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correction: for intercept+trend: H0: the coefficient of Y(t-1) = 0 => the data needs to be differenced to make it stationary (regardless of the trend) H1: the coefficient of Y(t-1) < 0 => the data follows a Trend Stationary Process (TSP) and you need to include the "time" variable in the ...

True, you should start testing for trend and intercept at first, BUT you should do this at level (i.e. no differences taken). in this case the Hypotheses are: H0: the trend coefficient = 0 => the data has no trend and needs to be differenced to make it stationary H1: the trend coefficient < 0 => the...

Create a new varaible ddy=d(y,2) [or d(d(y))] which is the double difference. When performing the unit root test, choose the 2 difference option to gea test for I(4). alternatively, if you want to actaully use the variable in its fourth difference form, then create it: 1-right click>new object> sere...