Stationarity and Cointegration analysis

Stationarityand Cointegration analysisBy Tinashe Unit root testing Cointegration Vector Auto-regressions Cointegration in Multivariate systems introduction Stationarityorotherwiseofaseriescanstron glyinfluenceitsbehaviourandproperties. Forinstancea shock diesawaywithstationaritybutispersistenti fnonstationary. Spuriousregressions -ifvariablesaretrendedovertimeitmayprodu cesignificantcoefficientsandhighR2butiti sameaninglessrelationship. Twotypesoftrend StochasticTrend-[randomwalk] DeterministicTrend Whydistinguishbetweenthem? Maylookthesamebuthaveverydifferentproper tiesDeterministic trendsDeterministic trends Taking the first difference of a trend stationary series removes the non-stationaritybut at the cost of introducing an MA(1) process in the invertible MA process cannot be written as an AR processDeterministic trendStochastic trends Consider the followingStochastic trends Take this process forward Speriods in time: As S approaches infinity the values of Y do not become independent of the error terms; and the drift term increases over time This process is know as the stochastic trend because it is dependent on the drift and the stochastic progression of error termsStochastic trendDetecting unit root-dickey fuller tests Dickey and Fuller (Fuller, 1976; Dickey)

Introduction •Modern econometric analysis emphasise the importance of unit root testing in conducting empirical econometric work. •Granger and Newbold (1974) non-stationary data yield misleading or spurious regression results i.e. regressions that do not make sense e.g

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