Dickey Fuller test for unit root
Вставка
- Опубліковано 8 вер 2024
- This video explains how the Dickey Fuller test can be used to test for the presence of a unit root in a series, and how this can be viewed a test for whether a series is non-stationary. Check out ben-lambert.co... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.co... Accompanying this series, there will be a book: www.amazon.co....
God bless you Ben Lambert!
God doesn't exist
@@hexoonable Really ?
I wish you could combine your excellent general explanations with concrete examples
Thanks for posting this video. It s very helpful in clarifying how stationarity is tested with the DF.
this is the best lecturer of all time
Hi, if the value of the magnitude of the t statistic is greater than the critical value then you should reject the null hypothesis of a unit root. Hope that helps. Thanks, Ben
You all probably dont care at all but does anyone know a trick to log back into an instagram account?
I was stupid forgot my login password. I love any tricks you can give me
@Elliott Mack instablaster =)
@Zane Turner I really appreciate your reply. I found the site on google and Im waiting for the hacking stuff now.
Takes a while so I will get back to you later with my results.
@Zane Turner it worked and I now got access to my account again. Im so happy:D
Thank you so much you saved my account :D
@Elliott Mack Happy to help :D
Could you also provide us with an actual example, just to see how it all comes together, thanks and great job by the way!
I don't fully capture yet, but I'll use it as quick remedy for my exam tmr. Thanks for great video!
Great Explanation!
This is so helpful even in 2020!
Amazing video !
First of all, thanks for the series, I'm currently taking an "advanced econometric methods & applications" class in my master year and i'm bingewatching this like it's game of thrones...
But I have a question... at the beginning of this video you say that if alpha = 0 you would have a random walk. But I thought from previous videos that a random walk would require rho to be 1 at the same time?
Gr
G
+Gert Thielemans No, Rho being equal to one is not a necessarily condition for the random walk process.
Hi @Ben! Can you please go into a bit more detail on how having p = 1 makes the series non-stationary and p < 1 makes it stationary? Not quite clear on that. Thanks!
The variance for series in the AR(1) model comes as inversely proportional to (1-p^2). Since the variance for a stationary series must be positive and constant, it has to be less than 1
This is simple model of AR(1) :
X_t = alpha + rho * X_(t-1) + e_t
That model applies to every point, So that means
X_(t-1) = alpha + rho * X_(t-2) + e_(t-1)
Thus, u can unravel the first model into
X_t = alpha + rho * ( alpha + rho * X_(t-2) + e_(t-1) ) + e_t
Suppose we ignore the alpha and errors/residuals
X_t = rho * X_(t-1) = rho² * X_(t-2) = rho³ * X_(t-3) = rho^n * X_(t-n)
I will always love you.
Under the alternative hypothesis (rho
Thanks Ben
Could please explain or guide me to a good explanation for the actuall concept of a unit root :]
if abs(t) is less than the critical DF value we accept the null not reject it
I am bit confused. To avoid the problem of non stationarity (which will hinder inference) we had first changed the regression eq to change in Xt = delta Xt + et. where delta is 1-p. When the matter gets solved here, then why there will be a problem in calculation of estimated values of delta?(referring to 3:46)
So with the Dickey-Fuller test, we are basically testing for the stationarity of the series ONLY in terms of the variance, right? Because if there is a constant term (i.e., alpha =/= 0), then regardless if rho is equal to 1 (as in the null hypothesis) or less than 1, the series is still non-stationary in general because, with a constant term, the series will have a trend and the expected value of the series is not constant at zero. Is this correct?
Youre the Goat
Why does rho
If alpha is non-zero, then the change in X per time will cause X to always accumulate more and more alphas. Doesn't this alone imply that the mean of X is changing over time, thus X is non-stationary? How could I possibly have X be stationary if alpha is non-zero?
Edit: I think I figured it out. It is indeed not strictly stationary. Instead, it would be trend-stationary.
Wow. Thanks mate!
Hi Ben, I understand the gyst of it, thanks! Could you explain in simple terms what a unit root is? Our textbook is pretty confusing... Thanks! Great videos!
I noticed that he didn't respond so I'll just take the liberty of doing it. Unit root simply means that rho = 1. Saying something is a "unit root random process" is simply saying that rho = 1 in that random process. As you can see above, the rho = 1 would mean that the equation would be nonstationary. So the presence of unit root = nonstationary process
Thanks Natasha
I have an interesting question. If we reject H0, so we say there's no presence of a unit root. Then do we reject the martingale too? Because there's no unpredictable pattern, then prices for example, are based on erlier events?
