| dc.description.abstract | This thesis contributes to four distinct fields on the econometrics literature:
forecasting macroeconomic variables using large datasets, volatility modelling,
risk premium estimation and iterative estimators. As a research output,
this thesis presents a balance of applied econometrics and econometric
theory, with the latter one covering the asymptotic theory of iterative estimators
under different models and mapping specifications. In Chapter
1 we introduce and motivate the estimation tools for large datasets, the
volatility modelling and the use of iterative estimators.
In Chapter 2, we address the issue of forecasting macroeconomic variables
using medium and large datasets, by adopting vector autoregressive
moving average (VARMA) models. We overcome the estimation issue that
arises with this class of models by implementing the iterative ordinary least
squares (IOLS) estimator. We establish the consistency and asymptotic
distribution considering the ARMA(1,1) and we argue these results can be
extended to the multivariate case. Monte Carlo results show that IOLS is
consistent and feasible for large systems, and outperforms the maximum
likelihood (MLE) estimator when sample size is small. Our empirical application
shows that VARMA models outperform the AR(1) (autoregressive
of order one model) and vector autoregressive (VAR) models, considering
different model dimensions.
Chapter 3 proposes a new robust estimator for GARCH-type models:
the nonlinear iterative least squares (NL-ILS). This estimator is especially
useful on specifications where errors have some degree of dependence over
time or when the conditional variance is misspecified. We illustrate the
NL-ILS estimator by providing algorithms that consider the GARCH(1,1),
weak-GARCH(1,1), GARCH(1,1)-in-mean and RealGARCH(1,1)-in-mean
models. I establish the consistency and asymptotic distribution of the NLILS
estimator, in the case of the GARCH(1,1) model under assumptions
that are compatible with the quasi-maximum likelihood (QMLE) estimator.
The consistency result is extended to the weak-GARCH(1,1) model
and a further extension of the asymptotic results to the GARCH(1,1)-inmean
case is also discussed. A Monte Carlo study provides evidences that
the NL-ILS estimator is consistent and outperforms the MLE benchmark
in a variety of specifications. Moreover, when the conditional variance is
misspecified, the MLE estimator delivers biased estimates of the parameters
in the mean equation, whereas the NL-ILS estimator does not. The
empirical application investigates the risk premium on the CRSP, S&P500
and S&P100 indices. I document the risk premium parameter to be significant
only for the CRSP index when using the robust NL-ILS estimator.
We argue that this comes from the wider composition of the CRPS index,
resembling the market more accurately, when compared to the S&P500 and
S&P100 indices. This nding holds on daily, weekly and monthly frequencies
and it is corroborated by a series of robustness checks.
Chapter 4 assesses the evolution of the risk premium parameter over
time. To this purpose, we introduce a new class of volatility-in-mean model,
the time-varying GARCH-in-mean (TVGARCH-in-mean) model, that allows
the risk premium parameter to evolve stochastically as a random walk
process. We show that the kernel based NL-ILS estimator successfully estimates
the time-varying risk premium parameter, presenting a good finite
sample performance. Regarding the empirical study, we find evidences that
the risk premium parameter is time-varying, oscillating over negative and
positive values.
Chapter 5 concludes pointing the relevance of of the use of iterative estimators
rather than the standard MLE framework, as well as the contributions
to the applied econometrics, financial econometrics and econometric
theory literatures. | en_US |
