Julia GARCH package

Generalized Autoregressive Conditional Heteroskedastic (GARCH) models for Julia.

What is implemented

• garchFit - estimates parameters of univariate normal GARCH process.
• predict - make prediction using fitted object returned by garchFit
• garchPkgTest - runs package test (compares model parameters with those obtained using R fGarch)
• Jarque-Bera residuals test
• Error analysis

Analysis of model residuals - currently only Jarque-Bera Test implemented.

What is not ready yet

• More complex GARCH models
• Comprehensive set of residuals tests
• n-step forecasts

Usage

garchFit

estimates parameters of univariate normal GARCH process.

arguments:

data - data vector

returns:

Structure containing details of the GARCH fit with the fllowing fields:

• data - orginal data
  
• params - vector of model parameters (omega,alpha,beta)
  
• llh - likelihood
  
• status - status of the solver
  
• converged - boolean convergence status, true if constraints are satisfied
  
• sigma - conditional volatility
  
• hessian - Hessian matrix
• secoef - standard errors
• tval - t-statistics

predict

make volatility prediction

arguments:

fit - fitted object returned by garchFit

returns:

one-step-ahead volatility forecast

Example

using GARCH
using Quandl
quotes = quandl("YAHOO/INDEX_GSPC", format="DataFrame")
ret = diff(log(array(quotes[:Adjusted_Close])))
garchFit(ret)

Author

Andrey Kolev

References

• T. Bollerslev (1986): Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics 31, 307–327.
• R. F. Engle (1982): Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50, 987–1008.