GARCH model - volatility persistence in time series (Excel)

Generalised autoregressive conditional hereroskedasticity (GARCH) is an extension over ARCH that has been proposed by Tim Bollerslev in 1986. It allows for even more persistent volatility and is extremely useful, especially in high-frequency financial and economic time series. Today we will learn how to apply it in Excel and how to interpret its results. Econometrics is easy with NEDL!
Please consider supporting NEDL on Patreon: / nedleducation

[@MlleNnCo]

Many thanks, I really needed these clear explanations to tackle a GARCH model project with R.

[@iceman280782]

Never have found such good explanations and excel templates for the Finance world. Good job!

[@rjmorpheus]

I wish I'd had these videos during my time in University. it would have made my life a whole lot easier. Subbed!!!!

[@stephenhobbs948]

Great tutorial. Quick, to the point.

[@ghcmartins]

I´ll be doing a Patreon donation, you totally deserve it! Great content explained in short time!

[@NEDLeducation]

Thank you so much for such kind words and for considering supporting our channel!

[@RonaldRKumar]

Thanks. Very helpful. Looking forward to seeing more video's from you. Best regards :)

[@user-ez5ju4cr2c]

Great videos! many thanks looking forward to your videos on the standard errors on alpha and beta. Hope it will be coming soon...

[@vinucharles1687]

Well explained the complex model in a short time

[@kergok5662]

best explanation. thanks a lot. your videos are so helpful

[@aravindganesan2908]

Thanks for this. Look forward to the video on standard error estimation for ARCH and GARCH models.

[@NEDLeducation]

Hi Aravind, and thanks for the feedback! I will definitely do a video on standard error calculations for ARCH and GARCH very soon (appoximately, next week). Stay tuned for more content!

[@sunday-thequant8477]

hey bro! i learn a lot from your videos! thanks!

[@mgk4908]

I take my hat off, you're the boss.🤝

[@nilanjanachakraborty1732]

Very helpful presentation. Clearly and systematically explained.

[@NEDLeducation]

Hi Nilanjana, and glad you liked the video! Stay tuned for more videos on financial econometrics - as a matter of fact, tutorials on TGARCH and GARCH-M will be available later this week.

[@nilanjanachakraborty1732]

@@NEDLeducation Thanks. I am using the GARCH (1,1) model for Option pricing on Excel. Could you put up something for estimating Heston Nandi Garch Option Pricing on Excel as well?

[@NEDLeducation]

@@nilanjanachakraborty1732 Hi again! I was already going to record some videos for Monte Carlo simulation applications to option valuation in the next couple of weeks. Using GARCH in this framework as well could be interesting, will definitely consider that!

[@younissnaffaa3145]

Excellent explanation

[@KenBeans]

U sound like a god to me. I cant imagine how long you have been doing this

[@NEDLeducation]

Hi and thanks so much for such kind words, means a lot to me! Glad the videos helped!

[@sokakopa2134]

Another great one.

[@ZahidRahimov]

Thanks a lot for interesting and useful video

[@abhijeetshelke9659]

Thank you

[@mohammadtayeh1192]

Brilliant ,,, very good one ,,, I like it so much thanks a lot

[@1999stijn]

Dude you saved my life

[@josejaramillo8596]

Gracias, muy interesante.

[@lalithseelanatha3933]

It is great.

[@mimriyath]

Thank you Awesome

[@lebagnard6018]

you rock man

[@thefuckingpearl]

Awesome

[@alem_mood]

Great Video! Clever and professional! Are you planning as next steps ARMA - ARIMA models and ARIMA - GARCH model? Would be greatly appreciated!

[@NEDLeducation]

Hi Ale and many thanks for the feedback! I do indeed plan to record videos on ARMA and ARIMA reasonably soon and post them approximately within a month.

[@Paragraf100]

What would be very interesting to see you make is a model that predicts/forecasts volatility in the future of a portfolio/stock/index based on historical data? Preferably a forecast based on cyclical nature and not linear, as most financial instruments trade in a cyclical manner and not linear.

[@NEDLeducation]

Hi and thanks for the suggestion! Forecasting is obviously much more complicated than simply knowing and applying models, as to forecast you also need to know which model of hundreds (and sometimes thousands) to apply. It is even unclear whether forecasting is conceptually possible for financial markets (with most finance academics arguing it might be impossible). As for forecasting and trading strategies based on these, I plan to do a video on cointegration strategies in the near future, and I will be excited to hear any other suggestions on models/techniques you would like me to cover. We have got a Google Drive with all the relevant spreadsheets, so you can always check these and perform the calculations with your own data (please check out the pinned comment if you are interested).

