This was extremely helpful!! Between my 3 econometrics textbooks (Griffiths, Greene, and Wooldridge), the information on MA models was sparse. This really cleared up the mindset behind this model!
Thank you so much for explaining this so well! My professor and textbook explain this concept very mathematically which is hard to understand for beginners, they should really give a simple example and then dive into the details as you did.
Gemini 1.5 Pro: This video is about moving average model in time series analysis. The speaker uses a cupcake example to explain the concept. The moving average model is a statistical method used to forecast future values based on past values. It is a technique commonly used in time series analysis. The basic idea of the moving average model is to take an average of the past observations. This average is then used as the forecast for the next period. There are different variations of moving average models, and the speaker introduces the concept with moving average one (MA1) model. In the video, a grad student is used as an example. The grad student needs to bring cupcakes to a professor's dinner party every month. The number of cupcakes the grad student should bring is the forecast. The professor is known to be crazy and will tell the grad student how many cupcakes he thinks were wrong each month. This is the error term. The moving average model is used to adjust the number of cupcakes the grad student brings based on the error term from the previous month. The coefficient is a weight given to the error term. In the example, the coefficient is 0.5, meaning the grad student will adjust the number of cupcakes he brings by half of the error term from the previous month. For example, if the grad student brings 10 cupcakes in the first month, and the professor says the grad student brought 2 too many, then the grad student will bring 9 cupcakes in the second month (10 cupcakes - 0.5*2 error term). The video shows how the moving average model works through a table and graph. The speaker also mentions that there are other variations of moving average models, such as moving average two (MA2) model, which would take into account the error terms from two previous months.
Great videos, thank you! I have a question. Period 1 value is our mean value but we don't know what is mean since we just started from point 0. How to calculate residual then? We know the true observation and we don't know the mean. Is it just a guess? But when we use any statistical package it does not ask us to input guess mean value.
Thanks this is a really clear explanation. My only question is when you are calculating your f_t column, why are you including the error from the current time period? Shouldn't you only be including the 0.5*e-t-1?
How come some MA(1) formulas have x_t = mu + (phi1) error_t + (phi2) error_t-1..... If you predicting at time t then how would you know error at time t (error_t), why are some formulas like this?
I still don't think this makes sense to me why is incorporating past error somehow gives us better prediction in the future in this case. Since this crazy professor will randomly choose an acceptable # of cupcakes, your past error shouldn't help in better predicting in the future.
Event though the professor selects a different number every time, at the end the average is stable. Assume you have a time series of images. Images, due to the unstable environment they're taken in or all other factors that manipulate images nature, are not always the same, although they are taken from the same scene. So, what is the goal here ?to find the mutual information in the images and ignore the noises. These noises are how crazy professor is , and the importance of error, which we can handle by its coefficient. By handling these factors, we can get close to recognising the mutual information. Remember, these are unsupervised models. There are no lable to rely on.
the idea is that you're trying to predict the next value. you get told what the next value is by the professor. if its random then there is no signal in there & the results are still meaningless
Observation: 5:32 Its always centered at 10 because the errors mean was 0 (per 1:02) and error was multiplied by Φ, which will have have a mean of 0. Feeling a little awkward commenting multiple times. Just trying to understand more by thinking aloud, and that someone may correct my understanding. :) Great videos!
This is a great explanation but in many equation they also add the current error (epsilon_t). I just don't get how are we supposed to know our current error if we are trying to forecast a value. Do we simply neglect that current equation for forecasting?
How is the average moving though? It was fixed for each prediction! Wouldn't it have to be recalculated each time for it to be moving? Also we didn't seem to use anything related to the error being normally distributed... is there a reason for that? why was it mentioned in the first place?
Where does the noise in the equation come from? In our data we only have time on the x axis and Y as the target variable. There is no error term. What I mean to ask is does the MA model first regress y on y lag terms like the AR model and then calculate error between the actual and predicted y terms? Then regress y against the calculated error terms(residuals)?
The error is a white noise coming from random shocks whose distribution is iid~(0,1). Ftting the MA estimates is more complicated than it is in autoregressive models (AR models), because the lagged error terms are not observable. This means that iterative non-linear fitting procedures need to be used in place of linear least squares. Hope this helps :).
what is the difference between taking the average of first 3 values and calculating the centered average at time period 2 and this method(average+error t+ error at previous time period)
Thank you Ritvik. Is there any recommendation on books for Time Series. I am currently in school doing my Masters and I am feeling all over the place with this subject. Any suggestion on how to crack this one will be appreciated.
Hi, I studied a Master in Quantitative Economics and I used this book: Econometric Modelling with time series by Gloria González Rivera. Feel free also to send me an email if you want some problem sets to practice. Best from Spain.
