Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

This post shows how to interpret the results of the augmented Dickey-Fuller (ADF) test easily with the help of Hank Roark’s R function. His R function provides kind descriptions of the results of a unit root ADF test. I explains why this description is consistent with the ADF hypothesis test.

# Easy Interpretations of ADF Test

The purpose of this and previous post are to be familiar with the ADF test.

In the previous post below, we have implemented ADF test for a unit root by using ur.df() function in urca R library.

In particular, we have encountered the some case where there may or may not be either trend or drift or both. In addition, it is a little time-consuming to interpret the results of the ADF test. Fortunately, Hank Roark provides a R function which generates the description of the ADF test result. Owing to this convenient R function, we can easily summarize the output of ADF test and save our time.

We use the same data as in the previous post and perform the ADF test whether the LRY time series contains a unit root or not.

### Hank Roark’s R function

Hank Roark’s R function can be found at https://gist.github.com/hankroark/968fc28b767f1e43b5a33b151b771bf9. I just added three lines to dislpay the formula of model.

### Interpretation

For the case of the LRY level variable, we have the following results which indicate the presence of a unit root. This is the same interpretations as in the previous post.

For the case of the LRY 1st diff. variable, we have the following results which indicate no unit root. This is also the same interpretations as in the previous post. In particular, this test displays some warning messages regarding the some inconclusive terms.

As can be seen in the previous post, logarithm of real income contains a unit root and can be stationary time series by differencing the first order.

### Structure of Hypothesis Testing

Now let’s understand the way Hank Roark’s R function deliver the output. I made the following summary table of the 3rd ADF regression model with a drift amd a trend for your better understanding.
From the above table, the case of the level of LRY corresponds to the (tau2 not rejected, phi3 not rejected, ph2 not rejected) which indicates the presence of a unit root and the absence of drift and trend. In contrast, the case of the 1st difference of LRY corresponds to the (tau2 rejected, phi3 rejected, ph2 rejected) which indicates no unit root but indecisive drift and trend.

### Concluding Remarks

In this post, we use Hank Roark’s R function to get output descriptions of ADF test. Since this is easy to use, it can be applied to VAR or VECM or some machine learning models which requires stationarity of variables. $$\blacksquare$$