[@Paragraf100]

NEDL However would it be possible to create a cyclical forecast in Sheets/Excel? The linear/exponential forecast functions are useful but not when it comes to things that move in a cyclical manner. NEDL is the God of Sheets, so I fully believe you can do this 😆😁

[@anirudhpokharel1489]

Nicely explained. Will you be doing a video on Kernel Density Estimation ?

[@NEDLeducation]

Hi Anirudh and thanks very much for the feedback! Yes, we will do a video on KDE sometime in the future.

[@NEDLeducation]

You can find the spreadsheets for this video and some additional materials here: drive.google.com/drive/folders/1sP40IW0p0w5IETCgo464uhDFfdyR6rh7 Please consider supporting NEDL on Patreon: www.patreon.com/NEDLeducation

[@ahmedaslamkhan4894]

Great video, very helpful. Can you please tell me how we can obtain p values for garch models to conclude if the data is statistically significant or not? Thanks

[@ahlemmassoud7707]

Hey Sava! Thank you so much for your content, this is my favorite channel by far. This is really helping me with my thesis. My question is: I am trying to model the exchange rate volatility using a garch (1.1) model. I'm using Python. Can you tell me whether I'm on the right track or not? Your response will be really helpful I estimated the mean equation using an ARIMA model. When using the arch package, which data should I include in the function? Should I use the Exchange Rate Returns or should I use the residuals of the ARIMA model? I'm only interested in modeling the volatility ( to use it when pricing options )

[@caiolahud8385]

I'm a fan of your work. Thank you very much for sharing your knowledge. I would like to ask a question regarding the Garch model and implied volatility in options. Could you tell me if it can be a good trade system to operate arbitrage between the implied volatility of an option and volatility by the garch model? I appreciate if you can answer me. Hugs from Brazil!

[@NEDLeducation]

Hi Caio and thanks so much for your feedback! Really glad the videos helped. Yes, volatility forecasts can be theoretically applied to option trading in the following way: First, forecast the volatility of the underlying until option maturity using (for example) GARCH. Second, calculate the implied volatility of the option. If the forecast volatility is higher than the implied volatility, buy the option, and if it is lower, sell the option. Additionally, you can also use volatility forecasts to speculate on exotic instruments, for example, VIX futures. Hope it helps!

[@matteobaraton6236]

Hello NEDL, Thanks for this amazing content, love your channel I have just a question, what if i take the basic equation of the returns : (Ri+1/Ri)-1 instead of the log returns ? The equation of the variance is modified ? Thank you Matteo

[@NEDLeducation]

Hi Matteo, and glad you are enjoying the channel! As for your question, yes, you can model the returns using the simple formula Pt/P(t-1) - 1 and use all ARCH/GARCH models as usual.

[@crib5561]

Excellent video mate, really helpful! One small question: I've noticed that the residual/realized volatility sometimes is defined as εt=vt*ut, where ut is normal and IID. If one were to use this definition of εt instead of yours, would that somehow affect the estimation procedure/log-likelihood function? Why is it that the definitions of εt differ?

[@NEDLeducation]

Hi, and happy you liked the video! As for your question, these are just two different conceptual ways of expressing the volatility process. Mathematically and for the purposes of computing log-likelihood, these are equivalent. Hope it helps!

[@juane5602]

Hello! Great explanation! I'm having a bit of trouble understanding where the lag residuals come from when we apply forecast methods on r and python packages?

[@NEDLeducation]

Hi Juan, and glad you liked the video! As for your question, you can code lagged residuals in Python using numpy or pandas instruments. It is quite feasible to build your own GARCH model in Python without relying on pre-built packages and simply using numpy, pandas, and scipy.optimize to maximise log-likelihood. Might do a tutorial on that sometime in the near future.

[@juane5602]

@@NEDLeducation Thanks for the quick answer! I will consider it. I was referring to the lagged residual on the GARCH formula. Where do the real observations come from when we make forecasts? I understand if we are using a constant mean model we'd compare the observation against the sample mean, but where do exactly future observations come from?

