Essays on Estimation and Forecasting Under Structural Break Models
This dissertation covers topics in estimation and forecasting under structural breaks, in
time-series and panel data models.
Chapter two considers the linear structural breaks model with m breaks (m + 1
regimes), and aim in improving the estimation of the parameters within each regime. We
form an optimal combined estimator of regression parameters based on combining restricted
estimator under the restriction of no breaks in the parameters, with unrestricted estimator
which considers the observations within each regime separately. We derive the analytical
finite sample risk and asymptotic risk and show that the risk of the combined estimator is
less than the unrestricted estimator. The simulation study and the empirical example of
forecasting the U.S. output growth confirm our theoretical findings.
Chapter three develops an optimal combined estimator to forecast out-of-sample
under structural breaks. We propose the combined estimator of the post-break estimator
with the full-sample estimator which uses all observations in the sample. Using a local
asymptotic framework, we obtain the asymptotic risk for the combined estimator and show
that it is strictly less than the risk of the post-break estimator, which is a common solution
for forecasting under structural breaks. We also introduce a semi-parametric estimator. Using a discrete kernel, this estimator assigns full weight of one to the post-break observations
and down-weights the pre-break sample observations. The kernel is found by cross validation. Simulation study and the empirical example of forecasting equity premium confirm
our analytical findings.
Chapter four proposes an efficient Stein-like shrinkage estimator for estimating the
slope parameters in the heterogeneous panel data models with cross-sectional dependence.
We combine the unrestricted estimator with the restricted one. The unrestricted estimator
estimates the parameters by considering the break points and only uses the observations
within each regime, while the restricted estimator estimates the parameters under the restriction of no breaks in the coefficients. We show analytically that the asymptotic risk of
the combined estimator is less than the unrestricted estimator. We also show the superiority of the combined estimator over the unrestricted estimator in terms of the mean square
forecast error. Simulation study verifies the main results of this chapter.