Time Series Talk : Augmented Dickey Fuller Test + Code

[@Moment_K]

As a quant finance masters student, your contributions to my learning is invaluable, by understanding the theoretical intuition first, any degree of mathematically rigorous syntax that follows becomes tenable, make me less inclined to let the obscurity of academic papers and dense textbooks get the better of me

[@KarthikShamsundar-dh4pv]

I know its personal but could you please tell me which program of Masters in Quantitative Finance you're enrolled in? And also I would greatly appreciate it if you could tell me the scope of pursuing this path. Currently I'm a Bachelors in Finance student.

[@hasting8422]

​Finance is probably not the appropriate major for being a quant sadly. Have you taken any advanced statistics and math courses?

[@PrismSR]

You're timing on these recent uploads could not be better! I'm currently taking Time Series II this semester and my professor just went over reviewing the topic of the Dickey Fuller and Augmented Dickey Fuller test from Time Series I. As someone who was having a hard time understanding all that was being taught things like ACF, PACF, EACF, ARMA model, tests like the ljung-box test, etc, your videos have really helped me understand what my professors have been trying to teach me in class. The videos published around April of last year especially helped me last semester. I didn't really understand what was being taught, but in the class recitations my CA went over how to apply the information in R, not Python. From it, I knew how to solve my homework and tests that were in R. I memorized the procedures taught to me, but I didn't truly understand how or why this knowledge worked in my application of the knowledge in R. You're videos have helped me a lot in understanding the Time Series material taught to me. You are so much more precise and clearer with your explanations than my professors have been. Because of you, I've been able to more fully understand these Time Series concepts. I managed to get an A in that class. I hope you keep up making these type of videos because Time Series concepts really are interesting, and I would've never really known that if you didn't clear the fog in my head! Thank you so very much!

[@ANURAGSHARMA091716]

This happens to all of us. We mug theory and derivations. I remember in an internship interview I couldn't even explain the AR and MA process satisfactorily even after scoring above 60% in time series course at the university. You can think of it as 75 in the relative grading system cz my professor had told us that he wouldn't give anyone above 80/100.

[@sahildewan8422]

Your videos are really helpful Ritik. For the first time I’d say that I’m hooked to some study videos. You really make the concepts look so easy. Great work!

[@ritvikmath]

Happy to hear that!

[@mynameisjoejeans]

I've watched so many videos and been through so many forums to try and understand this for my dissertation, and this is the first video I truly understood. Even better, you included the code for Python which is exactly what I'm using. Thank you so much this is the perfect video on the subject.

[@johnspivack]

Good video. Enough detail to make it meaningful but not overwhelming. Thanks.

[@เกี๊ยวอย่างเดียว]

Thank you for the video! This channel makes me understand time series a whole lot better. Best channel for time series!!

[@gpietra]

Unit root was one of the most obscure concept I have ever met. Thanks to you and a couple of other dudes online I reached a sufficient level of comprehension. Thank you!

[@kisholoymukherjee]

Which are the other couple of dudes. pls mention, I am looking for more resources to fully understand these topics

[@zdmsr]

I remember the Dickey Fuller test from back when I took Time Series analysis because the name is hilarious.

[@ritvikmath]

haha!

[@ANURAGSHARMA091716]

@@ritvikmath We use to call it Fully augmented Dick! :P

[@maiden5427]

@@ANURAGSHARMA091716 😂😂😂

[@shikhasen3981]

You are so amazing , and the videos are so comprehensive

[@gautamsethi3751]

Another excellent video from you--kudos! I have just a couple of small nitpicky comments. 1. I think you misspoke around 5:02 when you rejected (and didn't reject) the null; you switched them around. 2. And if you plan to fix that issue, then it would great if you could be consistent about using either critical values or p-values. While the two are related, they are very different concepts. In the theory part of the talk, you mention critical values but in the code you make the decision based on p-values. Aside from these relatively minor issues, this is a fantastic video!