[@peterc.2301]

Hello Sava and thank you for every single video in this channel! I would like to ask you the following question. After estimating the GARCH parameters for a stock for example, we could use the average of conditional volatilities (based on our GARCH parameters) as an estimation for stock's risk, instead of the classic st. deviation approach?

[@NEDLeducation]

Hi Peter, and glad you are enjoying the channel! As for your question, the approach you have outlined does make sense, however a more conventional way would be to calculate the long-run volatility as (omega/(1 - alpha - beta))**(1/2).

[@peterc.2301]

@@NEDLeducation Thank you so much for your help Sava!

[@amitkumarsingh4489]

@@NEDLeducation Hi Sava , i think there is tutorial you have on this

[@letmefizzle2907]

Thank you for the explanation! I was wondering if it is possible to add an independent variable to the GARCH(1,1) model. A lot of researches only look at the volatility of a stock, but is it also possible to add an independent variable (for example media sentiment) to see if that also influences volatility? And if this is possible, what would the GARCH-model formula look like. Thank you in advance and keep up the great work!

[@NEDLeducation]

Hi, and thanks for the excellent question! Indeed, you can include variance regressors in a GARCH specification. Just post your variable alognside the conditional variance calculations and introduce a coefficient that would relate the two. For significance testing, you can use a likelihood ratio test. I might do a video on variance regressors in GARCH at some point in the future as well.

[@sadjad18]

Dear Savva, Thank you so so much for your great work and valued videos. My question is: What is the best way to incorporate GARCH model results into the main regression we have. I saw some other comments regarding this subject. Is there a video about this? Thank you sooooo much again.

[@NEDLeducation]

Hi Mojtaba, and thanks for the excellent question! What statistical packages such as EViews do is they calculate the standard errors using the Hessian matrix (which in turn uses log-likelihood gradients). However, the implementation of this in Excel is quite cumbersome and can be imprecise. The most intuitive way would be to estimate a baseline GARCH model, record its log-likelihood, and then estimate a GARCH model with an additional mean regressor, applying log-likelihood ratio tests to assess its significance (namely, does it improve fit compared to GARCH with no additional mean regressors). I have got a video on the likelihood ratio test here: kzbin.info/www/bejne/eHWkeYiag7dqeKs

[@sadjad18]

@@NEDLeducation Thank you so much dear Savva

[@ramshasiddiqui8893]

HELLO NEDL, your explanation is fantastic I just want to ask about historical and implies volatility with GARCH model. it would be very helpful

[@NEDLeducation]

Hi Ramsha, and glad you liked the video! As for your question, "historical" and "implied" volatility in the GARCH framework are just the realised and the conditional volatility (volatility that is there and volatility that was expected as per the model). Or are you asking more about option-implied volatility for example?

[@jesper9280]

Hi NEDL, I have done the GARCH model exactly as you did it in this video, but Ive done it on my own data set. Now I have a problem, I need to get the Normalized Returns because there was heteroskedasticity in my data set. I need to do an OLS regression with those Normalized Returns. How do I get the Normalized Returns when I have performed the GARCH just like you did it in this video. Could you please help me?

[@NEDLeducation]

Hi Jesper, and thanks for the question! If I understand you correctly, you refer to normalised returns adjusted for heteroskedasticity. To get those, you can divide your returns by respective conditional volatilities given by GARCH and proceed with any further analysis. Hope this helps!

[@jesper9280]

@@NEDLeducation Hi NEDL, I don't think I understand it correctly. If I divide my return, let's say 0.63%, with a conditional volatility of 1.43% then the normalized return would be much to high, in this case around 44%. Or am I doing something completely wrong here? Would be great if you can help me out, it's for my thesis.

[@NEDLeducation]

@@jesper9280 Hi Jesper, when you normalise returns that way, the results are interpretable as how many standard deviations above the expected your return falls (or, if you like, as a kind of z-score). In your case, you could say that your normalised return is 0.44 standard deviations above the expected. Hope it helps!

[@DrFloyd-ef9eo]

Can you forecast conditional volatility for GARCH using this formula you have previously provided omega + alpha*e^2 but instead of alpha replace it with GARCH (Beta) or even for TGARCH using Theta from your TGARCH Video?

