Unit root?

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hei.so

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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 :)
 
hei.so wrote:If a time series has a unit root, it is not covariance stationary but then all random walks have unit roots.
Click to expand...
That’s correct: all random walks display nonstationarity.
 
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.
 
hei.so wrote:
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?
Click to expand...
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**
 
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