When studying time series, I once heard the statement that
unit root test is less powerful.
I hereby have two questions:
- What does it mean for a test to be powerful?
- What causes the unit root test to be less powerful?
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3For the concept of power, please [search our site](http://stats.stackexchange.com/search?q=power+analysis+hypothesis). "Less powerful" has no intrinsic meaning; your second question can only be answered if you tell us to what the unit root test is being compared. – whuber Jan 02 '14 at 21:36
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1[Power](http://en.wikipedia.org/wiki/Statistical_power) is the probability of rejecting the null when its false. As whuber says, you can search on the site; there's a particular example of a power comparison [here](http://stats.stackexchange.com/questions/80856/how-to-calculate-power-of-different-normality-tests-such-as-shapiro-wilk-ryan-t/80960#80960), for example. As for what causes a test to be less powerful, generally speaking, against some particular alternative, it's because there's information in the data that the test it's being compared to is using better than it. – Glen_b Jan 03 '14 at 00:30
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Without more information about what it's being compared to and under what specific alternative, it's hard to say much. – Glen_b Jan 03 '14 at 00:31
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I'm voting to close this question as off-topic because part of it has been answered and the other part cannot be answered. – Peter Flom Aug 11 '18 at 13:48