unit root: Information from Answers.com

In time series models in econometrics a unit root is present if the autoregressive representation of a variable y_t, the coefficient | b | is equal to 1 in , where y_t is the variable of interest at time t, b is the slope coefficient, and is a white noise error component. Whenever a unit root is present, the time series is said to be non-stationary or integrated of order one or I(1) according to Engle terminology.

Problems when a unit root exists:

The assumptions of the classical regression model state that both the dependent and the independent variable must be stationary and that the disturbance term must have a mean of zero and a finite variance. When the variables are non-stationary the use of OLS can produce invalid estimates. Such estimates Granger and Newbold (1974) called 'Spurious regression' results: high R² values and low t-ratios yielding results with no economic meaning.

Properties and Characteristics of Unit Root Processes:

• Shocks to a unit root process have permanent effects, they do not decay as it is the case with stationary processes.
• Non-stationary processes have no long-run means to revert to after a shock.
• Their variance is time dependent and it goes to infinity as t goes to infinity.
• I(1) processes can be rendered stationary and used for OLS estimation by taking their first differences Δy_t = y_t - y_{t - 1}

See also

• Dickey-Fuller test
• Augmented Dickey-Fuller test
• Phillips-Perron test (PP)
• Weighted Symmetric Unit Root Test (WS)