Good video!
what a great guy
5:00 "if the t is less than some critical value from the DF distribution then under no circumstance do we reject the null hypothesis" - ...but you wrote t < DF --> reject Ho..... I'm so confused, what you wrote seems opposite of what you said
"only in *those* circumstances" not "under no circumstances"
Hello , I have a question, when I manually find the Dickey Fuller statistic value, the statistic value is very slightly different from the value generated from the Eviews program, although I use the same data, what is the reason?,, I mean the normal Dickey Fuller test, not the developer
why the coefficient of the lagged variable on unit root testing must be negative when you run the model in EVIEWS for exemple ?
Thanks
Shouldn't the alternate hypothesis be mod(rho)
Hi, Can I clarify:
I can see how unit root implies difference stationary, and how rho < 1 implies stationary, rho => non-stationary.
But I see that the ADF test is used as a test for stationary, but it seems determining the UR doesn't determine anything about the stationarity of the non-differenced series? Is this correct?
I have a question please help me ; I have a export data but ı reach the trend stationary process, so can I use this data for VAR analysis? how can I transform the trend stationary process to sationary process
May I know is unit root test is a must for time series data? And why?
Could you please tell me why is the case rho greater than 1 not included?
Hi, This is because rho > 1 would represent an explosive series, which is typically not encountered in real life. Hope that helps, Best, Ben
thank you for clarifying. Really like the whole econometric series. Regards
Hi, Ben, at the beginning of the video, you said it was important for linear regressions to have stationary time series. Did you mean only the time series linear regression or all including for example, multiple linear regressionds using time series data?
+CH H Hi, thanks for your comment. It's for all types of time series regression. Best, Ben
Hi there! Could you please explain why its the alpha term that determines the stochasticity of the model rather than the rho term? Can't you have a stochastic/time series with drift with a constant?
Hi Ben . thank you so much for the videos. I understand everything that you have mentioned but can you please tell me how will I read the MacKinnon's Critical Value as required in the ned? like what is n ? and also to decide which one like constant, constant and trend and constant . Thank you .
what if we get mixed results of the three models at levels i.e C, C&T and None
Question, if a variable does not have a unit root... it is stationary or non stationary? Or is the dickey-fuller test not rejected?
what if rho is GREATER than 1 ??
@3:05 why pho
When Rho (in absolute value actually) is less than one, one can prove that the expectation, the variance and the autocovariance of the series do not dependent on the time t. Therefore the series is covariance stationary
Correct. You need some mental acrobatics here. It will also imply xt is stationary and therefore delta x is stationary. Adding to the previous answer, it will not only be covariance but also variance stationary.
its was really a wonderful lecture sir..i am checking stationary in stata. but i am confused what are the guidelines for unit root test. mean if the absolute value of t-statistic is grater than critical value at 5% level of significance then do we accept the null hypothesis or reject it ( ignoring the negative signs of critical value)..can you plzz help bro ?
Thanks for the explanation. I dont understand why t-test cannot be used here inspite of your explanation. Also why does not CLT apply for non-stationary series. Could you help me understand that part a bit more
Chidhu R his previous videos on time series should clarify that! Regards
cool !!
What if p = -1?
Hi Ben. At 1:15 you say that if rho is < 1, the time series is stationary. I don't quite understand why it should be "< 1" as opposed to it being "0". Lets say rho = 0.5 < 1, then the equation would be Xt = A + rho Xt-1 + e. Or even if rho = -1 < 1. How can this be a stationary process? Thanks!!
He is talking about an AR(1) Process...since there is a time lag of 1 i.e X(t-1). For any AR(1) process a condition for stationarity is that rho must be less than 1...This is a condition so just remember it...
Ad H Thx, but I don't think that answers my question. Just to go back to the equation, the alpha = A term is the drift and the last Et is the random variable that causes the random walk. If Xt = A + rho [Xt-1] + e, then I completely see why it's not-stationary if rho = 1. But if rho = 0.99999999 < 1, how can that change the classification from non-stationary to stationary? A conceptual answer would be much appreicated. Thanks.
We know the mean of process say Yt=Sum from i=0 to infinity (rho to power i ) x (e subscript t-i)..this si a standard formula form back substitution of Yt..but from this we command that Modulus Rho
Pasan Hapuarachchi If you are still wondering about the condition on rho look in my comment above where i explained it in detail :)
I had a question. Can dickey fuller be used for a MA series too, for example if there are elements of AR and MA in my data distribution can I use the dickey fuller test's result as the final deciding factor for stationarity?