[@RustuYucel]

Very good again. I have a naive question here that many times I am facing in these type of formulas. How PI value take places in these type of formulas? Is it because of periodicity assumptions? Just wondered

[@NEDLeducation]

Hi Rustu, and glad you liked the video! Thanks for the question, it is indeed very interesting how pi managed to crawl in there :) Long story short, it has to do with the maximum likelihood estimation using the probability density function of the standard normal distribution. And, in turn, pi comes up in there because the definite integral of e^(-x^2) from -inf up to +inf gives sqrt(pi). Hope it helps!

[@junaidijunaidi3247]

Good explanation, How can I count yearly of Garch volatility? thanks

[@user-df1ub2hm9z]

Hello, thank you for this video. I wanna ask, could I also apply this way for Exchange Rate Volatility? And what should I do if the data that I need is annual volatility? Thank you

[@NEDLeducation]

Hi, and thanks for the question! Yes, GARCH is absolutely applicable to exchange rates. Annual volatility can be retrieved from daily data by multiplying the long-run volatility as per the GARCH model onto the square root of the number of trading days in a year (e.g., 252).

[@user-df1ub2hm9z]

@@NEDLeducation I am a little bit confuse with this. So I need to calcute the SUM of all GARCH volatility first, then devide it by the number of data, and times it by SQRT(252)? Could you help me by writing the form? And for exchange rate, the first step is getting the return number from LN of the now per before value right? Thank you in advance :)

[@kaancetinkaya3157]

Great explanation, thank you for the video. I have a question I need annualized volatility to use Black and Scholes Option Model. How can I convert the daily GARCH volatilities which we calculated here to annual volatilities without any errors? Note: My sample size is two and a half years.

[@NEDLeducation]

Hi Kaan, and glad you liked the video! As for your question, you can calculate total variance by summing up all conditional variances (or squares of conditional volatilities), and then bring them to the annual frequency, so dividing by the sample size and multiplying by the number of trading days in a year (for example, the conventional 252). Taking the square root of that will give annualised volatility. More naturally, you can price options in the GARCH framework using the Heston and Nandi (2000) model, which is a GARCH extension of Black-Scholes.

[@NEDLeducation]

Alternatively, if you are concerned with pricing high-maturity options, you can annualise the long-run volatility calculated by GARCH using the conventional technique (multiply by root of 252).

[@kaancetinkaya3157]

@@NEDLeducation Thanks for your valuable answers. You are doing a very good job.

[@krishsejpal7031]

if i am forecasting volatility of GAMESTOP stock what constraints should i put for constant(mu) in excel solver since this stock had higher average returns due to the GAMESTOP short squeeze

[@Eiszteee]

Do you happen to know how to use the smoothed/GARCH volatilities in a linear regression? Now that heteroscedasticity has been acknowledged, I don't know how to implement these results in a linear regression. Thanks a lot! Keep up the good work!

[@NEDLeducation]

Hi, and thanks for the excellent question! Generally, it is quite challenging to implement both regression and GARCH estimations in the same model as they use different techniques (OLS and MLE, respectively). There can be two intuitive and straightforward implementations though. First, you can estimate a GARCH model, and then normalise your input data using conditional volatilities (effectively z-scoring them) and then plug this into a regression. Second (and this is something I prefer to a greater extent), you can include your independent variables into a GARCH MLE implementation and then use a likelihood ratio test to determine statistical significance. I show this approach here: kzbin.info/www/bejne/eHWkeYiag7dqeKs

[@Eiszteee]

@@NEDLeducation Thank you!!

[@RenormalizedAdvait]

This is basically a GARCH(1,1) process with one, one lag, for a general GARCH(p,q) one must resort to ACF and PACF plots.

[@sadeemalsh4851]

Thank you for the excellent explanation! I tried to do it and follow the steps but when I do the excel solver and wait the results a notification window appears with this comment “solver cannot improve the current solution, all constraints are satisfied” But the thing that the constant mu become more than 1%. I don’t know what’s the problem. Please advise

[@NEDLeducation]

Hi, and glad you liked the video! A constant of more than 1% can be reasonable depending on which data you are using.

[@255sdr8]

Thank you for the super helpful video!!! I still have 2 questions: - Do we use the "solver" to ensure stationarity? I have a feeling that I might run into problems with stationarity in my study of cryptocurrencies. - Is a standard GARCH(1,1) used in the video? I can't wait to see more from you. Many greetings from Germany

[@NEDLeducation]

Hi, and thanks for the question! Yes, it is standard GARCH(1,1). As for solver, it is used to find maximum likelihood parameter values. If you are concerned with the stationarity of the data, you can always run the returns through Dickey-Fuller or KPSS tests, here are the videos dealing with these: kzbin.info/www/bejne/gXSpfZmHfb-Ceq8 and kzbin.info/www/bejne/q5PdeWR4f9qIqNE. Hope this helps!

