variables behave differently, the conventional asymptotic theory cannot be appli- cable. When the order of integration is different, the variance of each process behave differently. For example, if Yt is an I(O) variable and Xt is I(1), the OLS estimator from the regression Yt on Xt converges to zero asymptotically, since the denominator of the OLS estimator, the variance of Xt, increase as t increase and thus it dominates the numerator the covariance between Xt and Yt. That the OLS estimator does not have an asymptotic distribution.(It is degenerated with the conventional normalization of VT. See Ch. 21 for details) 2.2 Comparison of Trend-stationary and Differencing Stationary Process The best way to under the meaning of stochastic and deterministic trend is to compare their time series properties. This section compares a trend-stationary process(6)with a unit root process(4)in terms of forecasts of the series, variance of the forecast error, dynamic multiplier, and transformations needs to achieve atonality 2.2.1 Returning to a Central Line The TSP model( 6) has a central line u+at, around which, Xt oscillates. Even if shock let Xt deviate temporarily from the line there takes place a force to bring it back to the line. On the other hand, the unit root process(5) has no such a central line. One might wonder about a deterministic trend combined with a ran- dom walk. The discrepancy between Yt and the line Yo +at, became unbounded ast→∞o 2.2.2 Forecast Erro The TSP and unit root specifications are also very different in their implications for the variance of the forecast error. For the trend-stationary process( 6), the svariables behave differently, the conventional asymptotic theory cannot be appli￾cable. When the order of integration is different, the variance of each process behave differently. For example, if Yt is an I(0) variable and Xt is I(1), the OLS estimator from the regression Yt on Xt converges to zero asymptotically, since the denominator of the OLS estimator, the variance of Xt , increase as t increase, and thus it dominates the numerator, the covariance between Xt and Yt . That is, the OLS estimator does not have an asymptotic distribution. (It is degenerated with the conventional normalization of √ T. See Ch. 21 for details) 2.2 Comparison of Trend-stationary and Differencing -Stationary Process The best way to under the meaning of stochastic and deterministic trend is to compare their time series properties. This section compares a trend-stationary process (6) with a unit root process (4) in terms of forecasts of the series, variance of the forecast error, dynamic multiplier, and transformations needs to achieve stationarity. 2.2.1 Returning to a Central Line ? The TSP model (6) has a central line µ + αt, around which, Xt oscillates. Even if shock let Xt deviate temporarily from the line there takes place a force to bring it back to the line. On the other hand, the unit root process (5) has no such a central line. One might wonder about a deterministic trend combined with a ran￾dom walk. The discrepancy between Yt and the line Y0 + αt, became unbounded as t → ∞. 2.2.2 Forecast Error The TSP and unit root specifications are also very different in their implications for the variance of the forecast error. For the trend-stationary process (6), the s 6