In autoregressive time series models the presence of unit root causes a violation of the assumptions of classical linear regressions. A unit root means that the observed time series is not stationary. When nonstationary time series are used in a regression model one may obtain apparently significant relationships from unrelated variables. This phenomenon is called spurious regression.

One of the most widespread unit root test is the Augmented Dickey Fuller (ADF) test. The standard Dickey Fuller test estimates following equation:

_{}

The case where _{} corresponds to the random walk which is
non-stationary. The Dickey Fuller test tests whether _{}. This t-statistic does not converge
to the normal distribution but instead to the distribution of a functional
of Wiener process.

The Dickey Fuller test is only valid for AR(1) processes. If the time series is correlated at higher lags, the augmented Dickey Fuller test constructs a parameter correction for higher order correlation, by adding lag differences of the time series:

_{}

The order of p could be chosen by minimising information criteria such as Akaike or Schwarz.

**[notes]**

Dickey Fuller show that under the null hypothesis of
a unit root the statistic does not follow the Student t-statistic.
This Add-In interpolate the critical and p-values from a table of
MacKinnon (1991,1996).

The order of differences lags could be chosen by minimising Information
criteria (Akaike, Schwarz, …).

The Add-In includes also two function to calculate critical and p-values.

This Add-In is written in VBA. The source code is not free.

**[related links]**

All links will be open in a new window

fortran program, by MacKinnon, calculates critical and p-values. (HTML)

ADF Test. A brief introduction. (PDF)

Examples os spurios regressions, really funny (PDF)

Links to other sites from these pages are for information only and Kurt Annen accepts no responsibility or liability for access to, or the material on, any site which is linked from or to this site.

screenshot of unit root test (adf-test) add-in

**[download]**

for downloading click on the filename

File: **setup_web-reg_unit-root.exe
**Filesize:

The [web:reg] unit root test (adf test) Add-In was
written by Kurt Annen. This program is freeware. But I would highly
appreciate if you could give me credit for my work by providing me with
information about possible open positions as an economist. My focus
as an economist is on econometrics and dynamic macroeconomics. If you
like the program, please send me an email.

[unit root test (adf-test) add-in]

©
2005 Kurt Annen