What is kpss application test
A test which is used for test the null hypnothesis of stationary against the alternative of unit root.This test is also knows as most powerful test.When a non stationary data is concerned with a shift it is unconditionally volatility of the unit root.
The test of kpss is fail to detect ,if null hypnothesis test is confirmed by the kpss test.Then we perform a complementry test which is enabling us to test the null hypnothesis of the homogenitys of the unconditionally variance against the alternate of time of the un-co ditional volatility.
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Defination of complementry test
The test of KPSS stationarity is full based on null hypnothesis of the absense random walk.In the hypnothesis of null (yt) is stationary around the level r0
Yt = r0 + et t=1 …… T
We can define the KPSS Stastic as follows
Full form of KPSS Test is the kwiatkowski Phillips schmidt shin.This test is based on linear regression which breaks up a series into the three parts a deterministic term (Bt) , random wal (rt) and a stationary test error (et)
Xt = rt + Bt + E1 when the data is stationary around a fix level .this test uses ols for find the eqation which is depended on where you want to rest a level stationary or trend stationary. IT is simplified version without the time trend component which is used to test level stationary
The KPSS data is normally transformed in log before the running test for run any exponential trends into linear ones
Running the KPSS Test
Note when you writing spss doesn’t have any option for this test in R kpss.test (x,null = c (“level”,”trend”) , [short = true ) where X is a numerical vector or univariate time series null is “level ” or (trend ( you can also written as “L” or “T” / Lshort indicates if the short versin (True) or long version (fails ) should be used
Interpreting the result
I kpss test the author derived one sided Lm statistics for the test when the stats of Lm is greater than the critical value the the hypnothesis of null is rejected by the test and compare to your choser alpha level. For example’ p – value is = 0.002 (2%) would cause the null hypnothesis istl to be rejected at an alpha level of 0.05 (5%)
The main disadvantage of the KPSS test is that It have a hight rate of type 1 error (which is tends to reject the nill hypnothesis too much) .if we attempts to control these error (by having the larger p values ) then that negatively impacts the test power
There is a way to deal with the potential for high type 1 error the combination of the kpss with an ADF test.If the result from both test Suggest that the series is stationary ,the it is probably.