[@hassanbcef2503]

i think he's right at 5:02

[@user-rw6iw8jg2t]

Great Math explaination thanks man ! It's simply phenomenal.

[@asif09ansari]

Let's "delve into the weeds of the mathematics" please!

[@quant-prep2843]

he dont know, so he didnt lol

[@abdielbrayden3429]

I guess Im randomly asking but does anyone know a trick to log back into an instagram account..? I stupidly forgot the login password. I would appreciate any assistance you can give me!

[@kadenjavier331]

@Abdiel Brayden instablaster ;)

[@abdielbrayden3429]

@Kaden Javier I really appreciate your reply. I got to the site on google and im in the hacking process atm. Seems to take a while so I will reply here later with my results.

[@abdielbrayden3429]

@Kaden Javier it worked and I now got access to my account again. Im so happy:D Thank you so much, you really help me out :D

[@mingchuanzhou9363]

Thank you so much !!! You contributed a very logical and tidy interpretation of the DF test, and I am looking forward to seeing your more useful learning videos and resource.

[@BChow-td7qh]

It's great teaching, makes me understand the time series better!!

[@yaqiwu763]

Omg, you are life saver, much more clear, thumbs up

[@BhuvaneshSrivastava]

Just Awsumm as Usual 🙏

[@AlphaBay14]

Hey mate! Thanks for the videos. One question, let’s say I runs the ADF on my time series and the pvalue is indeed less than my alpha but visually I can see the variance is not constant and after plotting the ACF I have serial autocorrelation. Given the my ADF says that my time series is stationary, how can I interpret this difference with what I see and the result of the ACF? Should I just proceed to model an ARIMA model and run a white test or what is your advice? Thanks a lot

[@ankitbiswas8380]

so what happens for complicated models where you have delta as well as multiple Betas like you showed here ...we calculate the t-delta and check if its lower than DF-critical value and if yes then the T.S is stationary but how does the Betas influence then ? You said for each Beta we need to calculate t-Beta and check their values with t-distribution critical value and comment whether they are significant or not ...is it possible that some t-Betas < t-critical and some t-Betas>=t-critical ? What happens then ? does it not affect the result of t-delta or do we just decide the stationarity of time series based on t-delta everytime ?

[@chirag4895]

i have the same question , he did not explain the significance of the T test of the beta variables

[@mehmetnazif5837]

does the ordinary t test on t-2 values indicate unit roots? or is it just significance of the lagged variables? or are they both the same thing? what is the alternative hypothesis in testing the coefficients of the t-2 or bigger lag variables.

[@Yassine-ym4vf]

Thank you Ritvik !

[@masonscott2768]

So cool! Thank you for making this video!

[@theophilusashun301]

Very much appreciated , making understanding concept pretty easy.. thank you so much.

[@at7915]

You're the GOAT!

[@itzRoblar]

Hi! I am a little bit confused regarding your explanation of the null hypothesis. Between 3:00 and 3:28 you say that under the null hypothesis, we expect stationarity since y_(t-1) disappears. This would mean that a rejection of the null hypothesis is a rejection of delta being 0 and hence a rejection of stationarity. However, at 4:20 ->, you say that a rejection of the null would mean that you reject the possibility of a unit root which means we have stationarity. In my mind, the argument makes sense compared to the top left h0, but i'm thrown off by your comment between 3:00 and 3:28 (although that also makes sense in terms of testing for delta = 0). Can you please elaborate a bit on this?

[@aimenmalik8929]

hello there, i have a query that,if i have a stationary time series data, then no matter how many sub-sequence i get form it. All the sub_seq should should be stationary. but what i observe is p_value is changing,. and even some sub_seq are throwing up p-value to be >0.05(means non-stationary).why is it so ??

