The qualitative difference between stationary and non-stationary AR(1)

[@SpartacanUsuals]

Hi, glad to hear you liked it. I will add that suggestion to my list! Thanks, Ben

[@tonyfang4970]

Sketched the same thing in Python, hope it helps! import numpy as np import pandas as pd import matplotlib import matplotlib.pyplot as plt # define each datapoint as a normal r.v. def generate_datapoint(params): mu = params[0] sigma = params[1] return np.random.normal(mu,sigma) # Set the number of datapoints T = 100 B = pd.Series(index=range(T)) B.name = 'B' for t in range(T): # Now the parameters are dependent on time # Specifically, the mean of the series changes over time params = (t * 0.1, 1) B[t] = generate_datapoint(params) plt.plot(B) plt.xlabel('Time') plt.ylabel('Value') plt.legend(['Series B']);

[@JesseMaurais]

I just mocked up a similar simulation in R, but I animated it, increasing rho by 0.01 from 0 to 1 in each frame, at 2 frames per second, using the same white noise data. Watching how the data changes makes a lot more sense now. Thanks for the videos.

[@SpartacanUsuals]

Hi Jesse, many thanks for your comment and effort reproducing the above in R. Would you mind sharing it below here? I think some people would potentially be interested to reproduce above in R. Best, Ben

[@JesseMaurais]

z = rnorm(1000) gen = function(rho) { x = numeric(length(z)) x[1] = z[1] for (i in 2:length(z)) { x[i] = rho*x[i-1] + z[i] } x } display = function(rho) { x = gen(rho) plot(x, main=as.character(rho)) lines(x) } for (it in 1:100) { display(it/100) Sys.sleep(0.5) }

[@SpartacanUsuals]

Jesse Maurais That's great. Many thanks for this! Am sure it will be useful. Best, Ben

[@IanBorgessen]

Thanks!

[@tonyfang4970]

@@SpartacanUsuals Sketched the same thing in Python, hope it helps! import numpy as np import pandas as pd import matplotlib import matplotlib.pyplot as plt # define each datapoint as a normal r.v. def generate_datapoint(params): mu = params[0] sigma = params[1] return np.random.normal(mu,sigma) # Set the number of datapoints T = 100 B = pd.Series(index=range(T)) B.name = 'B' for t in range(T): # Now the parameters are dependent on time # Specifically, the mean of the series changes over time params = (t * 0.1, 1) B[t] = generate_datapoint(params) plt.plot(B) plt.xlabel('Time') plt.ylabel('Value') plt.legend(['Series B']);

[@debashisbanerjee260]

Amazingly explained. Probably the best video on this topic on internet.

[@asadkhanbb]

@Ben Lambert, I got addicted to your videos on Econometrics. Thanks

[@alvise2165]

GREAT Explanation! now is all more clear!

[@MrScattterbrain]

Ben, thank you so much for these videos on time series. And, in particular, for this one. This answered all little confusions and doubts that I used to have.

[@harshitnarula8449]

Wow this is really helpful..ive been really strugling with econometrics at uni..but these videos are so well explained! Thanks so much..Cheers!

[@luistato7437]

Ben, you are absolutely mental. I really appreciate this, thanks so much!

[@ThuHuongHaThi]

I basically understand this as: the closer rho is towards 1, the more time it takes for the time series to return to its mean

[@elfadlaouielfadel932]

you have explained this course very well.thank you very much.

[@ljw1419]

Really helps, best Time Series Econometrics videos on youtube, thanks !

[@Hatorye]

Yet another amazing video. Thanks, Benny

[@Konzor]

hey ben, Very helpful videos! Thanks for that! But i got a question: is there any playlist which cover the hole time series stuff? Can't find a playlist/course on you channel.

[@schnickerfritzel]

Hi Ben! thank you for posting this video, helps me clear up my confusion :) Although I do wanna clarify one thing: so does this mean that non stationary AR(1) process is synonymous with random walk process? and it also follows a unit root?

[@hedgehog_fox]

Great Matlab demo!

[@arthvini02]

Thanks a lot for this video!

[@johncharles3907]

Can you explain the math again very slowly and clearly? :) Good illustrations!

[@rupikakhanna306]

It was a very useful video for starters. I was wondering if you could post something on ADF and (weak form) stock market efficiency tests.

[@saulmirandaaliaga]

Love your videos, mate! Thank you so much!

[@pedroluque7371]

Hi Ben, thanks for your videos!

[@neodrone1]

Great explanation. Thanks!

[@alexlo6393]

this is a great video!

[@MootBoogie]

what is Rho in this context? like how is it defined? wow this makes so much sense now, thanks!

[@zurzakne-etra7069]

think it's called the autoregressive coefficient...

[@Sam-gn6og]

The explanation of the ARX model you gave is very simplistic, would make a Control Engineer cringe. There is a mathematical stability theory behind the difference equations of the parametric models (ARX.....ARIMAX) Econometrists hardly know about

[@Sam-gn6og]

@Peripo They do...if their analysis is to be taken seriously.

[@alexgold432]

Very good video. The et in the non stationary equation is IID as is the case with the stationary one?

[@nancyaliaga7079]

You legend! Thank you very much for all your videos!

[@javierromera1997]

Thank you Ben

[@mamadoudiaby4474]

Hello sir, I am studing the debt sustainability of WAEMU countries. It is said in littterature that when dependent variable which is primary surplus and independent variable which is debt are both stationary this mean that there is sustainability. In my case both are not stationary and this signals unsustainability of debt. For my GLS regression I am wondering wether I should take those variables in level or differenced them first? Thanks

[@volkanky]

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

[@shreyajain8028]

If there are 2independent and 1 dependent variable in a regression and DF test needs to be applied and the significance of the two independent variables is 0 and for dependent variable it is 0.1156. Which of the variables are having unit roots?

[@kpatel306]

Hi Ben Thanks a lot fort this video. I have a query related to statiority test - do we required series to be stationary while doing the linear regression forecasting? e.g. forecasting based on economic variables. Thanks KP

[@becoruthia]

Thank you, explained a lot.

[@jacinthdavid1122]

Can someone explain how we got the conditional means for AR(1) process? Really confused about that.

[@Institute.research]

need answer if some variables are at level and others are the first difference so what I can do so can go at first difference or at level and how the equation will

[@oscarlu9919]

I think 4:28-4:41 is some kind of intuition to understand the magnitude of p

[@louisbatalha8912]

That is great Sir

[@youngbin0200]

You re just amazing

[@graceliao5978]

you're the best

[@justinlundgren50]

Brilliant! Thanks!

[@dudeB15]

thank you ben

[@gabriellegall8278]

thank you so much

[@Albert-cs1uh]

really helpfull!

[@AngshumanPalKolkata313]

You started with X(0) = 0?

[@tempvariable]

thanks

[@larsahnlandnordfors9170]

What is rho?

[@urabi3tube]

I have a question it might be silly but it's very important, why when we analyse time series we use AR model or MA Arima in others words why we use the lagged values as explanatory variables??? please be advice :)

[@nabeelsyed5228]

Hey Ben i have an exam next wednesday, its basically a stats exam and i have no idea what is going on in it, my prof doesnt know how to teach and i was hoping you could help me out please respond, my exam is covering a couple chapters, ill send u the topic when i get my textbook