EGARCH model: exponential asymmetric volatility persistence (Excel) 

my mistake, you calculate the square vt into the sqrt and present out the sqrt

Hi Carlos, and thanks for the comment! Glad you enjoyed the video!

Hi, and thanks for the question! For ARIMA(0,1,2) you will need to calculate the first differences of the time series (I = 1), do not include any lags (AR = 0), and include two lagged residual terms in the estimation (MA = 2). You could fit it iteratively by applying OLS and inputting residuals from the past iteration to the next one until convergence or use maximum likelihood. Not sure what you are referring to with EGARCH(0,4) though, as it does not make sense to include no immediate disturbance terms in the variance equation (you need at least one) alongside four lags of conditional volatility.

@@NEDLeducation i think i need send you picture to explain my question, may i know and send it to your email address or sosial media account?

Hi Vaibhav, excellent question! This is due to the fact that immediate disturbance terms are scaled by conditional volatility and that the threshold (or, as it is also called, leverage) term theta is included. This is one of the reasons EGARCH can be more flexible than more standard GARCH approaches. Hope it helps!

@@NEDLeducation Hi, thanks a lot for the video:). But This explanation is still a bit confusing to me. How is immediate disturbance terms scaling by conditional volatility and not involving alpha in the long run volatility related?

Hi Andy, and thanks for the question, I have got a video on alternative distribution specifications in GARCH, check it out if you are interested: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pwGXftsrWYE.html. Obviously, you can use the same logic to perform EGARCH or any other GARCH parametrisation by simply changing the probability density function in log-likelihood calculations. Hope it helps!