Asymptotic Mean Square Error and Convergence Rates for

The 6th ICSA International Conference
21 - 23 July 2004, Singapore
Asymptotic Mean Square Error and Convergence Rates for
Stochastic Trend Estimation
Department of Statistics, University of California, Davis, USA
The focus of this paper is on trend estimation for a general state-space model
Yt=t+t, where the dth difference of the trend {t} is assumed to be i.i.d. and
the error sequence {t} is assumed to be a mean zero stationary process. A
fairly precise asymptotic expression of the mean square error is derived for the
estimator obtained by penalizing the dth order differences. Optimal rate of
convergence is obtained and it is shown to be ''asymptotically equivalent'' to a
nonparametric estimator of a fixed trend model of smoothness of order d-.5. A
criterion for selecting the penalty parameter and degree of difference d is
given along with an application to the global temperature data.