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I am having some troubles with the unit root test. The are some concepts that I do not fully understand. Could you please tell me if what I write in the following four passages is correct? I am new to the concept so please bear with me :-)

1) "If we do not consider white noise, when the value of the characteristic equation is equal to 1, meaning that the time series possesses a unit root, the time series is stationary. On the other hand, if the value is different from 1, this means that the time series is non-stationary."

2) "Simplifying and not considering white noise, we can state, that there are three main forms of non-stationarity for a time series: trend, drifts or both. A time series having a drift, is a time series whose variance changes over time. A time series having a trend is a time series whose average changes over time. A time series having a drift and a trend is a time series whose variance and mean change over time."

3) "If the coefficient given to any one of the variables in an AR model is different from one, then the time series presents non-stationarity and random walk theory is violated. By contrast, if we have a unit root, then the time series does not possess a trend nor a drift and the random walk hypothesis is valid in the analyzed time period."

4) "In a Unit Root Test, the null hypothesis is that the time series possesses a unit root. This implies that the time series has neither a trend nor a drift and this further implies that the random walk theory is valid in that time series."

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