ECON217_HW_UnitRoot

ECON217_HW_UnitRoot - H.W. (unitroot) 1. Consider a...

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1 H.W. (unitroot ) 1. Consider a Difference Stationary Model X t - X t-1 = β + ε t , where ε t is a stationary ARMA term and X 0 = α . a. Rewrite X t as a function of α , β and ε i . b. Verify that the variance of X t is t-dependent and ε t has a permanent effect on X t . c. Show that the variance of the forecast error X t+h - E(X t+h I t ) increases as h increases. d. Show that we cannot obtain a stationary series by removing a trend term from X t . e. Which data transformation should be used to achieve stationarity? 2. Consider a Trend stationary model X t = α + β t + ε t , where ε t is a stationary ARMA term. a. Verify that the variance of X t is t invariant and the effect of ε t on X t dissipates asymptotically. b. Show that the variance of the forecast error X t+h - E(X t+h I t ) is (asymptotically) constant.
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This note was uploaded on 09/29/2010 for the course ECON Econometri taught by Professor Fairlie during the Winter '09 term at UCSC.

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