Asumsi distribusi

Model GARCH di Python

Chelsea Yang

Data Science Instructor

Mengapa membuat asumsi

  • Volatilitas tidak teramati langsung

  • Model GARCH memakai residual sebagai guncangan volatilitas $$ r_t = \mu_t + \epsilon_t $$

  • Volatilitas terkait dengan residual: $$ \epsilon_t = \sigma_t * \zeta (WhiteNoise)$$

Model GARCH di Python

Residual terstandar

  • Residual = return terprediksi - return rata-rata $$ residuals = \epsilon_t = r_t - \mu_t $$
  • Residual terstandar = residual / volatilitas return $$ std\,Resid = \frac{\epsilon_t}{\sigma_t} $$
Model GARCH di Python

Residual dalam GARCH

gm_std_resid = gm_result.resid / gm_result.conditional_volatility

plt.hist(gm_std_resid, facecolor = 'orange',label = 'standardized residuals')

Histogram residual terstandar

Model GARCH di Python

Ekor gemuk

  • Probabilitas lebih tinggi melihat return besar (positif/negatif) dibandingkan normal

Contoh ekor gemuk

Model GARCH di Python

Skewness

  • Ukuran kemencengan suatu distribusi probabilitas

Contoh kemencengan

Model GARCH di Python

Distribusi t-Student

contoh distribusi t

Parameter $\nu$ pada distribusi t-Student menentukan bentuknya

Model GARCH di Python

GARCH dengan distribusi t

arch_model(my_data, p = 1, q = 1,
           mean = 'constant', vol = 'GARCH', 
           dist = 't')

                              Distribution                              
========================================================================
                 coef    std err          t      P>|t|  95.0% Conf. Int.
.-----------------------------------------------------------------------
nu             4.9249      0.507      9.709  2.768e-22 [  3.931,  5.919]
========================================================================
Model GARCH di Python

GARCH dengan distribusi t miring

arch_model(my_data, p = 1, q = 1,
           mean = 'constant', vol = 'GARCH', 
           dist = 'skewt')

                                Distribution                               
===========================================================================
                 coef    std err          t      P>|t|     95.0% Conf. Int.
.--------------------------------------------------------------------------
nu             5.2437      0.575      9.118  7.681e-20    [  4.117,  6.371]
lambda        -0.0822  2.541e-02     -3.235  1.216e-03 [ -0.132,-3.241e-02]
===========================================================================
Model GARCH di Python

Ayo berlatih!

Model GARCH di Python

Preparing Video For Download...