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 bOLS denote the OLS estimate of b from a particular sample. Let T be the sample size.
Then the test statistic T*(bOLS
-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.
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