8. Time Series Analysis I

[@SeikoVanPaath]

Timestamps: 0:00:33 Maximum-Likelihood Estimation (Recap from Lecture 6) 0:10:24 Generalized Maximum Estimation (from Lecture 6) 0:27:47 Stationarity and Wold Representation Theorem 0:47:58 Autoregressive and Moving Average (ARMA) Models 1:07:10 Accommodating Non-Stationarity: ARIMA Models 1:12:38 Estimation of Stationary ARMA Models

[@samirsaci6723]

You da man :)

[@emoneytrain]

time series segment starts at 26:46

[@kirtimangopanayak8851]

Evan thank u

[@c0t556]

Thank you! Saved me 26 minutes in my life!

[@Tyler-hf4uc]

You're the real hero.

[@brenobutcher]

I hope you win the Nobel prize some day!

[@petemurphy7164]

You are awesome!!!

[@sukwini684]

Statistics student at University of Cape Town South Africa and I love this channel. Thanks guys!

[@troymann5115]

Even though some folks didn't like the MLE and regression slides because they were math, it is a very nice bonus to this lecture. Several of the things he talks about I have used in various problems. Very practical.

[@chrstfer2452]

Who is here who dislikes math? Lol

[@StephanieHughesDesign]

When I graduated with my BA Econ. and MBA Intl. Econ. Time Series and Regression was taught in non related Statistics courses and lightly glossed over in my 2 required Econometrics courses. It was terrible. This fills the vacuum. My Stats Profs. did not even know what Econ. was let alone understand it. Great job, MIT OCW!

[@SphereofTime]

Generalized M estimation(1.Leastsquares 2.MAD 3.Maximimlikelihood 4.Robust m estimation)

[@lddidi]

I don't think it is nice to post quantitative stuff all in power point. I don't know what he is talking about when camera cast on instructor not on the power point.

[@roberth5435]

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

[@eduardolopes243]

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

[@offv6971]

The powerpoint is available on the website...

[@nebimertaydin3187]

Why is the camera guy not pointing to slides while instructor explaining slides

[@tag_of_frank]

zzzzz If you have powerpoint, show examples, show plots, fit data. This is painful.

[@alxndrdg8]

i came. i saw symbolic language. i could not understand. i left. i thank Prof for letting me make wise decision in 2:30 mins.

[@raneena5079]

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

[@BoodyCount88]

Well, I guess that MIT also has lecturers that underdeliver just like at my university.

[@lbb2rfarangkiinok]

@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.

[@jds3816]

Really useful for my a basic understanding of time series, have to do my thesis on this and I didn't even realise it was a stocastic process...

[@vinayreddy8683]

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

[@waterslager]

He knows his stuff, but he is not relaying that information very well. His method of teaching is not effective. He is all over the place and his thoughts are not organized in a way for people to follow through. I am afraid that he is making the subject of statistics boring. Statistics should be fun and more engaging. and what is up with the slides? he sounds like a consultant...the more you confuse people the more you make money :) ...

[@qiuyangxia9682]

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

[@F.G.30.4.91]

any recommendations for better vids on the topic?

[@manashisarkar9775]

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.

[@johStephan]

My analysis after watching this for 30 minutes: It is clear that the person behind the camera has no idea what the person in front is talking about and does quite some weird switching back and forth between slides and presenter.

[@ИванВайгульт]

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.

[@Flylikea]

Yes, but still great material

[@DaSexPixels]

I believe there is an error on the slide with AR(1) model. The variance of X sub t should be sigma squared over one minus phi squared. Phi is not squared in the slides.

[@jnscollier]

He's speaking another language to me. What he's saying clearly has meaning to those people that can interpret it and he clearly has passion and knows what he's saying with supreme command. He's obviously spent a long time and a lot of trial and error to get to the level he's at. I doubt my brain will ever achieve such a high level of understanding.

[@scottab140]

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

[@NilavraPathak]

This is not for beginners. It is awesome though if you have intermediate Time Series understanding.

[@VishalSharma16]

Why can't someone just explain the concept first and then go inside those formulas :/

[@cesar3550]

vishal shawarma

[@tsengelcareer]

Qualitative material in the form of PowerPoint presentation is just plain lazy and hard for students who doesn't know this material, very hard to follow. I would expect something more from an institution such as MIT

[@yevg3907]

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

[@reformed_attempt_1]

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

[@123wht123]

how demanding! and that to for free.

[@llevine6510]

the order of the lecture is indeed questionable. Should talk about ar and ma first and then go to arma and arima.

[@yaksprite]

58:41, Var expression should have phi^2 in the denominator, rather than phi

[@manashisarkar9775]

I had to watch this at least 5 times to understand.

[@mengwang7406]

this fantastic lecture is partially ruined by the sleepy cameraman.

[@richardqin3272]

those symbols are killing me

[@彻A]

Richard Qin me, too

[@QuantApplicantMattKulis]

if you understand this stuff you amaze me.

