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Unformatted text preview: 1 Nonstationary stochastic processes Stationary processes satisfy E[x t ] = Var[x t ] = 2 < Cov[x s ,x t ] = t-s all independent of t Many economic series do not satisfy these conditions E[GDP 1970 ] > E[GDP 1870 ] Hence they are nonstationary and cannot be represented using AR or MA models Deterministic nonstationarity Suppose the mean of a series is a linear trend x t = + t + e t where e t is stationary. x t is nonstationary t = + t a function of t but the derived series e t is stationary Hence we can analyse time series properties of x t by detrending it. This type of nonstationarity is called deterministic nonstationarity Deterministic trend models applied to economic data often show spurious breaks in trend. This means that the estimated parameters change over time UK GDP at factor cost (log) 1965-99 Actual and linear trend 4.1 4.3 4.5 4.7 4.9 5.1 Mar-65 Mar-70 Mar-75 Mar-80 Mar-85 Mar-90 Mar-95 GDP Factor cost Linear Trend 2 Deterministic forecasts - levels Deterministic nonstationarity also implies that forecasts have certain intuitively implausible properties The uncertainty about any forecast for a future time period s (neglecting parameter uncertainty) is Var(e s ) = 2 the same for all s Uncertainty about the level...
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This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.
- Spring '10