# Covariance Stationary

Only a problem with AR models? Edit: Meaning the lack of…

yes I guess

Anybody actually understand it and want to break it down for me?

I still can’t get a handle on Time Series. I know all the terms but don’t EXACTLY what the procedures are for the models. And this will be an item set – Time Series is mentioned in 3 study sessions. Someone feeling like giving a tutorial?

Tomorrow…

SWEET!

*puts up a tent* I’m ready for the tutorial

Clearnig the grounds, sweeping the floor, holding the flash light firm. I am planning to build a plaster-of-paris barricade otta here to listen to the speech on Time Series from JDV!

In case you forgot…We are waiting JDV… Anish

I’m still at home…Driving to the office for this soon.

Some questions I had on this topic while reviewing last night 1) Linear trends seems to be a “good thing” in linear trend models, but when we get to AR models, they are evidence of non-stationarity and must be corrected? What am I missing? 2) Is stationarity directly related to whether or not there is serial correlation? i.e. Does the fact that a model in non-stationary imply that there is autocorrelation? 3) The text says we can detect covariance stationarity by “running an AR Model and testing correlations” Can you translate? Does this mean looking at the significance of the t stats or something else? 4) The Secrect Sauce says for an AR1 model to be covariance stationary, b1 must be less than zero. Is this right? - I thought it just needed to be less than 1. Thanks JDV! You are our hero! And one last “other time series” question 1) The books really only give treatment to seasonality in the context of AR models, but the log-linear model mentions it as well. If we see a question on seasonality is one model more appropriate than the other?

Joey, seriously you should set up a paypal account so that we can make “donations” to it for all these great tutorials! Thanks!

thanks Joey!!! looking forward for your explanation. spend a whole morning on time series again. now trying to work some questions to reinforce the topic but not arriving anywhere!!

Nerdattax: #4 is a typo in SS.

#4 is not a typo. In order to test if b1=1 you have to perform a dickey-Fuller test (exactly why is beyond our scope). This says that you have to take b1-1 and figure out if it is equal to 0 or not. If b1 is less than zero than not a unit root. If b1 is equal to zero than you have a unit root.

I agree with anish on On #4. it is if b1 - 1 = 0 that it is a unit root, not if b1 = 0. (because the unit root is when b1 = 1).

#4 is not a typo. In order to test if b1=1 you have to perform a dickey-Fuller test (exactly why is beyond our scope). This says that you have to take b1-1 and figure out if it is equal to 0 or not. If b1 is less than zero than not a unit root. If b1 is equal to zero than you have a unit root. i agree. i posted a question on dickey fuller earlier as well.

nerdattax Wrote: ------------------------------------------------------- > Some questions I had on this topic while reviewing > last night > > 1) Linear trends seems to be a “good thing” in > linear trend models, but when we get to AR models, > they are evidence of non-stationarity and must be > corrected? What am I missing? > It’s probably a good thing in your time series models too. You have to correct for them but it’s not so tough. My longest involvement with time series models was not in finance but with the EPA when we would fit airborne pollution models to air sample data. If you are trying to reduce pollution you want that linear trend. Any way you look at it though you have autocorrelated data because pollutants that were there yesterday are probably still there today. > 2) Is stationarity directly related to whether or > not there is serial correlation? i.e. Does the > fact that a model in non-stationary imply that > there is autocorrelation? > Covariance stationarity is about whether the model has the property that the mean doesn’t change and the covariance of X(t) and X(s) depends only on s-t. Data that is non-stationary needs to be made stationary for the time series analysis to work. > 3) The text says we can detect covariance > stationarity by “running an AR Model and testing > correlations” Can you translate? Does this mean > looking at the significance of the t stats or > something else? > At least on the surface it’s like multiple regression. You propose a model, test it, and then check out goodness-of-fit measures like the t-statistics. I don’t think that including observations with significant t-stats and not including others is necessarily the right thing to do but it’s what is in the book. > 4) The Secrect Sauce says for an AR1 model to be > covariance stationary, b1 must be less than zero. > Is this right? - I thought it just needed to be > less than 1. > Right |b1| < 1 does it. This looks like a misprint > Thanks JDV! You are our hero! > > And one last “other time series” question > > 1) The books really only give treatment to > seasonality in the context of AR models, but the > log-linear model mentions it as well. If we see a > question on seasonality is one model more > appropriate than the other? I think seasonality means you fit an AR model.

mwvt9 Wrote: ------------------------------------------------------- > #4 is not a typo. > > In order to test if b1=1 you have to perform a > dickey-Fuller test (exactly why is beyond our > scope). This says that you have to take b1-1 and > figure out if it is equal to 0 or not. > > If b1 is less than zero than not a unit root. If > b1 is equal to zero than you have a unit root. This might be - I would say testing whther b1=1 or b1 - 1 = 0 is about the same.

Joey comes through again! Many thanks for all the answers & insight!