I'm trying to model a time series variable that represents a percentage, strictly bounded between 0 and 1, that is also non-stationary about the mean.
Is there a model form that is able to account for non-stationary behavior while producing forecasts within the [0,1] interval?
I came across the following work while researching the topic which I believe could be extended to answer this particular question (just a hunch based on a quick reading):
Park, Joon Y., and Peter CB Phillips. "Nonlinear regressions with integrated time series." Econometrica 69.1 (2001): 117-161.
Park, Joon Y., and Peter CB Phillips. "Nonstationary binary choice." Econometrica 68.5 (2000): 1249-1280.
Hu, Ling, and Robert de Jong. Nonstationary Censored Regression. mimeo, Ohio State Uni, 2006.
Unfortunately, I'm unaware of any implementation (preferably in
R) of the ML estimators discussed.
Per Alecos' requests, below is a plot of the series that led to this question
and the de-trended series