# Unit root test

In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.

## General approach

In general, the approach to unit root testing implicitly assumes that the time series to be tested ${\displaystyle [y_{t}]_{t=1}^{T}}$  can be written as,

${\displaystyle y_{t}=D_{t}+z_{t}+\varepsilon _{t}}$

where,

• ${\displaystyle D_{t}}$  is the deterministic component (trend, seasonal component, etc.)
• ${\displaystyle z_{t}}$  is the stochastic component.
• ${\displaystyle \varepsilon _{t}}$  is the stationary error process.

The task of the test is to determine whether the stochastic component contains a unit root or is stationary.[1]

## Main tests

Other popular tests include:

Unit root tests are closely linked to serial correlation tests. However, while all processes with a unit root will exhibit serial correlation, not all serially correlated time series will have a unit root. Popular serial correlation tests include:

## Notes

1. ^ Kočenda, Evžen; Alexandr, Černý (2014), Elements of Time Series Econometrics: An Applied Approach, Karolinum Press, p. 66, ISBN 978-80-246-2315-3.
2. ^ Dickey, D. A.; Fuller, W. A. (1979). "Distribution of the estimators for autoregressive time series with a unit root". Journal of the American Statistical Association. 74 (366a): 427–431. doi:10.1080/01621459.1979.10482531.