## Wednesday, November 25, 2015

### Unit Root Testing on Wrong Assumptions on DGP

I have shown a tutorial video on ADF unit root test. In the video I have data generated and tested the unit root test and showed how the ADF test can behave when the assumptions are mis-specified.

In the time series among many following three equations are important. These equations are given as:
${{Y}_{t}}=\rho {{Y}_{t-1}}+{{e}_{t}}$
${{Y}_{t}}=\alpha +\rho {{Y}_{t-1}}+{{e}_{t}}$
${{Y}_{t}}=\alpha +\beta t+\rho {{Y}_{t-1}}+{{e}_{t}}$

In all these equation the nature of time series will significantly differ depending upon the value $\rho$. If the value of $\left| \rho \right|<1$ then the series will be stationary, if $\left| \rho \right|=1$ then the series will be non-stationary and $\left| \rho \right|>1$ then the series will be explosive.

See the video here:

A non stationary process:

## Tuesday, November 10, 2015

### Exact process to do ADF Unit Root Test

Exact process to do ADF Unit Root Test
Here is my video post in which I have shown the exact process to perform an ADF Unit Root test with the real dataset. I have also shown what happens with the ADF values when we mis-judge the assumptions. Further below, I have shown the the step wise process with a flowchart diagram.

Exact process to do ADF Unit Root Test
• A.1 See the p-value of ADF Test
• A. 2 if p-value is less than level of significance usually 5%
(reject the null hypothesis of unit root), thus the data is stationary. STOP the process
B. if p-value is greater than 5% level of significance
• B.1 then see the p-value of estimated trend
• B.2 if p-value < 5%, then the data has unit root.
Stop the process and repeat the process on difference data from initial step.
C. if p-value > 5%, then the trend is insignificant, Go to step-2.
• C.1 See the P value of ADF Test
• C.2  if p-value is less than level of significance usually 5%
(reject the null hypothesis of unit root), thus the data is stationary. STOP the process
D. if p-value is greater than 5% level of significance
• D.1 then see the p-value of estimated intercept
• D.2 if p-value < 5% for estimated intercept then the data has unit root. Stop the process and repeat the process on difference data from initial step.
E. if p-value > 5% for estimated intercept then the intercept is insignificant, Go to step-2.
• E.1 See the P value of ADF Test
• E.2  if p-value is less than level of significance usually 5% (reject the null hypothesis of unit root), thus the data is stationary. STOP the process
F. if p-value is greater than 5% level of significance then the data is non stationary. Stop the process and repeat the process on difference data from initial step.

Here, In a Diagram, I have shown a stylized picture.

Source: Pfaff, B. (2008) Analysis of Integrated and Cointegrated Time Series with R. Second Edition. Springer, New York