Julia GARCH package

Generalized Autoregressive Conditional Heteroskedastic (GARCH) models for Julia.

What is implemented

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

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

What is not ready yet

• Asymmetric and non-normal GARCH models
• Comprehensive set of residuals tests

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 n-step volatility prediction

arguments:

• fit - fitted object returned by garchFit
• n - the number of time-steps to be forecasted, by default 1

returns:

n-step-ahead volatility forecast

Example

using GARCH
using Quandl
quotes = quandl("YAHOO/INDEX_GSPC", format="DataFrame")
ret = diff(log(Array{Float64}(quotes[:Adjusted_Close])))
fit = 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.