The unit root can lead to
major problems in economic time series analyses. I obtain the asymptotic
distributions of the ordinary least squares (OLS) estimator when the true model
is trend stationary for the following three cases: 1) the null model is a
random walk without drift, and the auxiliary regression model does not contain
a constant; 2) the null model is a random walk with drift, and the auxiliary
regression model contains a constant; and 3) the null model is a random walk
with drift, and the auxiliary regression model contains both a constant and a
time trend. In the third case, the asymptotic distribution of the OLS estimator
is determined by the first order of the autocorrelation, and we can distinguish
between the random walk and trend stationary models, unlike in previous
studies. Based on these results, the real US gross domestic product is
analyzed. A time trend model with autoregressive error terms is chosen. The
results suggest that the impacts of a shock can become larger than the original
shock in some periods and then gradually decline. However, the impacts continue
for a long period, and policy makers should account for this to design better
economic policies.
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