Dear experts,
I am working on stock market time series. I have applied EGARCH model to analyse volatility dynamics. I have queries on its output as follows-
1.) What to do when mean equation coefficients in EGARCH output are coming with insignificant constant and signicant AR term coefficient?
2.) what actually arch term, Garch term, gamma term means? whether we can say arch (alpha) term explains volatility clustering, GARCH (beta) term explains persistense, gamma(Leverage) term explains leverage effect.
3.) How to check persistence in EGARCH with only beta value or with sum of arch and garch term both? what means if arch and garch term sum exceeds one in EGARCH output? model estimation is wrong or can conclude with explosive volatility comments without making model estimation wrong. because i applied AR 1,2,3,4,5 - MA 1,2,3,4,5 - ARMA 1,1 - 1,2 - 2,2 - 2,1 - 3,1 - 1,3 - 1,4 - 3,3 etc. but even after getting ARCH effect in return series EGARCH output of mean equation is coming out with insignificant constant and significant and insignicant somewhere these AR, MA, ARMA terms.
4.) In variance equation output alpha is coming with negative but signicant value at 5% what does it means?
Please guide me......
For question 1, insignificant constant simply implies that the constant is not different from zero and thus you can drop it from your mean equation. In addition, the significant autoregressive term does not equal zero.
For question 2, you are right.
For question 3, the exponential GARCH model has several advantages over the pure GARCH specification. First, since the log ( conditional variance) is modelled, then even if the parameters are negative, the log of conditional variance will be positive. There is thus no need to artificially impose non-negativity constraints on the model parameters....don't worry about negative signs
have a look at the following link on YouTube and other related videos
https://www.youtube.com/watch?v=KGkNXnK5dTk
As has been rightly pointed by Amira, An advantage of the EGARCH model over the basic GARCH ( 1,1) specification is that it is an asymmetric model that specifies the logarithm of conditional volatility and avoids the need for any parametric constraints, If the leverage coefficient ( Gamma) is negative and significant , it indicates the presence of an asymmetric behavior. A significant GARCH term indicates volatility persistence.
It might be useful to read the following short papers on EGARCH:
“A one line derivation of EGARCH”, Econometrics, 2(2), 2014, 92-97.
“The correct regularity condition and interpretation of asymmetry in EGARCH”, Economics Letters, 161, 2017, 52-55.
“On the invertibility of EGARCH(p,q)”, Econometric Reviews, 37(8), 2018, 824-849.
Additionally, how can we compare the results of Egarch in Eviews and Matlab. The outputs differ in coefficients. Eviews gives C4, C5, C6 etc... no alpha, beta or gamma. Matlab gives a leverage coefficient. A coefficient for Arch and a coefficient for Garch. and a constant. How can we compare the results and interpret ?
In Eviews, C4 represents the constant (omega), C5 represents the ARCH term (alpha), C5 represents the leverage coefficient (gamma) and C6 represents the GARCH term (beta). I think this will help.
Hi everyone,
I have a question on this matter. I have modelled both my GARCH (1,1), EGARCH (1,1) and GJR. Now that I have my 3 models and coefficients I am wanting to work out the % of volatility of my time series data (FTSE100). A few papers have used the unconditional variance of the GARCH to find the variance. Is it ok to model conditional
variance model and then use the unconditional variance for volatility as a %? Furthermore, does anyone know where I can find/ work out the unconditional and the conditional variance of a EGARCH (1,1) and GJR Model?
In EGARCH in Mean model, if the coeffient of conditional volatity is positive and significant, it does imply that there is positive and significant relationship between say stock market returns and conditional volatility. If the asymmetric term is
negative and significant, bad news is in turbulant state and this increases predictable volatility more than unexpected increase in good news of similar magnitude. On the other hand, a positive asymmetric term implies that positive shocks have
greater impact on volatility more than negative shocks of the same magnitude. Note that negative asymetric term (bad news) inceases volatility more than what good news of equal magnitude could do. while positive asymmetric term (good news) decreases volatity however, investors are more prone to negative news than positive news.
@Amira
Good suggestion. But keeping the constant term in the estimated model even if it is insignificant may be a good idea to minimise omitted variable bias. Dropping it may lead to the problem associated with the Regression through the origin.
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