[@suvkaka]

Please make a video with mathematical details of ADF

[@dianaayt]

I have a time series with daily values for over 50 years. if i do the ADF if says it is stationary with p-value 0.0000. this is weird cause ACF obviously shows seasonality being the same every 365 days. I tried only doing the ADF in 5 years and it says it is not stationary! Should I divide the series in small sections? I'm very confused why it would say that the complete series is stationary when it is not

[@_Sam_-zh7sw]

Hi Ritvik.....wanted to know if this playlist is in proper sequence? Because how come AR video is after this stationarity video?

[@karimaelouahmani7078]

Thank you so much , but I'm wondering if we still can use the ADF to test the stationarity of a serie that I'm not assuming is an AR(p)

[@keewee235]

nice vid, much appreciated

[@luisakrawczyk8319]

thanks a lot for this video! The theoretical part was explained better than anything I've found online. In the code part I would have liked to see a distinction between drift and trend together with an explanation of the output, that would have been amazing (also in R) :D

[@axe863]

Good video but having moments that are "Changing over time" is not a sufficient condition for non-stationarity. You can have a stochastic reverting dynamics without non-stationarity. A good example of this is being the case is Component Garch. Non-Stationarity is a stronger condition of the moments being a sufficiently smooth function of time.

[@kisholoymukherjee]

Hi @ritvikmath, can you please share the link to the Dickey Fuller Distribution like you said in the video, that it is in the distribution but I can't find it?

[@dodolookr]

Bit counterintuitive that D-F t-stat < DF_crit to rejecct the null.

[@VictorOrdu]

Great explanation. Thank you!

[@waseembaig4625]

I never studied this in my class. Wanted to understand this concept for my MSc dissertation, thank you for explaining it in just 9 minutes!!

[@oliviamomeu6932]

what is the method used for estimating the coefficients? is it OLS(ordinary least squares)?

[@yashgawde610]

At 4:56, when t calculate is less than t critical then we fail to reject null hypothesis.

[@abhinavbhatnagar7796]

I can not find link to Dicky Fuller distribution in the description

[@AndresVeraF]

thanks you very much! your videos helpme a lot

[@DmitryShevkoplyas]

Beautiful! Thank you!

[@esplover1994]

Very nice explanation...thanks :) could you also make a Video on the KPSS-test?

[@ritvikmath]

thanks for the suggestion!

[@TheSambita20]

At 6:08 timestamp of this video whatever the other stuffs you mentioned, i am not able to understand how you derived that, could you please help?

[@ankitbiswas8380]

exactly ...even I couldnt get that part ..were you able to understand that portion later ?

[@QuantYogi]

can anyone pls tell difference btw AR1 and AR2 test from application point of view, I did not want to dig deep into this I am doing this to complete a project (Pair Trading) where I need to check the stationarity of time series, and which method should be followed ?

[@souravdey1227]

Can you please do a video on the intuition of t-distribution

[@user-wr4yl7tx3w]

But to get to stationarity, you had to take the first difference. How is predicting the first difference useful, given that you are interested in making predicting of the original series?

[@allenfiallos5788]

Hey you please make videos on your previous examples with a deeper dive into the math portion. like examples on each model with numbers and perhaps implementing R if possible. Thank you

[@soumo3464]

One request, although you said it's a high level video, please try to explain the code at least. Avoiding that defeats the purpose of the video, that makes one go and search through books and other codes. I realise its helpful if I try to understand it myself but this just makes me devote more and more time to each video and makes me rethink should I watch these videos in the first place. Keeping all these aside your videos are good for beginners.

[@abhishekdas5851]

Hi can you suggest me a book for understanding all these concepts along with VAR? BTW ur teaching method is excellent!

[@yak_music]

Hello, I don't understand why the fact that y(t-1) isn't stationary implies that we can't use the T-Test.

[@kulknira1]

Don't you think H0 and H1 should be exhaustive and should cover all possible values (0, < 1 and > 1 as well). Let me know your thoughts.

