Perbandingan Model ARCH (1) dan GARCH (1,1) Ditinjau dari Perilaku Kurtosis dan Fungsi Autokorelasi

Isran K Hasan, Ismail Djakaria, Demas Novaleda Abdul Karim

Abstract


Tulisan ini membahas tentang perbandingan model ARCH (1) dan GARCH (1,1) dengan melihat perilaku kurtosis dan fungsi autokorelasi baik secara analitik maupun menggunakan simulasi. Metode yang digunakan adalah studi literatur. Hasil yang diperoleh menunjukkan bahwa secara analitik kedua model memiliki kurtosis lebih dari tiga yang berarti model tersebut merupakan model dengan distribusi ekor tebal serta kedua model tersebut mempunyai fungsi autokorelasi return kuadrat yang turun secara perlahan. Hasil simulasi numerik perbandingan MSE nilai kurtosis data dan kurtosis model menunjukkan bahwa model GARCH (1,1) memiliki MSE terkecil dengan nilai 3,702. Selanjutnya, hasil numerik perbandingan MSE untuk fungsi autokorelasi diperoleh GARCH (1,1) memiliki MSE terkecil pada dua data yaitu SMGR.JK dan JMSR.JK masing masing memiliki nilai 0,0025 dan 0,0015, sedangkan untuk data MNCN.JK MSE terkecilnya adalah model ARCH (1) dengan distribusi  dengan nilai 0,0048.

Keywords


Fungsi Autokorelasi; Heterokedastik; Kurtosis; Model ARCH; Model GARCH

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References


R. S. Tsay, Analysis of financial time series. New York: Wiley, 2002.

R. F. Engle, “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation,” Econometrica, vol. 50, no. 4, p. 987, Jul. 1982, doi: 10.2307/1912773.

T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” J. Econom., vol. 31, no. 3, pp. 307–327, Apr. 1986, doi: 10.1016/0304-4076(86)90063-1.

H. Malmsten and T. Teräsvirta, “Stylized Facts of Financial Time Series and Three Popular Mod- els of Volatility,” Eur J Pure Appl Math, p. 35, 2010.

R. Bilondatu, N. Nurwan, and D. R. Isa, “A Model ARCH (1) dan GARCH (1,1) pada Peramalan Harga Saham PT. Cowell Development Tbk.,” BAREKENG J. Ilmu Mat. Dan Terap., vol. 13, no. 1, pp. 009–018, Mar. 2019, doi: 10.30598/barekengvol13iss1pp009-018ar676.

C. M. Lim and S. K. Sek, “Comparing the Performances of GARCH-type Models in Capturing the Stock Market Volatility in Malaysia,” Procedia Econ. Finance, vol. 5, pp. 478–487, 2013, doi: 10.1016/S2212-5671(13)00056-7.

H. Herwartz, “Stock return prediction under GARCH — An empirical assessment,” Int. J. Forecast., vol. 33, no. 3, pp. 569–580, Jul. 2017, doi: 10.1016/j.ijforecast.2017.01.002.

R. F. Engle and A. J. Patton, “What good is a volatility model?,” Quant. Finance, vol. 1, no. 2, pp. 237–245, Feb. 2001, doi: 10.1088/1469-7688/1/2/305.

R. Cont, “Empirical properties of asset returns: stylized facts and statistical issues,” Quant. Finance, vol. 1, no. 2, pp. 223–236, Feb. 2001, doi: 10.1080/713665670.

D. Ayuningtyas, “5 Saham LQ45 Beri Cuan di Atas 20%, Mari Simak Kinerjanya,” market. https://www.cnbcindonesia.com/market/20191104102926-17-112353/5-saham-lq45-beri-cuan-di-atas-20-mari-simak-kinerjanya (accessed Feb. 27, 2020).

E. Zivot and J. Wang, Modeling financial time series with S-plus, 2nd ed. New York, NY: Springer, 2006.

C. He and T. Teräsvirta, “Fourth Moment Structure of The GARCH ( p , q ) PROCESS,” Econom. Theory, vol. 15, no. 6, pp. 824–846, Dec. 1999, doi: 10.1017/S0266466699156032.

T. Bollerslev, R. Y. Chou, and K. F. Kroner, “ARCH modeling in finance,” J. Econom., vol. 52, no. 1–2, pp. 5–59, Apr. 1992, doi: 10.1016/0304-4076(92)90064-X.

X. Bai, J. R. Russell, and G. C. Tiao, “Kurtosis of GARCH and stochastic volatility models with non-normal innovations,” J. Econom., vol. 114, no. 2, pp. 349–360, Jun. 2003, doi: 10.1016/S0304-4076(03)00088-5.

C. Francq and J.-M. Zakoian, GARCH models: structure, statistical inference, and financial applications. Chichester, West Sussex: Wiley, 2010.




DOI: https://doi.org/10.34312/jjom.v2i2.4642

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