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ARMAX-GARCH-K-SK Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications)

version (545 KB) by Alexandros Gabrielsen


Updated 04 May 2016

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ARMAX-GARCH-K-SK Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications)
Firstly, it allows the estimation, forecasting and simulation of the family of ARMAX-GARCH of any order of AR, MA, ARCH and GARCH terms of the GARCH, GJR-GARCH, EGARCH, NARCH (Nonlinear ARCH), NGARCH (Nonlinear GARCH), AGARCH (Asymmetric GARCH), APGARCH (Asymmetric Power GARCH), and NAGARCH (Nonlinear Asymmetric GARCH) with the Gaussian, Student-t, Generalized Error, Modified Cauchy, Hansen's Skew-t, Logistic, Laplace, Rayleigh, Centered Cauchy, Extreme Value Distribution Type 1, Generalized Exponential and Gram and Charlier expansion series with constant higher moments.
Secondly, the toolbox allows the estimation, forecasting and simulation of the Autoregressive Conditional Kurtosis Model proposed by Brooks, et al (2005).
Thirdly, the toolbox incorporates the Leon, A., Rubio, G., and Serna, G., (2004) "Autoregressive Conditional
Volatility, Skewness and Kurtosis" model, allowing for the calculation of time-varying skewness and kurtosis at the same time.

Fourthly,, the toolbox allows the evaluation of volatility forecasts using a number of loss functions and the estimation of Value-at-Risk for a given confidence level and horizon period.

Finally, a number of examples are presented to illustrate the application of this toolbox in Market Risk and Financial Risk Management.

The main functions are:
1. garch.m, garchk.m & garchsk.m which estimates the ARMAX-GARCH-K-SK family of models.

2. garchfind.m, which finds the combination of models and distributions that better fits the data based on a set of criteria (i.e. largest log likelihood value and the smallest AIC and BIC criteria).

3. garchsim.m & garchksim.m, which simulates returns, conditional variances and kurtosis.

4.garchfor.m & garchfor2.m - garchkfor.m & garchkfor2.m - garchskfor.m & garchskfor2.m, which estimates mean, volatility, skewness and kurtosis forecasts given the model, distribution, and number of forecasts.

5. garchvar.m & garchvar2.m - garchkvar.m & garchkvar2.m - garchskvar.m & garchskvar2.m, which estimates Value-at-Risk for a given confidence level and horizon period for both long and short positions.

6. garchvolfor.m, which is an application in Volatility Forecasting & Value-at-Risk. It allows the comparison of volatility and Value-at-Risk estimates for a data vector and for a variety of GARCH models and distributions and at different forecast periods as well as sort the results according to only a sub-set of forecast periods.

1. With the help of the VFLF and VaRLR functions a number of volatility loss functions and the VaR unconditional, independence, conditional and regulatory tests are also estimated. The volatility loss functions are the following: MSE; MAD; MLAE; HMSE; HMAE; MAE; MAPE; R2LOG; QLIKE; SR. The VaR back-testing tests are: percentage of failures, TUFF; Likelihood Ratio Unconditional Coverage, Independence Coverage, and Conditional Coverage; Basel II Accord, Basel. For more information which tests are included please refer the VFLF and VaRLR functions.

2. For further information regarding the full functionality and a set of examples of the ARMAX-GARCH-K Toolbox please refer to the readme files.

3. Additional files for garchvar.m and garchvolfor.m can be found in:

I would like to thank you for your comments and your suggestions regarding additional features that should be included.

Please feel free to contact me with comments, suggestions, or bugfixes.

Cite As

Alexandros Gabrielsen (2021). ARMAX-GARCH-K-SK Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2013a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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