[@255sdr8]

@@NEDLeducation Hi NEDL, thanks for the quick reply! The videos helped a lot to check the stationarity for my data. You have the ability to explain things easily which helps me a lot as a beginner in time series analysis. Thanks again!

[@oussamaarfi8899]

Hello Sir, I have followed your instructions but my problem is that when I run the solver after adding the same constrains it results to alpha equals zero and both Rrealised and GARCH charts are nearly identical. Do I need to do the ARCH model first to obtain the adequate result? Thanks for answering my previous question you are amazing!!.

[@Lingeshwaranthestig]

Same issue here, request help please

[@Lingeshwaranthestig]

I was using monthly data and so got this error, and replaced with daily data and got the result. Thank you creator!

[@sathvikshivakumar1821]

Using any conditioning variable(s) of your choice, can you estimate a conditional beta model

[@user-vb4fe1jc7q]

How is it that the conditional variance calculated in matlab and via your approach in excel have different results . Need Help

[@davidhofer6444]

I have a question regarding the alpha and beta optimized values in the ARCH and GARCH models. I come up with an alpha of 0,39 and a beta of 0,59, similar to your values. On the internet however everone seems to come up with alpha values of under 0,1 and a beta of about 0,9, so i am unsure what to do Thanks for all the videos though. They are super helpful

[@NEDLeducation]

Hi David, and thanks for the excellent question! Happy to hear you are applying the concepts from the tutorial in your own calculations. The alpha and beta really depend on the characteristics of the volatility process (how impactful is initial disturbance persistence versus conditional variance persistence). It is not unusual to find alphas as low as 0.1 or as high as 0.4 in different samples or for different assets.

[@davidhofer6444]

@@NEDLeducation Thank you for the quick answer. That is very reassuring. Alpha and Beta should be below 1, but close to 1. Is then a GARCH model still okay, when the sum of alpha and beta is around 0,97

[@NEDLeducation]

@@davidhofer6444 Yes, it is quite typical for daily financial data.

[@zaifa348]

Hi I want to know how can I use the data obtained here, the alpha beta coefficients and standard error to predict (forecast) volatility for 7 trading days

[@NEDLeducation]

Hi Zaifa, and thanks for the question! To forecast volatility using GARCH, you simply have to extrapolate conditional volatility into the future using the coefficients obtained and set realised volatility in future days to be equal to conditional volatility. Hope this helps!

[@zaifa348]

@@NEDLeducation can you please type out an example with any imaginary coefficients so that I know how to proceed 🙏🏽

[@mohammedmagdy9835]

GARCH models can be used to assess and forecast stock volatility. Can we use this to predict stock returns?

[@NEDLeducation]

Hi Mohammed, and thanks for the question! Generally, ARCH/GARCH models are used to explain the volatility dynamics of time series, not to predict returns. However, if you believe volatility impacts expected returns of stocks (as a risk premium for market variance, for example), you might enjoy this video on GARCH-M (GARCH-in-mean) model: kzbin.info/www/bejne/jZuQfpiNrc1-lac

[@carlossjara]

Grate videos! You suposse e2t es additive process ¿What change in L if you suposse multiplicative process?

[@NEDLeducation]

Hi Carlos, and glad you liked the videos! As for your question, the log-likelihood procedure allows to convert the product of the probability density functions into the sum of their logs, transforming a multiplicative process into an additive one. Hope it helps!

[@shubhambaldewa3692]

What is the significance of the Constant (mu) variable ? Its not used in any of the formulas also so why do we consider it? also why are we showing the long run volatility as well ?

[@MartijnMols]

should I use linear or log returns?

[@bambangsutrisno_umj]

How to implement GARCH (1,1) in Excel or EViews for an event study analysis (calculating cumulative abnormal volatility)? Thanks in advance.

[@NEDLeducation]

Hi Bambang, the event studies for cumulative abnormal volatility are a very different concept to conventional event studies with abnormal returns, might do a video on that sometime in the future. GARCH models can be used in this context to derive the expected variance for the test. Hope it helps!

