models were estimated by using the GRG (Generalized Reduced Gradient) Non Linear method which is available in Excel’s Solver and also the Adaptive Random Walk Metropolis (ARWM) method which is implemented in Scilab. The estimation results obtained from both estimation tools were close each other, indicating that Excel’s Solver is able to estimate the models. Log-likelihood ratio test and AIC (Akaike Information Criterion) showed that the model with ESN distribution outperforms the models with other normal-type distributions in each model and observed data cases, even the ESN distribution can outperform the Student-t distribution on a model and oberseved data. Furthermore, the GARCH(1,1) model with adding a regression process into the return equation provide a better fit than the basic model, where the best fit on both observed data is provided by the AR(1)-GARCH(1,1) model with the Student-t distribution.
URI: https://repository.uksw.edu/handle/123456789/23198
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