Unit root?

Can someone dumb down unit root for me? What is it?

If a time series has a unit root, it is not covariance stationary but then all random walks have unit roots.

Question 29 from the CFAI mock morning session: dependent variable exhibits a unit root but the indepedent variables do not. What does this mean and is it good or bad?

A time series has a unit root if the slope coefficient is 1. Refer to the formula:

  • Mean reverting value = b1 / (1 - b0). If b0 = 1 then the series does not have a finite mean reverting level and thus it does not exhibit Covariance Stationery - an important assumption of Autoregressive Models.

  • How to test for unit roots? Use Dickey-Fuller test.

  • How to deal with it? You difference the data. Normally it will be the previous lag so it is called first differencing.

Hope this helps :slight_smile:

That’s correct: all random walks display nonstationarity.


X_t_ = _b_0 + b_1X_t-1

then if _b_1 = 1 is a unit root.

That’s all it means.

Exactly, if the coefficient in an AR(1) is 1, you have a unit root problem. In this case, Xt-Xt-1=b0+et (i.e. random walk with a drift , or just random walk if b0=0). You won’t have a defined mean-reverting level, which is at the foundations of an AR model.

you need to reread the material. it’s pretty important. and you need to remember the rules on comparing data with unit roots / cointegrated series.

**reading 11 is an easy way to pick up points**

Can anyone further explain the answer to question 29 of the 2015 CFAI mock exam? “But the null hypothesis is not rejected for the dependent variable, defective assemblies per hour” - what is the math used behind this conclusion?

I think we are supposed to find a critical value for the t-stat (= about 1.65) and then compare the t-stat of each variable (the dependent variable and the two independent variables) to 1.65 to determine if the null should be rejected or not. Just looking for guidance on which numbers to be pulling out of exhibit 2 to analyze.

Why you are using these regression models, it is to predict. If it is not covariance stationary it just means it cannot be used for models and cannot be used to predict. We know random walks are unit root and have almost perfect correlation with its previous value but it does not mean you can use a random walk model to predict.

“dependent variable exhibits a unit root but the indepedent variables do not. What does this mean and is it good or bad?” - if either of them are unit root then the model is no good. This is question where you use multiple series to model and you need to check for cointegration.

can anyone follow up on this? I’m not sure how to interpret exhibit 2

They say it should be apparent from the t-ratio and significance levels from exhibit 2 whether each variable is signficant or not. So what’s the deal here? is there a critical t-value that we’re comparing the t-statistics to or what is the missing step to find signficance/insignificance in order to reject/fail to reject?

I remember this one. Basically for both independant variables the p value was 0, therefore you can reject H0:

H0 : the serie has a unit root (b1=1).

However for the dependant variable, the p value was high >10% therefore you fail to reject H0 and it may have a unit root