I have a non-stationary series and a stationary differenced series, the differences have a (small) non-zero mean. I am wondering how we interpret that in terms of the original series. As the differences will revert to and move around the mean (-0.12) the original series will tend to 'drift' downwards? Is this what is meant by a stochastic drift (as opposed to a deterministic drift)?
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It means that your sequence heads downward over time, since the differences tend to be less than 0.
Stochastic drift can be removed by first differencing, it is drift in the random walk caused by repeated >0 or <0 observations of the noise parameter.
Deterministic drift is seen as caused by some component "x" can be removed by adding an appropriate function based on that "x" prior to differencing. X is commonly time.
