Characteristics of a hypothesis
Habitat Location characteristics of a hypothesis a plant or animal lives.
Hadean Geologic eon that occurred from 3800 to 4600 million years ago. Fundamentals of Physical Geography, 2nd Edition. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. If a root of the process’s characteristic equation is larger than 1, then it is called an explosive process, even though such processes are sometimes inaccurately called unit roots processes.
The presence of a unit root can be tested using a unit root test. If the process has a unit root, characteristics of a hypothesis it is a non-stationary time series. Note that the variance of the series is diverging to infinity with t. Use of OLS relies on the stochastic process being stationary.
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When the stochastic process is non-stationary, the use of OLS can produce invalid estimates. To estimate the slope coefficients, one should first conduct a unit root test, whose null hypothesis is that a unit root is present. If that hypothesis is rejected, one can use OLS. However, if the presence of a unit root is not rejected, then one should apply the difference operator to the series.
If the process has multiple unit roots, the difference operator can be applied multiple times. If it is known that a series has a unit root, the series can be differenced to render it stationary. It is hence called a difference stationary series. The diagram above depicts an example of a potential unit root. The red line represents an observed drop in output.
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