Algebra of Integrated Time Series: Evidence from Unit Root Analysis

Abstract

It is argued if xt~I(1) and yt~I(1), then running a regression xt on yt would produce spurious results because et would generally be I(1). However, there may exist a 'b' such that et = xt - byt is I(0), then running a regression xt on yt would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, xt and yt are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if xt~I(dx), yt~I(dy), then zt = bxt cyt ~I(max(dx,dy)). In this research, we offer evidence against this proposition.