Different results in the unit root test. Why?

[angchanyy]

Situation: I had tired a 1000-data generated by random error(i.i.d.), then I sub it into different unit root tests. I got different results among the tests. The following are the test statistics I got:

For R project:
adf.test @ tseries ~ -10.2214 (lag = 9)
ur.df @ urca ~ -21.8978
ur.sp @ urca ~ -27.68
pp.test @ tseries ~ -972.3343 (truncation lag =7)
ur.pp @ urca ~ -973.2409
ur.kpss @ urca ~ 0.1867
kpss.test @ tseries ~ 0.1867 (truncation lag =7)

For MATLAB:
(adf test) ~ -0.43979

Questions:
1. Why there are different test statistics? Even in tests under same test name, say Phillips-perron test (pp.test & ur.pp), they have different test statistics.
2. Don't the Phillips-perron test based on the Dickey-Fuller distribution table? How the value being so negative (-9xx)?
3. What is truncation lag? Is it the same with lag terms?

 

[Future Bruno]

Answers:1. Different test statistics can occur due to different test parameters and methods used by different software packages. For example, the R package uses a different method of calculating the test statistic than the MATLAB package. Additionally, different test parameters may be used in each package, such as the lag option for pp.test and ur.pp.2. The Phillips-Perron test is based on the Dickey-Fuller distribution table, but the results are adjusted for autocorrelation in the data. This can result in a more negative test statistic, which would explain why the values you have are so negative. 3. The truncation lag is related to the lag terms, but it specifies the number of lags to be used in the test, rather than the number of observations used in the test. For example, if the truncation lag is set to 7, the test will only use the first 7 lags.

 

[ravenprp]

1. There are different test statistics because each unit root test has its own assumptions and methodology. These differences can lead to varying results depending on the data being tested. For example, the ADF test assumes a specific trend in the data, while the Phillips-Perron test does not. Additionally, different tests may use different lag lengths or critical values, which can also impact the results. It is important to carefully consider which test is appropriate for your data and to interpret the results accordingly.

2. The Phillips-Perron test is based on the Dickey-Fuller distribution, but it also takes into account the estimated autocorrelation in the data. This can result in negative test statistics, as seen in your results. This does not necessarily mean that the data is stationary, but rather that it does not exhibit a unit root.

3. Truncation lag refers to the number of lagged terms included in the test. This can vary depending on the test being used. In your results, the truncation lag for the PP test and KPSS test is 7, while for the ADF test it is 9. Lag terms refer to the number of lagged differences included in the test. These can also vary depending on the test and the data being used. It is important to understand the differences between these terms and how they may affect the results of the test.