**Definition:**A Dickey-Fuller test is an econometric test for whether a certain kind of time series data has an autoregressive unit root.

In particular in the time series econometric model
y[t] =
by[t-1] + e[t], where
t is an integer greater than zero indexing time, and
b=1, let
b^{OLS}
denote the OLS estimate of
b from a particular sample.
Let T be the sample size.

Then the test statistic T*(b^{OLS}
-1) has a known, documented distribution. Its value in a particular sample
can be compared to that distribution to determine a probability that the
original sample came from a unit root autoregressive process; that is,
one in which b=1.

(Econterms)

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