[@NEDLeducation]

Alternatively, GARCH methodology can be used to test if a particular event induces abnormal volatility directly by plugging a dummy variable into the conditional variance equation. Was already planning to do a video on variance regressors with GARCH so might investigate this particular case.

[@bambangsutrisno_umj]

@@NEDLeducation Thanks for your explanation. Hopefully, you can make a video for cumulative abnormal volatility in the future.

[@404baron]

can you pls tell me what is the constant mu ?

[@NEDLeducation]

Hi Jawed, and thanks for the question! The constant (mu) is the average return, equivalent to the intercept (constant) in OLS regressions.

[@vuhanh2944]

Hello Nedl Teacher, I have headache about Garch, I am writing a research. The research describes the GARCH model estimation and selection process with tabular data, and empirically applies the table data on GDP growth, total capital and labor growth of 4 economic sectors: Transportation - Warehouse, Agriculture - Forestry - Fisheries, Industry - Construction, and Services from 2011 to 2019 in Ho Chi Minh City, Vietnam. Do I have to analysis by 12 excel tables consisting of: GDP, Labour, Capital of 4 economic sectors: Transportation - Warehouse, Agriculture - Forestry - Fisheries, Industry - Construction, and Services? am I right Teacher?

[@NEDLeducation]

Hi Hanh and many thanks for the question! Ultimately, you can go a number of ways when analysing such a dataset, but I suggest the most natural approach would be to have four models, for each of the sectors, that regresses GDP growth on labour growth and total capital growth. The coefficients for the labour and capital in the regression will demonstrate the contribution of each of the two factors into GDP growth and you then can analyse whether the production functions for the four sectors are different. If you identify heteroskedasticity in residuals, you can by all means apply GARCH/ARCH with labour and capital being mean regressors and variance behaving according to GARCH(1,1) or ARCH(1,0) and see where each of the estimations takes you. The only concern is the data from 2011 to 2019 might be to small of a sample if observations are annual, but if they are at least quarterly, the should be no problem. Hope it helps.

[@vuhanh2944]

@@NEDLeducation Dear Teach, regarding to GDP, I have monthly data from 2011 - 2019 for 4 sectors said above. In the case of going ahead with four models approach and If there is only GDP without Labour and Capital I will still use GARCH and ARCH, is it right?. However I cannot measure each of the sector that regresses GDP growth on labour growth and total capital grow, am I right?. Further more, May I know if I should use Cobb-Douglas production function or Multivariate linear regression in which Y is GDP, X1 is Labor, and X2 is Capital?

[@vuhanh2944]

Dear Teach, regarding to GDP, I have monthly data from 2011 - 2019 for 4 sectors said above. In the case of going ahead with four models approach and If there is only GDP without Labour and Capital I will still use GARCH and ARCH, is it right?. However I cannot measure each of the sector that regresses GDP growth on labour growth and total capital grow, am I right?. Further more, May I know if I should use Cobb-Douglas production function or Multivariate linear regression in which Y is GDP, X1 is Labor, and X2 is Capital in the case of I have quarterly data of all GDP, Labour and Capital from 2011-2019?

[@NEDLeducation]

@@vuhanh2944 For monthly data, it is perfectly fine to estimate any of the models you suggested. If monthly data is available for GDP, and labour and capital stock are not available at this frequency, you can test whether the volatility of economic growth abides by GARCH/ARCH processes, which is also interesting with respect to your four sectors. If you do have such data (GDP, capital, and labour), you can perform multivariate regressions with GARCH/ARCH volatility as well, nothing wrong about it! As for production functions you might test - excellent question. Cobb-Douglas is generally used the most in such econometric studies, as it is not as simplistic as the linear function but also allows to perform econometric tests easily. For example, if your production function is GDP = A0*Labour^A1*Capital^A2, you can take natural logarithms of both sides and get ln(GDP) = ln(A0) + A1*ln(Labour) + A2*ln(Capital), and if you take first differences, you can get the regression equation ln(GDPt/GDPt-1) = A1*ln(Labourt/Labourt-1) + A2*ln(Capitalt/Capitalt-1). So if you regress logarithmic growth rates of GDP onto those of Labour and Capital, you can get Cobb-Douglas powers A1 and A2 as your regression coefficients. For linear production function, you can do the same with linear first differences in GDP, labour, and capital instead of logarithmic growth rates. Hope it helps!

[@vuhanh2944]

@@NEDLeducation Dear Teacher, thank you very much for your teaching. I will do according to and will ask you again if I meet troubles.

