My dissertation research is composed of two parts: a theoretical part on semiparametric efficient estimation and an applied part in energy economics under different dynamic settings. The essays are related in terms of their applications as well as the way in which models are constructed and estimated. In the first essay, efficient estimation of the partially linear model is studied. We work out the efficient score functions and efficiency bounds under four stochastic restrictions---independence, conditional symmetry, conditional zero mean, and partially conditional zero mean. A feasible efficient estimation method for the linear part of the model is developed based on the efficient score. A battery of specification test that allows for choosing between the alternative assumptions is provided. A Monte Carlo simulation is also conducted.
The second essay presents a dynamic optimization model for a stylized oilfield resembling the largest developed light oil field in Saudi Arabia, Ghawar. We use data from different sources to estimate the oil production cost function and the revenue function. We pay particular attention to the dynamic aspect of the oil production by employing petroleum-engineering software to simulate the interaction between control variables and reservoir state variables. Optimal solutions are studied under different scenarios to account for the possible changes in the exogenous variables and the uncertainty about the forecasts.
The third essay examines the effect of oil price volatility on the level of innovation displayed by the U.S. economy. A measure of innovation is calculated by decomposing an output-based Malmquist index. We also construct a nonparametric measure for oil price volatility. Technical change and oil price volatility are then placed in a VAR system with oil price and a variable indicative of monetary policy. The system is estimated and analyzed for significant relationships. We find that oil price volatility displays a significant negative effect on innovation. A key point of this analysis lies in the fact that we impose no functional forms for technologies and the methods employed keep technical assumptions to a minimum.
We propose a new class of dynamic patent count panel data models that is based on dynamic
conditional score (DCS) models. We estimate multiplicative and additive DCS models, MDCS and ADCS
respectively, with quasi-ARMA (QARMA) dynamics, and compare them with the finite distributed lag,
exponential feedback and linear feedback models. We use a large panel of 4,476 United States (US)
firms for period 1979 to 2000. Related to the statistical inference, we discuss the advantages and
disadvantages of alternative estimation methods: maximum likelihood estimator (MLE), pooled
negative binomial quasi-MLE (QMLE) and generalized method of moments (GMM). For the count
panel data models of this paper, the strict exogeneity of explanatory variables assumption of MLE fails
and GMM is not feasible. However, interesting results are obtained for pooled negative binomial
QMLE. The empirical evidence shows that the new class of MDCS models with QARMA dynamics
outperforms all other models considered.
Oil is perceived as a good diversification tool for stock markets. To fully
understand this potential, we propose a new empirical methodology that combines
generalized autoregressive score copula functions with high frequency data and
allows us to capture and forecast the conditional time-varying joint
distribution of the oil -- stocks pair accurately. Our realized GARCH with
time-varying copula yields statistically better forecasts of the dependence and
quantiles of the distribution relative to competing models. Employing a
recently proposed conditional diversification benefits measure that considers
higher-order moments and nonlinear dependence from tail events, we document
decreasing benefits from diversification over the past ten years. The
diversification benefits implied by our empirical model are, moreover, strongly
varied over time. These findings have important implications for asset
allocation, as the benefits of including oil in stock portfolios may not be as
large as perceived.
Joint models initially dedicated to a single longitudinal marker and a single
time-to-event need to be extended to account for the rich longitudinal data of
cohort studies. Multiple causes of clinical progression are indeed usually
observed, and multiple longitudinal markers are collected when the true latent
trait of interest is hard to capture (e.g. quality of life, functional
dependency, cognitive level). These multivariate and longitudinal data also
usually have nonstandard distributions (discrete, asymmetric, bounded,...). We
propose a joint model based on a latent process and latent classes to analyze
simultaneously such multiple longitudinal markers of different natures, and
multiple causes of progression. A latent process model describes the latent
trait of interest and links it to the observed longitudinal outcomes using
flexible measurement models adapted to different types of data, and a latent
class structure links the longitudinal and the cause-specific survival models.
The joint model is estimated in the maximum likelihood framework. A score test
is developed to evaluate the assumption of conditional independence of the
longitudinal markers and each cause of progression given the latent classes. In
addition, individual dynamic cumulative incidences of each cause of progression
based on the repeated marker data are derived. The methodology is validated in
a simulation study and applied on real data about cognitive aging coming from a
large population-based study. The aim is to predict the risk of dementia by
accounting for the competing death according to the profiles of semantic memory
measured by two asymmetric psychometric tests.
This version is the author accepted manuscript. The final version is available from Wiley at http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12081/full.; A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta distribution of the
second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight forward theory for the asymptotic distribution of the maximum likelihood estimator. Score driven models of this kind can also be based on conditional t-distributions, but whereas these models carry out what, in the robustness literature, is called a soft form of trimming, the
EGB2 distribution leads to a soft form of Winsorizing.
An EGARCH model based on the EGB2 distribution is also developed. This model complements the score driven EGARCH model with a conditional t-distribution. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.
In dynamic conditional score models, the innovation term of the dynamic specification is the score of the conditional distribution. These models are investigated for non-negative variables, using distributions from the generalized beta and generalized gamma families. The log-normal distribution is also considered. Applications to the daily range of stock market indices are reported and models are fitted to duration data.
A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight-forward theory for the asymptotic distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 distribution and the model is fitted to exchange rate data. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.
We compare two EGARCH models which belong to a new class of models in which the dynamics are driven by the score of the conditional distribution of the observations. Models of this kind are called dynamic conditional score (DCS) models and their form facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The EGB2 distribution is light-tailed, but with higher kurtosis than the normal. Hence it is complementary to the fat-tailed t. The EGB2-EGARCH model gives a good fit to many exchange rate return series, prompting an investigation into the misleading conclusions liable to be drawn from tail index estimates.
We analyse the Generalised Hyperbolic distribution as a model for fat tails and asymmetries in multivariate conditionally heteroskedastic dynamic regression models. We provide a standardised version of this distribution, obtain analytical expressions for the log-likelihood score, and explain how to evaluate the information matrix. In addition, we derive tests for the null hypotheses of multivariate normal and Student t innovations, and decompose them into skewness and kurtosis components, from which we obtain more powerful one-sided versions. Finally, we present an empirical illustration with UK sectorial stock returns, which suggests that their conditional distribution is asymmetric and leptokurtic.