Question

Time Series transformation

Let an annual series Yt be stationary. However, the series transformed and differentiated Dt = ln(Yt) - ln(Yt-1) is stationary. Moreover, we suppose that it obeys the following theoretical model: Dt = -0.12 + 0.75 Dt-1 + et, in which the error term and is a white noise of variance σ2 = 0.012.

How can I transform this model to get the original one before the transformation?

Answer 1

As,   we can write ,

and since, the transformed and differentiated series follows model given by -

, where   is white noise with variance 0.012, we can write the original model as -

i.e. will be the original model.