A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

Modelling spillover effects in spatial stochastic frontier analysis

In the last two decades, authors have begun to expand classical stochastic frontier (SF) models in order to include also some spatial components. Indeed, firms tend to concentrate in clusters, taking advantage of positive agglomeration externalities due to cooperation, shared ideas and emulation, resulting in increased productivity levels. Until now scholars have introduced spatial dependence into SF models following two different paths: evaluating global and local spatial spillover effects related to the frontier or considering spatial cross-sectional correlation in the inefficiency and/or in the error term. In this thesis, we extend the current literature on spatial SF models introducing two novel specifications for panel data. First, besides considering productivity and input spillovers, we introduce the possibility to evaluate the specific spatial effects arising from each inefficiency determinant through their spatial lags aiming to capture also knowledge spillovers. Second, we develop a very comprehensive spatial SF model that includes both frontier and error-based spillovers in order to consider four different sources of spatial dependence (i.e. productivity and input spillovers related to the frontier function and behavioural and environmental correlation associated with the two error terms). Finally, we test the finite sample properties of the two proposed spatial SF models through simulations, and we provide two empirical applications to the Italian accommodation and agricultural sectors. From a practical perspective, policymakers, based on results from these models, can rely on precise, detailed and distinct insights on the spillover effects affecting the productive performance of neighbouring spatial units obtaining interesting and relevant suggestions for policy decisions.

Modeling the spatial dynamics of economic models

The advances that have been characterizing spatial econometrics in recent years are mostly theoretical and have not found an extensive empirical application yet. In this work we aim at supplying a review of the main tools of spatial econometrics and to show an empirical application for one of the most recently introduced estimators. Despite the numerous alternatives that the econometric theory provides for the treatment of spatial (and spatiotemporal) data, empirical analyses are still limited by the lack of availability of the correspondent routines in statistical and econometric software. Spatiotemporal modeling represents one of the most recent developments in spatial econometric theory and the finite sample properties of the estimators that have been proposed are currently being tested in the literature. We provide a comparison between some estimators (a quasi-maximum likelihood, QML, estimator and some GMM-type estimators) for a fixed effects dynamic panel data model under certain conditions, by means of a Monte Carlo simulation analysis. We focus on different settings, which are characterized either by fully stable or quasi-unit root series. We also investigate the extent of the bias that is caused by a non-spatial estimation of a model when the data are characterized by different degrees of spatial dependence. Finally, we provide an empirical application of a QML estimator for a time-space dynamic model which includes a temporal, a spatial and a spatiotemporal lag of the dependent variable. This is done by choosing a relevant and prolific field of analysis, in which spatial econometrics has only found limited space so far, in order to explore the value-added of considering the spatial dimension of the data. In particular, we study the determinants of cropland value in Midwestern U.S.A. in the years 1971-2009, by taking the present value model (PVM) as the theoretical framework of analysis.

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Joint value at risk: a new conditional risk measure

In this PhD thesis a new firm level conditional risk measure is developed. It is named Joint Value at Risk (JVaR) and is defined as a quantile of a conditional distribution of interest, where the conditioning event is a latent upper tail event. It addresses the problem of how risk changes under extreme volatility scenarios. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. A feasible class of nonparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the two stage M-estimator are derived, and a simulation study is reported to illustrate its finite-sample properties. Parametric estimation methods are also discussed. The relation with the VaR is exploited to introduce a volatility contribution measure, and a tail risk measure is also proposed. The analysis of the dynamic JVaR is presented based on asymmetric stochastic volatility models. Empirical results with S&P500 data show that accounting for extreme volatility levels is relevant to better characterize the evolution of risk. The work is complemented by a review of the literature, where we provide an overview on quantile risk measures, elicitable functionals and several stochastic orderings.

Mars delivery service - development of the electro-mechanical systems of the Sample Fetch Rover for the Mars Sample Return Campaign

This thesis describes the development of the Sample Fetch Rover (SFR), studied for Mars Sample Return (MSR), an international campaign carried out in cooperation between the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The focus of this document is the design of the electro-mechanical systems of the rover. After placing this work into the general context of robotic planetary exploration and summarising the state of the art for what concerns Mars rovers, the architecture of the Mars Sample Return Campaign is presented. A complete overview of the current SFR architecture is provided, touching upon all the main subsystems of the spacecraft. For each area, it is discussed what are the design drivers, the chosen solutions and whether they use heritage technology (in particular from the ExoMars Rover) or new developments. This research focuses on two topics of particular interest, due to their relevance for the mission and the novelty of their design: locomotion and sample acquisition, which are discussed in depth. The early SFR locomotion concepts are summarised, covering the initial trade-offs and discarded designs for higher traverse performance. Once a consolidated architecture was reached, the locomotion subsystem was developed further, defining the details of the suspension, actuators, deployment mechanisms and wheels. This technology is presented here in detail, including some key analysis and test results that support the design and demonstrate how it responds to the mission requirements. Another major electro-mechanical system developed as part of this work is the one dedicated to sample tube acquisition. The concept of operations of this machinery was defined to be robust against the unknown conditions that characterise the mission. The design process led to a highly automated robotic system which is described here in its main components: vision system, robotic arm and tube storage.

Cross-population radio galaxies as a test of the jet-accretion relationship

Radio galaxies (RGs) are extremely relevant in addressing important unknowns concerning the interaction among black hole accretion, radio jets, and the environment. In the classical scheme, their accretion rate and ejection of relativistic jets are directly linked: efficient accretion (HERG) is associated with powerful edge-brightened jets (FRIIs); inefficient accretion (LERG) is associated with weak edge-darkened jets (FRIs). The observation of RGs with an inefficient engine associated with edge-brightened radio emission (FRII-LERGs) broke this scheme. FRII-LERGs constitute a suitable population to explore how accretion and ejection are linked and evaluate the environment's role in shaping jets. To this aim, we performed a multiwavelength study of different RGs catalogs spanning from Jy to mJy flux densities. At first, we investigated the X-ray properties of a sample of 51 FRIIs belonging to the 3CR catalog at z<0.3. Two hypotheses were invoked to explain FRII-LERGs behavior: evolution from classical FRIIs; the role of the environment. Next, we explored the mJy sky by studying the optical-radio properties of hundreds of RGs at z<0.15 (Best & Heckman 2012 sample). FRII-LERGs appear more similar to the old FRI-LERGs than to the young FRII-HERGs. These results point towards an evolutive scenario, however, nuclear time scale changes, star population aging, and kpc-Mpc radio structure modification do not agree. The role of the Mpc environment was then investigated. The Wen et al. 2015 galaxy clusters sample, built exploiting the SDSS survey, allowed us to explore the habitat of 7219 RGs at z<0.3. Most RGs are found to live in outside clusters. For these sources, differences among RG classes are still present. Thus, the environment is not the key parameter, and the possibility of intrinsic differences was reconsidered: we speculated that different black hole properties (spin and magnetic field at its horizon) could determine the observed spread in jet luminosity.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.