[@zhao00707]

I like how he tried to link relative areas

[@皮凯鱼说的对]

I really don't understand why camera is always on the instructor when it extremely matters for viewers to see the powerpoint first ...

[@mitocw]

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

[@皮凯鱼说的对]

Thanks a lot

[@ibraheemmoosa]

What is the point of the camera pointing to someone's head when their fingers are pointing somewhere else?

[@bygnahzdivad]

honestly, as far as profs go, he's not as bad as mine, which means that he's great

[@theshreyansjain]

tired of the handwaving arguments. can anyone recommend a textbook for this?

[@paraglidingSafety]

box and jenkins

[@manashisarkar9775]

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 :)

[@c0t556]

The professor is basically reading the slides... and the recording is so off!

[@fidelesteves6393]

What I understood of this lecture: There is a function called 'lag' which I didn't know that could ever be a math function. Then there are linear combinations of this function, each defining one kind of process. It is too much...

[@dennisestenson7820]

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

[@LemmaofIto-mz9ee]

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

[@manashisarkar9775]

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!!

[@sibeesanchay6980]

man this handwaving is so painful

[@Bmmhable]

Definitely not a class to take notes and learn the topic. Probably decent review if you've studied it before. One of the weaker MIT lectures in my opinion.

[@User_-ec9ot]

Very BAD notation that led to mistakes here and there. I am quite impressed.

[@nardok2303]

Not sure why the slide time is so short’ making it impossible to know the background while the professor is talking

[@curryeater259]

Hank Paulson?!?!??!?!

[@lochestnut]

omg cant unsee it

[@bettys7298]

sharp eyes!

[@HenryKHLai]

Should variance Xt, Var(Xt) = sigma^2/(1 - phi^2). He seems miss the square in phi.

[@leoferrari2137]

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

[@sitendugoswami1990]

Wow they do have some bad lecturers at MIT!

[@nikhil141088]

Bad presentation.

[@mohammedaasri2774]

Thanks

[@tomaspianist]

The prof just reads of what is written, I can do that too. Very poor and insufficient explanation

[@farzanmadadizadeh3838]

Thank you very much indeed. It was very helpful.

[@SphereofTime]

Simple random walk covariance correlation

[@wittggestein]

Use the board and forget about power point slides.

[@caverac]

Isn't the variance of the AR(1) s^2/(1-phi^2)? (57:10)

[@yaksprite]

yes

[@Hank-ry9bz]

6:15 why biased estimate for mle of ols

[@mehmetyilmaz7060]

The way Prof explains the things are so boring...

[@Daniel-ws9qu]

the dude literaly is pointint his finger to the slide but the camera does not show one letter of whats written on the slide. goo lecture doe

[@4suc6]

One of the worst so far

[@edansw]

classic statistics are such a pain to watch. All those assumptions and complicated distribution functions to achieve basic regression terms. So lucky those annotations are ignored in modern papers.

[@ankitmohapatra9195]

He uses beamer yay :D

[@qazaqtatar]

Is this really MIT?

[@mitocw]

Yes, this really is MIT. :)

[@WallaceRoseVincent]

Anyone interested in working through the course together?

[@AnkurNeggi]

I would be

[@Oliver_Kaiser]

How are the sheets at 00:45 made? Is it a special program or PowerPoint?

[@riccaccio1]

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

[@Oliver_Kaiser]

@@riccaccio1 Thank you :)

[@jure4835]

36:37 Wait a second. shouldn't it be y_hat = Z * (Z^T * Z)^-1 * Z^T * y ? Isn't the projection matrix the hat matrix?

[@Bmmhable]

Yes.

[@ع.الأمين]

thank you for this video, I'd like to know what could be the quantitative criteria to rank time series by a decision maker, I suppose that each time series represents an alternative. Thanks

[@delagarzaglz]

+‫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

[@ع.الأمين]

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

[@gamebm]

I am quite confused, how do I get the last equation on slide 12?

[@gamebm]

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 (?)

[@gamebm]

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.

[@gamebm]

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.

[@gamebm]

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

[@SphereofTime]

31:20

[@pruthvikgowda9977]

Confused me 😂😂

[@jds3816]

Some of the things he explains are not very clear, I don't understand how you lose degrees of freedom when p tends to infinite. Can someone explain this? (I refer to point 40:00)

[@amengioio]

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

[@jds3816]

What do you mean by regression?

[@karimk496]

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.

[@jds3816]

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.

[@pulltheskymusicgroup4475]

🇹🇿😊👏

[@tsunningwah3471]

nononon

[@arunkumaracharya9641]

How did math grow so big without any real meaning....say not even 0.0001% relevance or has it but modern world just can't quite sense it?

[@aoliveira_]

Very badly produced video. I don't want to see his face when he is explaining something. I want to see the slides.