ARCH model - volatility persistence in time series (Excel)

Autoregressive conditional hereroskedasticity (ARCH) is very common in financial and macroeconomic time series. How one can model such volatility processes? One of the techniques is the ARCH model proposed by Robert Engle in 1982. Today we will learn how to apply it in Excel and how to interpret its results. Econometrics is easy with NEDL!

[abdullahgul]

Thank You for the Video. It was very helpful.

[budinugroho]

Thank you, sir, for the way you explain, step by step as well, it is easy to understand for such a newbie like I am

[aravindganesan]

Thank you so much for the regular content. Appreciate the intuitive explanation behind model parameters.

[dasundesilva]

Dude, you are doing god's work. Thank you so much!

[Cybermemos]

My respects NEDL, you have really helped me a lot

[alexandreable]

Thank you, this is what I miss in stats/AI, most just show how to use libs but not how to calculate.

[tanyongsheng]

Great video. Suggest more videos like arima model (excel) and also arma-garch (excel) if possible.

[balkrishnaparab]

Ever grateful for the effort you are taking to make these abstruse topics accessible to students. However, with regard to the constraints on ARCH (Alpha), should it not be strictly < 1? Please guide.

[rmdfra]

Hello! Here's a question about the compasion of realised vs conditional vol. You call residuals the realised vol, but the residuals themselves (observation - mu) have been given by the solution to the optimization problem, since mu has changed after using solver. To which extent can these residuals be called realised vol? Your channel is amazing! Thank you.

[davidhofer]

Hey there,

another question about the ARCH values - I am analysing the S&P, HangSeng as well as DAX indexes and while i have an Alpha of 0, 52 for the S&P (which graphically means that the models reacts nicely to ther actual volatility), I only have 0, 20 and even 0, 14 for the DAX and HangSeng respectively (in the latter two cases the Log Likelihood is also just a little better than even the constant vola assumption). How is it possible that for the S&P it follows actual vola that nicely while the other two models dont seem to work that well (are the values wrong :/ )

[ourmemories]

Thank you for your response to previous comment. I have two questions. From what I have read, the (mu) is supposed to come from ARIMA process. But here, your (mu) is coming from log-likelihood function, even though I cannot see (mu) in your log-likelihood formula. How can you estimate (mu) from log likelihood function when it is not even present there. Why are you not using ARIMA first?

[vadimkorontsevich]

Saava, what is Constant(mu) in A5 and what is his relation to main formulas in D2, D3. Why do you assume, that he is equal to A1? 2:55 What is ARCH - Process? Could you explain it please?

[vaibhavbadgi]

Can you please make a video on ARIMA and ARMA model considering S & P 500 Index value

[AlphaTriad]

Hi, it would be interesting to compare and provide an example of the EWMA approach that Riskmetrics improved in 2006 (RM 2006).

[vuhanh]

You are very great and wisdom teacher, how can I spread this knowledge to human I will do my best.

[ivanklful]

Thank you very much teacher for all these awesome videos! Now it expands my practical knowledge much beyond, so it intrigues me to ask you further questions, ok?! So, in the model demonstrated here we are trying to predict future volatility based on some past volatility data, right? So at the moment we know only volatility in the past but not in the future, so example at the date of let's say 13 of August 2019, we know volatility of 11 of August 2019, and 12 of August 2019, but not the volatility of 20 of August 2019, so up to the some date we can use only volatility in the past, right?! So in reality what is time period in past most optimal to use to predict some volatility in the future? In this particular case it is 5 years?! Can we use some moving average of let's say around 1000 working days in the past or let's say 1200 as equivalent of 5 years? What is the most optimal time period to use?

[libradogalindonava]

Please, could you consider make a FX forecast using Arch model? It would be very helpful for me!
Regards.

[ourmemories]

In your Error term (epsilon^2), you are adding the white noise (u_t). But in many other places for ARCH model, I see it has been multiplied with v_t. Will that make some difference. Why is this so?

[priyanshsingh]

Hi! Thank you so much for this tutorial! As I was putting my data through the ARCH process and following your steps, my log-likelihood value would increase as in yours, however, my ARCH (alpha) value would become zero, and my conditional variance would stay the same. My conditional variance would equal my unconditional variance, and when I would plot my graph as in yours, the conditional volatility would just be a straight horizontal line. Am I missing a step or does that suggest something in the data?

[vipultawde]

Hi, really loved the videos you make, surprised that it took me so long to discover it. I had a query though, Lets say i am attempting a sales forecast of Walmart (a well known Kaggle competition) using a ARIMA model and i have its output. Like 1-Feb-2021 = 221 pcs of XYZ, 2-Feb-2021 = 242 pcs of XYZ. Can GARCH be used in this scenario, how do i combine it with the ARIMA estimates ?