● Why there are so many unit root testing ?
The answer lies within the test and the power of the test.
The size entails out on the level of the significance i.e. the probability of committing Type I error (alpha).
The Power of the test: The probability of rejecting Ho when Ho is false.
Power is calculated by subtracting the probability of Type II error.
Say, probability of the Type II error is beta.
So, Power = 1 - beta.
The maximum power is 1 (if probability of accepting a false hypothesis is 0)
In most of the unit root tests:
Ho: Non Stationary
Ha: Stationary.
Say that if the first model is a true model is a true model, we estimate the 2nd model (when the pure random walk in there we estimate 2nd model).
If thr process is stationary @ 5 % i.e. alpha = 5% then the Null hypothesis is rejected.
However, this is not the true level of significance, this is the nominal level of significance, the true level of significance is much higher.
If we experiment in the different models the true level of significance appears to be different. This is hence pointed out by "Lowell".
Most of the Dicky Fuller tests have less power. They tend to accept Ho more frequently (to accept a false Ho repeatedly).
The reasons are - power depends on the span of the data (power s high when the span is larger) 30 obs in 30 yrs - more power (high span), 100 obs in 100 days - less power (low span).
》Say that if phi (coefficient of the main equation) is nearly = 1, say 0.95 (not strictly equal to 1, we mag declare the test non stationary).
》If we have more than one unit, then test is Dicky Pandulene.
》If there are structural breaks, then the conventional units will not catch the structural breaks and Token Watson discusses non stationarity arises due to 2 errors, viz.
♢ one will be stochastic trend (the conventional unit root will capture this.
♢ structural breaks (conventional unit root procedure will not catch this issue).
Again Madalla and Kim rejected the acceptance of ADF due to its low power, its inability to detect structural breaks etc.
Reference: My guru Prof Thomachan, University of Calicut, Kerala.
To be contd...
Thank you
Aditya Pokhrel
MBA, MA Economics, MPA.
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