Can you answer your question now?
Can anybody help me in one question? If -1
+Gabriel Cheng Sorry, I made a mistake. What I mean is what will be the difference in the test result between ρ
Can you explain what you mean by "so it's not a problem" at 3:00 and "we're better off than we were in this place" at 3:15? I don't know what you're referring to by a "problem" or being in a "better" place...
You wont be able get t stat under other case
I wish my teacher could teach us like that lol
hey thanks for the vids!!! quickk Q why is alpha in the Xt-Xt-1 eqn surely it would go? :)
we're just subtracting X_(t-1) from both sides of the equation.
@@frodo3332 Thanks man I was looking exatcly for that in the comment section
why you keep mentioning central limit theorem please? I don't understand how that has anything to do with you hypothesizing delta=0/row=1? Thank you!
Lizi zhu When the process is non stationary standard assumptions for asymptotic analysis do not hold. Therefore the central limit theorem doesn't apply.
Lizi zhu Hi Lizi you are from Cardiff phd economics class right?
Lizi zhu It means if it is not stationary it doesnt converges to mean asymptotically. I think
gabrielwong1991 Gabriel?
gabrielwong1991 how did it go with the section B of the assignment? can you send me your email-address/contact at 14razy@gmail.com?
Where exactly does the condition rho < 1 come from?
Hey Alex. I have tried explaining it beneath. Too bad the youtube comment section does not support any sort of math-type. Anyways here goes.
For x_t to be stationary you need rho
x_t = a+ pa + p^2 x_(t-2) + p e_(t-1) + e_t
I will just do one more substitution and then finish the pattern:
x_t = a + pa + p^2 [a+p x_(t-3) + e_(t-2)] + p e_(t-1) + e_t
x_t = a + pa + p^2 a + p^3 x_(t-3) + p^2 e_(t-2) + p e_(t-1) + e_t
going along tracking the series all the way back to x_0 then gives:
x_t = a [1+p+p^2+...+p^(t-1)] + p^t * x_0 + e_t + p e_(t-1) + p^2 e_(t-2) + ...+p^(t-1) e_1
Now lets take the expectation of this remembering that you have assumed that the e's were independent and identically distributed with mean zero.
E[x_t|x_0] = a[1+p+p^2+...+p^(t-1)] + p^t x_0
Now lets consider what happens to the two terms IF rho is numerically less than 1 i.e. -1 < p < 1.
As for the first term it's a geometric series: en.wikipedia.org/wiki/Geometric_series. Then the first term converges to:
a/(1-p) and the second term p^t x_0 is an exponentially decaying function converging to zero as t goes to infinity.
And that is stationarity of the time series i.e. the mean has an attractor and is pushed away from this by the error term.
Now consider the unit-root case, i.e. p = 1. Then the geometric series a[1+p+p^2+...+p^(t-1)] does not converge to anything at all! It wanders up and down arbitrarily given fully by the shocks to the error term.
The last case (not so interesting for economists and other social scientists because it is very rare). pho > 1. Then the series explodes towards infinity (just look at the term p^t *x_0.
Aegis90 Thanks for answering this question so thoroughly. Much appreciated. Best, Ben
Hey Ben. No problem. I'm currently studying for my finals in this topic (among others) and it helps me just as well explaining it to others :)
@@Aegis90 Hi, can you please explain how is central limit theorem playing role her. Because he mentioned multiple times ?
@@snehgupta4115 under CLT, we can use t-statistics. If not, we cannot.
Ahhh im confused lets take it from the beginning. On the first model with Xt. The null hypothesis is Ho: absolute value of ρ=1 which implies unit-root which implies non-stationarity! Ha: absolute value of ρ
Hi, thanks for your message. Ok, I think that the confusion lies here in your interpretation of the use of the second regression (the one in differences.) You are correct with the null hypothesis of the levels series being non-stationarity. We are not interested in whether the differences regression is stationary - we know it always is if the levels is an AR1 process. However, we can use this second regression to test whether the first is stationary, by carrying out a coefficient test on the delta. This test has the null of delta=0, so non-stationarity, and an alternative of delta
Hi Ben.First of all really thanks for this super-quick reply.Much appreciate it.Just a last clarification.When you say [..] This test has the null of delta=0, so non-stationary[..] when you say Non-stationary you are talking about the first model now. Correct?
your volume is too low