Title: Linear trends, fractional trends and initial conditions
Authors: Heiko Rachinger - University of Vienna (Austria) [presenting]
Abstract: Efficient estimation is analyzed for linear trends in long memory time series. First, we consider the case of a long memory Type II error process and show that a generalized least squares (GLS) estimator that corrects the serial correlation of the error term is efficient. Second, we take into account an initial condition which bridges the two alternative definitions of long memory, Type I and Type II. In this case, a weighted least estimator (WLS), which is the efficient estimator for Type I, outperforms the GLS even for short initial conditions. It reaches efficiency when the initial condition becomes more remote. Consequently, the choice between the two estimators depends on presence and length of the initial condition. In order to illustrate the methodology, we estimate the GDP growth rates of three countries and test whether these rates are positive.