[@patrickwmckenzie]

My alpha and beta converge to 0, maximising my LL to ~7600, using very similar data to yours. What could be going wrong?

[@heshammostafafahmy]

In Practice How is the GARCH Model is useful in trading ? can you please explain and do a video on that ?

[@NEDLeducation]

Hi Hesham, and thanks for the question! You can use GARCH model to forecast volatility for tomorrow using the pre-estimated alpha and beta parameters as well as the conditional volatility and abnormal return for today. Additionally, you can use the GARCH framework to run other return regressions to make them more robust to heteroskedasticity. Hope it helps!

[@heshammostafafahmy]

@@NEDLeducation right have you tried calculating the r2 coefficient or person correlation of the predicted volatility vs the actual volatility. I keep getting a very low score which implies it wasnt really predicting anything and it seems the predictions was almost lagging the actual volatility

[@NEDLeducation]

@@heshammostafafahmy Hi Hesham, it is almost always the case that R-squared for return regressions is quite low, as there is a lot of idiosyncratic risk that cannot be easily explained by any factors you wish to include in the model.

[@Black182heart]

gamma is derived by dividing omega by LRV. And the sum of Alpha + gamma+ Beta should equal 1. But it doesn't. Am I missing something?

[@NEDLeducation]

Hi and many thanks for the question! Gamma is just an additional parameter, and as it is defined as the ratio of omega to long-run variance, you do not need to optimise it when solving for GARCH parameters. Alpha+gamma+beta should indeed be equal to one. It is just that in the spreadsheet the long-run-VOLATILITY is reported, not long-run-VARIANCE. If you divide omega (cell B6) onto long-run-variance (cell B10 squared), you will indeed get 1-alpha-beta. Hope it helps.

[@Black182heart]

@@NEDLeducation thank you for the clarification.

[@cuysaurus]

How do we predict out of sample?

[@annmaryalexander]

How do we obtain conditional variance in E views?

[@NEDLeducation]

Hi, and thanks for the question. As you have estimated an ARCH/GARCH model in EViews, you can click the "View" tab and select the option ARCH/GARCH Graph/Conditional Standard Deviation, and it will plot the graph for you. Additionally, I am planning to record a series of tutorials on EViews in the not so distant future. Hope it helps!

[@annmaryalexander]

@@NEDLeducation Thank you so much. .

[@sushantabhattacharyya7154]

Can we compare the long run volatility for two separate time series and comment.

[@dasundesilva5588]

How is the conditional mean equation calculated?

[@NEDLeducation]

Hi Dasun, and thanks for the question! If you refer to the conditional mean of the return, in the simple GARCH model it is assumed to be constant and equal to mu. More sophisticated models for the mean equation in GARCH can be derived using the GARCH-M framework, for example, here: kzbin.info/www/bejne/jZuQfpiNrc1-lac If you refer to the conditional variance, it is calculated as omega + alpha*lagged squared residual + beta*lagged conditional variance. Hope it helps!

[@vaibhav1131]

Hi - I have a feq questions based on what I read in research papers. The text Is here "s far as the literature on forecasting oil prices or returns volatility is concerned, quantitative forecasting models could be divided into three main categories; namely, time series volatility models, implied volatility models, and hybrid models. Time series volatility models can be further decomposed into three sub-categories; namely, historical volatility models, generalized autoregressive conditional heteroscedasticity (GARCH) models, and stochastic volatility (SV) models. Historical volatility models are averaging methods that use volatility estimates (e.g., standard deviation of past returns over a fixed interval) as input and assume that conditional variances are level-stationary-these models could be further divided into two subcategories depending on whether they use a pre-specified weighting scheme (e.g., random walk (RW), historical mean (HM), simple moving averages (SMA), weighted moving averages (WMA), exponentially weighted moving averages (EWMA), simple exponential smoothing (SES)) or not (e.g., AR, ARMA, ARIMA). GARCH models consist of two equations - one models conditional mean and the other models conditional variance, use returns as input, and assume that conditional variances are level-stationary - these models could be further divided into two subcategories depending on the nature of their memory; namely, short memory models (e.g., ARCH, ARCH-M, GARCH, IGARCH, GARCH-M, APARCH, EGARCH, TGARCH), which assume that conditional variances' autocorrelation function (ACF) decays exponentially, and long memory models (e.g., CGARCH), which assume that conditional variances' ACF decays slowly. GARCH models have been widely used in the literature due to their ability to capture some peculiar features of financial data such as volatility clustering or pooling, leverage effects, and leptokurtosis, which are typical of crude oil prices-see for example Day and Lewis (1993) and Agnolucci (2009). As to SV models, they could be viewed as variants of GARCH models where the conditional variance equation has an additional error term, which from a modeling perspective makes this class of models more flexible-for a detailed discussion of SV models and their relation to GARCH models, see survey articles by Ghysels et al. (1996) and Chib et al. (2002). On the other hand, implied volatility models are forward looking models in that they use market traded options information in combination with an options pricing model (e.g., Black Scholes Model) to derive volatility. Finally, hybrid volatility models are combinations of different models (e.g., regime switching GARCH used by Fong and See, 2002); the design of these models has been motivated by the highly volatile nature of crude oil prices" . I have a few questions here 1) What does conditional variance is assumed to be stationery at level means ? 2) What does short and long memory mean ? 3) In GARCH while estimating conditional mean and conditional variance which mean returns are considered? Reference - www.sciencedirect.com/science/article/pii/S0140988311003008?via%3Dihub

