Jump to content

Unit root test

From Wikipedia, the free encyclopedia

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

[edit]

In general, the approach to unit root testing implicitly assumes that the time series to be tested can be written as,

where,

  • is the deterministic component (trend, seasonal component, etc.)
  • is the stochastic component.
  • 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

[edit]

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

[edit]
  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.

References

[edit]