There are much economic and financial data which are restricted by some bounds, such as expenditure shares, unemployment, norminal interest rate, or target zone exchange rate. How to interpret and analyze time series whose behaviors can be well approximated by means of integrated processes, I(1), but are ¡§limited¡¨ in the sense that their range is constrained by fixed bounded is what this thesis develops. One method to analyze bounded variable of this paper is ¡§The Bounded Unit Root¡¨ which provided by Cavaliere (2005), and the other is using Gibbs sampling simulation and trying to recover the part of hidden variables. We would examin some empirical problems that has often been tackled in the literature and we give three time series which include Danish kron/Deutshe mark, Belgium Franc/ Deutshe mark, and Japan 1 mouth interbank interest rate for examples. We conclude that these three time series data are I(0) in classical unit root test framework, but are all I(1) in The Bounded Unit Root test framework. And the results of Gibbs sampling simulation are that Danish kron/Deutshe mark and Belgium Franc/ Deutshe mark are I(0), but Japan 1 mouth interbank interest rate is I(1).