8. Time Series Analysis I 

You da man :)

Evan thank u

Thank you! Saved me 26 minutes in my life!

You're the real hero.

I hope you win the Nobel prize some day!

You are awesome!!!

Who is here who dislikes math? Lol

I'm doing my thesis on time series. How's your defense went?

@Vorraboms problem is, the pay is not that impressive. A poor paying job in the field will pay better. Increasing competition takes away from the job security that was one of the few incentives to the career.

You're not gonna get very far in math/statistics if you're scared of notation

Patrick Winston, also of MIT, points out that the blackboard is a better delivery method than the slide show. The pace is more appropriate.

That isn't Power Point. It's LaTeX.

The powerpoint is available on the website...

Agree. What you could do is to open the lecture notes here: ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/lecture-notes/MIT18_S096F13_lecnote8.pdf and scroll these slides on a separate tab as he talks.

Yes, but still great material

are you the prof in the video lol? your hard can be somebodys softy buddy

what the hell is powerpoint? and, do you have a better idea? I think it's the best form of material

how demanding! and that to for free.

vishal shawarma

Richard Qin me, too

+bassam bayad can't agree more. and several mistakes in functions in his ppt.

any recommendations for better vids on the topic?

Agree it's presented as harder than it has to be, and he's not at all organised in his approach. Took me several views to get the material.

jnscollier I think you reached that level a long time ago and continued further and pose statement for responses and insight.

agreed - the comment about X having a smaller variance than η when φ is negative was odd

box and jenkins

The struggle is real. He's leaving the proof to the reader. I've managed to understand most of the reasoning behind what he's saying, but it's taking a long time since he leaves a lot of stuff out for the students to figure out by themselves. He seems mostly correct though. I didn't cross check the things he said are "easy to derive by writing out the expansion", but for the most part, the hand waving is just him skipping over material. Good mental exercise for me though :)

Lag is an operator. It simply returns what the value was yesterday. Unfortunately, the notation makes this subject quite opaque. :(

Lag is just seen to be some form of filtration process - more easily seen to be a model's "memory".

I did not get how (1-x)^-1 became 1+x+x^2+.... for an operator! I thought "x" has to be some numeric variable in general, but he used it for an operator!!

yes

omg cant unsee it

sharp eyes!

The full lectures slides are available on the course site: ocw.mit.edu/18-S096F13, so you can follow along that way as well.

Thanks a lot

+‫ع. الأمين‬‎ HI I think you can use the error between the real data and the forecast such as the mean absolute error or the percentaje mean absolute error

Thanks. Now I use an aggregation operator to rank time series. Basically, I don't need forcasting.

Yes.

It is LaTeX and more precisely the beamer template which is quite popular.

@@riccaccio1 Thank you :)

I probably have missed some important detail, if one aims to replace all the lagged eta_t terms with X_t terms by substituting the remaining individual eta_t terms using the inverted relation, each expansion coefficient is an infinity summation itself (?)

Ok, I think I probably got it, the first term on the r.h.s. of the equality might have missed a (-1) factor and the summation in "i" should start from "1". It will be easier to understand the "strategy" when compared with the two equalities on slide 14 below "With lag operators" and notice the "-1"s in the first one. Since Prof. Kempthorne goes through the derivation rather briefly, these typos are not really helpful for someone who wishes to follow the lectures by simply watching them.

56:00 for whom was wondering why the locations of the roots affect the stationary of the time series. (1) intuitively, the random walk gives rise to a time series whose variance increases without bound (as discussed in the previous lecture by Lee) and therefore does not satisfy the definition of covariance stationery (2) mathematically, it is an AR(1) with a root on the unit circle. In fact, all of these will become clear as explained by the next slide, unless you cannot wait so you paused and googled it... the idea is that one can try to formally evaluate the variance and write it down in terms of the roots of the polynomials \phi (where one essentially inverts \phi first, which is an infinite-order MA model, facilitating the calculations), the resulting expression is only convergent (and therefore manifestly a constant) when all the modules of all the roots are larger than unit.

1:10:58 in the expression below "equivalently", the "+" should be "=", as stated by the professor. The relevant derivation (also applies to previous models) is shown in this quora post www.quora.com/What-does-it-mean-that-roots-lied-on-the-unit-circle-or-outside-of-unit-circle-or-inside-of-unit-circle-Why-is-unit-circle-important-to-identify-stationarity

I would be

Joseph Stanton p cannot grow faster than n. When p > n, you cannot really do regression. You will have more "unknowns" than "equations"

What do you mean by regression?

Imagine you have two points and you want to fit a line in a plane. Do we have any freedom to play with the line? If we have one point then you can fit any line. Now in 3 dimension space, if we have 3 points and we want to fit a surface, ... . n = p perfect fit but not a good model because we overfit. n < p, then model cannot be identified.

Thanks. I have already finished the thesis, I never knew about linear regression in a three dimensional space. Also I did not know that was a method for estimating parameters since we are dealing with time series I assumed it would make more sense to use method of moments or MLE to calculate parameters and estimate a model.

Yes, this really is MIT. :)