[@NEDLeducation]

Hi Vaibhav, and thanks for the question, very exciting to see you have so thoroughly examined the literature on volatility models, was enjoyable to read through your take on it! As for your question: 1) It basically implies conditional volatility has a long-term equilibrium level it converges towards and always tends to. In standard GARCH, it equals sqrt(omega/(1-alpha-beta)). 2) It mostly revolves around the speed of conditional variance decay. Standard GARCH decays exponentially, which is considered to be "short" memory, other models can be developed to incorporate a more slow decay process. 3) In standard GARCH, the mean is constant and it is a parameter (mu) to be calibrated. You can include standard mean regressors into the equation as well to account for potential mean return determinants. In GARCH extensions, for example, GARCH-M, the mean is assumed to be dependent on conditional variance (the logic of risk premium). I have just released a video on that, check it out if your are interested: kzbin.info/www/bejne/jZuQfpiNrc1-lac Hope it helps!

[@vaibhav1131]

@@NEDLeducation Thanks for the clarification. just became a patron :)

[@NEDLeducation]

@@vaibhav1131 Thanks so much for your support, really appreciate it!

[@faizaahmed6488]

Plz make vedio on how to estimate garch parameter with different distribution ang lags

[@sangeethanagarakatte5851]

Please shows us how BEKK GARCH model works on excel

[@kishornaik4948]

How to use Garch model to test influence of volatility on herding behaviour

[@iceman280782]

How I can calculate TGARCH and EGARCH in Excel?

[@NEDLeducation]

Hi Marcel, and thanks for the question! For EGARCH, you can simply tweak the conditional variance equation to represent natural logarithms. TGARCH requires more tinkering, including the use of conditional volatility instead of conditional variance. I might do videos on both in the near future. Hope it helps!

[@iceman280782]

@@NEDLeducation hi. This would be really great if you can do this. I read that both are the most used Garch models besides the normal one. I tried to looked it up in books but couldn’t find excel solutions for both models.

[@NEDLeducation]

@@iceman280782 Hi Marcel, the video on TGARCH is here, check it out if you are interested: kzbin.info/www/bejne/mX2lo617gq2Dq5Y

[@iceman280782]

@NEDL super great 😊 I already had a look at it and now it is understandable for me. Thank you very much

[@muntedme203]

Forecasting please.

[@NEDLeducation]

Hi, and thanks for the comments! I do plan to record some videos on forecasting, including on the use of GARCH to forecast variance.

[@arielmodesto4696]

if you can do a diveo about fiaparch i will be grateful # brasil#

[@bixis5081]

15:08 "average return caanot be 0,1% becouse that is a lot" me trying to fit this on bitcoin where mu is 0,29%

[@NEDLeducation]

Hi, and thanks for the comment! :) Obviously, you can tweak the parameter restrictions based on the dataset you are working with. Alternatively, if you wish to avoid coding parameter restrictions for GARCH models at all, there is a nice and intuitive workaround, I cover it in this video for example: kzbin.info/www/bejne/pqiqiZmqqNeKj6c Hope it helps!

[@bixis5081]

@@NEDLeducation sure i set it up few times higher and i think it worked out fine, thanks for the videos

[@mohammadtayeh1192]

need you email please