TimeModels.jl

Please note: Currently unmaintained and not guaranteed to work with Julia 0.6!

A Julia package for modeling time series.

GARCH model

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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 following 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")
ret = diff(log(quotes["Close"]))
ret = ret - mean(ret)
garchFit(convert(Vector,ret[end-199:end]))

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.