mgarchBEKK | R Package for Simulating , Estimating and Diagnosing MGARCH

by vst R Version: 0.0.5 License: Non-SPDX

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mgarchBEKK is a R library. mgarchBEKK has no bugs, it has no vulnerabilities and it has low support. However mgarchBEKK has a Non-SPDX License. You can download it from GitHub.

mgarchBEKK is an R Package designed to simulate, estimate, predict and diagnose MGARCH processes, in particular of BEKK and mGJR (bivariate asymmetric GARCH) specifications. Please note that this package is being revised after a long time. The original codebase is currently available on The objective is to standardize the simulation, estimation, prediction/forecasting and diagnostics processes and optimize for speed in the long run. Therefore, please expect significant API changes, ie. function names, parameters and their meaning may change along the way. TODO: Provide a complete README file.

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The latest version of mgarchBEKK is 0.0.5

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How to use & interpret bivariate GARCH GJR model using mGJR()

QUESTION

How to use & interpret bivariate GARCH GJR model using mGJR()

Asked 2017-Nov-15 at 07:06

I am using a bivariate GJR model using mGJR() command from R.

The instruction from the package "mgarchBEKK" says I input first time series, second time series, and so on. I am trying to use the unexpected returns as my input and need coefficients from these.

I thought I needed to input my pre-calculated unexpected returns as my first time series, second time series and so on into my model.

However, when I run mGJR(), it gives out the output saying "$resid1" and "$resid2" which look like the residuals (i.e. unexpected returns) which I've been looking for.

If so, do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?
Besides, how does my bivariate GJR GARCH model looks like if I try to describe it using the coefficients derived from my output below? How can I get the coefficients for the model that I need for my analysis from the long output I have below? Specifically, I find that I have a total of 17 coefficients where one of them is zero. I find that these coefficients are grouped by 4 where the last one is only one left.
For instance, I find $est.params$1, $est.params$2, $est.params$3, $est.params$4, $est.params$5 where there is a total of 17 parameters. However, I am not sure how mathematically these are expressed explicitly within the formal bivariate GJR GARCH formula.

Please note that this is "bivariate" GJR GARCH not just GJR GARCH. Thus, I have 17 parameters where I have 4 blocks each with 4 coefficients plus one parameter making it a total of 17. However, I don't know which parameter corresponds to which variable coefficient. I tried to provide as much information as possible but if any clarification needed please let me know.

The output I get using the expected return is the following:

mGJR(eps1, eps2, order = c(1, 1, 1))

...

ANSWER

Answered 2017-Nov-15 at 07:06

The mGJR command is used to estimate a GARCH (Generalized autoregressive conditional heteroscedasticity) model. GARCH models are used to model volatility of time-series (most commonly asset returns). That (and lots of parameters) is what you can access from the fitted GJR object.

If you want to know more about GARCH models paired with examples in R, I can recommend the following books by R. Tsay:

do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?

Usually the input for GARCH models are in the past observed returns. (see e.g. the above quoted books or this article by R. Engle, the person who initially proposed the ARCH model)

There are some tests to determine if there are any linear dependencies in the time series. If there are, they need to be removed with a mean-model (such as VARIMA models). Examples and different cases are also in Tsays Analysis of Financial Time Series. The full process for volatility model building is nicely explained on page 133.

Short: Your eps1 and eps2 need to be these (mean-model corrected) return series.

Besides, how does my bivariate GJR GARCH model looks like if I try to describe it using the coefficients derived from my output below? How can I get the coefficients for the model that I need for my analysis from the long output I have below?

It takes a bit of digging but when looking at a publication from Schmidbauer & Roesch (2008) and the code of the mgarchBEKK it looks like the mGJR specification is what the authors Schmidbauer & Roesch call a bivariate asymmetric quadratic GARCH (baqGARCH), which on page 5 of linked publication is defined as:

The parameters from the fitted GJR object represent in descending order: C, A, B, Gamma, w. as on page 7 of the publication (the values in smaller font in the parenthesis are t-values):

Here a reproducible example for fitting mGJR and accessing the parameters:

Source https://stackoverflow.com/questions/47164375

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