[@JoaoVictor-sw9go]

Thank you very muchfor the video! I have a question and would be extremely grateful if anyone could have clarity for me. I'm analyzing some data for my final graduation project and have performed ADF test on a couple of time series for velocity of money in Brazil, and it is a series that visually does't look stationary. My question is: can the ADF test be performed on any time series? Or it has to be an AR compatible (if that makes sense)? Another question is: there a parameter on the ADF test in the statsmodels library for the regression model (if it has constant, trend etc), what do they mean and how do I decide which model I should use? The p-value and stat changes a lot based on the model I select. Thank you again! The videos are great.

[@mikelmenaba]

I believe that the ADF is not telling us if a TS is stationary or not, but telling us if an AR time series model holds a unit root or not. So, I imagine that if your TS is not AR compatible, then the ADF test is not giving you any information on the stationarity of it. So, if I were you, I would first check the AutoCorrelation and PartialAutoCorrelation functions, to see if there is strong correlations with any of the lags. If this is the case, you would be able to assess that this TS has a strong autoregressive component, and then, the ADF test would help you test for stationarity. (I am by no means an expert in the subjects)

[@ap2139]

@ritvikmath I think that there is a little typo in your formula for the ADF test. I believe that the summation shall go from 1 to p-1 rather than from 1 to p

[@kanejiang2938]

I am so confused that when unit Root , the △y is stationary. but the yt is not stationary? why?

[@kanejiang2938]

I got it . becuase the △y is stationary. so Yt is not stationary

[@EricK-bh2sk]

Thank you so much !!!

[@ann-rm3vj]

this is a left tail test ? I concluded this because alt hypothesis has less than sign . Please confirm : )

[@elvistapfuma7970]

you ar brilliant

[@yassinewaterlaw6597]

If delta is =0 that mean that our serie is a random walk with drift ???

[@EvsEntps]

Yes.

[@dr.kingschultz]

How about the case when it is bigger than 1

[@enicay7562]

Thank you

[@YuanzheZhang-c8f]

why you dont prove the seasonality of the ar1

[@patricka0196]

Why do you have your bicycle lock combination tattooed on your arm?

[@ghazypheda]

what mean d sub t in economics ?

[@chillwithme798]

null hypothesis against 1st diff is stationary.

[@wroanee]

I don't understand why there is no absolute of fi! in the unit roots video of yours there was an absolute there on fi.

[@dadimanoj9051]

Why is the alternative hypothesis not equal to 1

[@jwbpark]

Where is dickey fuller distribution video?

[@kewtomrao]

Do you have patreon for me to support this wonderful series?

[@lizzyzhou4954]

First of all, thanks! I subscribed your channel right away. Then, for the unit root, when |phi|=1, that doesn't mean phi=1. How about the case where phi is a complex number? Finally, could you please also make code examples in R? Thanks again!

[@Tapsthequant]

Thank you for the video please let's get into the math too... Thank you

[@DouwSteenkamp]

You can see this man is a true mathematician for writing his "e" as an epsilon🤣

[@ritvikmath]

😂

[@harshitdaga2225]

ye kya ho raha hai? mai kaha aa gya bhaya 🤔

[@lopyus]

lol you look exactly like my stats prof except a few years younger XD

[@prosimulate]

Slick.

[@adamkolany1668]

So what when phi_1>1 ?? You are not conviencing with that what you are saying here …

[@quant-prep2843]

Dont comment here, he will not reply because he don't know

[@VikramSinghT2]

When u difference the lag variables then mu should be zero...

[@lawjef]

Is there any reason this guy places himself in the middle of the video? He is discussing econometrics and he thinks that the viewer needs to see his face not just in the entire video but in the middle of the entire screen. What possible value does that add? Name one other econometrics / maths / statistics / economics / finance channel that thinks “yep, it will help explain the math if I am covering half the screen with my face”. You need a fairly inflated ego to think your face is worth that much YT real estate