PHYS 1061 Study Guide - Quiz Guide: Cointegration
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We have 3 cases: <1 (cid:1) t 0 as t . So the shocks to the system gradually die away: =1 (cid:1) t =1 t. So shocks persist in the system and never die away. So just an infinite sum of past shocks plus some starting value of y0: >1. Now given shocks become more influential as time goes on, since if >1, Going back to our 2 characterisations of non-stationarity, the r. w. with drift: yt = + yt-1 + ut and the trend-stationary process yt = + t + ut (1) (2) The two will require different treatments to induce stationarity. The second case is known as deterministic non-stationarity and what is required is detrending. The first case is known as stochastic non-stationarity. = yt - l yt = yt - yt-1. If we take (1) and subtract yt-1 from both sides: yt - yt-1. We say that we have induced stationarity by differencing once .
