MA Model Code Example : Time Series Talk

A) As per my understanding, the following are the 3 scenarios :
a) Actual Time series data vs Its lagged values :- This is ACF
b) Actual Time series data vs Its lagged residuals : This is MA model
(Example : Yt = μ + εt + θ1εt-1)
c) Residuals after fitting any model(say AR) vs its lagged residuals : This is the check for white noise that we do on residuals to ensure that there is ~0 autocorrelation amongst the residuals.

Doubt 1 : When ACF & MA models represent 2 different things(as mentioned in a) & b) respectively), then why is ACF used to determine the order of MA models ?

B) As per MA equation : Yt = μ + εt + θ1εt-1 where εt is said to be white noise .
Therefore, this MA Model, models the relationship between actual time series data and the white noise terms.

Doubt 2 : When εt is already white noise (for example obtained from the AR model), then why do we need to model it in the first place ? Isn't the residual being white noise from the AR model enough to ascertain that nothing else can be modelled as the residuals are white noise ?

A very basic question: If in the example you illustrated- If the error was already white noise, what was the rational of building a model on top of the mean value(50) ? Since , as a diagnostic norm - we always look whether the residuals are white noise or not and here in this example if the residual or error is already white noise, why is there even a need for MA Model ?

Great Great . do not stop the lectures on time series , they are great
thank you

Has anyone figured out what order to watch the Time Series Talk playlist in? The videos themselves are amazing as others have pointed out, but if I could only figure out the order it would be even more helpful.

Thank you.

How are the coefficients of the error terms determined? Is there any rule? Are they given arbitrarily?

Is there at all any logical link between the actual observed data (time series) and the MA-model? The error term seems to be generated by random numbers with mean zero and a standard deviation of one, that is a standard normal distribution. So if this has nothing to do with the time series you actually want to analyze and forecast, how do you compute the coeficcients in the MA-model? To me AR models make perfect sense, but MA-models are very confusing. Thanks in advance for any feedback or advice :)
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Excellent presentations 🙏

why do we use acf for calculating order of MA process

this test is based on assumption of 2 randomly related data, so the random data is actually connected with each other,which is not truly random

These vids are awesome! Thanks so much, you deserve more views!

I think there is a huge amount of value in seeing how an artificial time series data set would be created. I think this is a strong re-enforcement of the concepts you have taught in the time series playlist. I could see it being an interesting/useful excerscise/video for you to provide an artificial time series data set, ask your viewers to fit a model to it, and then you would provide a solution video to correctly fitting the model or in this case, potentially deriving the correct function that generated the artificial time series data to begin with.

Great video as ususal . These videos are superhelpful as a grad student to me and I am truly grateful for your explanations

Thanks a ton for some very good pointers!