The Dickey-Fuller test is a test that uses the statistics to know the presence of a stochastic trend behavior in time series of the variables that make up the test, by means of a hypothesis test.

In other words, the Dickey-Fuller test will help us to know if there is a significant presence of trend in the time series of the variables that we are analyzing. For this, a hypothesis test will be carried out that allows knowing the veracity of said trend.

## What is the Dickey-Fuller test for?

This contrast is applied in econometría (branch of economics that uses mathematical and statistical models to explain economic systems, events or interpretations of the economy and the market) in order to verify whether or not there is a trend in the time series.

In addition, to analyze these types of trends, the Dickey-Fuller test is the easiest to use, compared to other tests that are more complex and require more knowledge or analyze other types of facts that do not interest us.

## Dickey-Fuller approach and calculation

To be able to carry out this test, we must set a null hypothesis that will be the presence of this stochastic trend in the observations we make, compared to an alternative: the non-stochastic trend in the observations.

To know whether or not there is a trend in an autoregression, in a time series in an AR (1) model, the first regressor has to tend to 1 or be very close. This is because of the mean reversion property in a stationary stochastic process.

If the first coefficient of an AR (1) model is close to 1, the longer it takes for the observations to return to the mean value. The stochastic trend in the observations is given as a function of the number that we assign to the first regressor of the autoregression, which will be the contrasted one.

The hypotheses will be:

- H0 (null): Stochastic tendency in time series
- H1 (alternative): No stochastic trend in time series