On observation-driven time series modeling

Koopman, S.J. [Promotor]Blasques Albergaria Amaral, F. [Copromotor

Missing observations in observation-driven time series models

We argue that existing methods for the treatment of missing observations in time-varying parameter observation-driven models lead to inconsistent inference. We provide a formal proof of this inconsistency for a Gaussian model with time-varying mean. A Monte Carlo simulation study supports this theoretical result and illustrates how the inconsistency problem extends to score-driven and, more generally, to observation-driven models, which include well-known models for conditional volatility. To overcome the problem of inconsistent inference, we propose a novel estimation procedure based on indirect inference. This easy-to-implement method delivers consistent inference. The asymptotic properties of the new method are formally derived. Our proposed estimation procedure shows a promising performance in a Monte Carlo simulation exercise as well as in an empirical study concerning the measurement of conditional volatility from financial returns data

Realized wishart-garch:A score-driven multi-Asset volatility model

We propose a novel multivariate GARCH model that incorporates realized measures for the covariance matrix of returns. The joint formulation of a multivariate dynamic model for outer-products of returns, realized variances, and realized covariances leads to a feasible approach for analysis and forecasting. The updating of the covariance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while the analysis relies on straightforward computations. In a Monte Carlo study, we show that parameters are estimated accurately for different small sample sizes. We illustrate the model with an empirical in-sample and out-of-sample analysis for a portfolio of 15 U.S. financial assets

On the optimality of score-driven models

Score-driven models have been recently introduced as a general framework to specify time-varying parameters of conditional densities. %The underlying idea is to specify a time-varying parameter as an autoregressive process with innovation given by the score of the associated log-likelihood. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback–Leibler divergence between the true conditional density and the postulated density of the model. A key limitation of such an optimality property is that it holds only locally both in the parameter space and sample space, yielding to a definition of local Kullback–Leibler divergence that is in fact not a divergence measure. The current paper shows that score-driven updates satisfy stronger optimality properties that are based on a global definition of Kullback–Leibler divergence. In particular, it is shown that score-driven updates reduce the distance between the expected updated parameter and the pseudo-true parameter. Furthermore, depending on the conditional density and the scaling of the score, the optimality result can hold globally over the parameter space, which can be viewed as a generalization of the monotonicity property of the stochastic gradient descent scheme. Several examples illustrate how the results derived in the paper apply to specific models under different easy-to-check assumptions, and provide a formal method to select the link-function and the scaling of the score

Highlights from the Pierre Auger Observatory

The Pierre Auger Observatory is the world's largest cosmic ray observatory. Our current exposure reaches nearly 40,000 km$^2$ str and provides us with an unprecedented quality data set. The performance and stability of the detectors and their enhancements are described. Data analyses have led to a number of major breakthroughs. Among these we discuss the energy spectrum and the searches for large-scale anisotropies. We present analyses of our X$_{max}$ data and show how it can be interpreted in terms of mass composition. We also describe some new analyses that extract mass sensitive parameters from the 100% duty cycle SD data. A coherent interpretation of all these recent results opens new directions. The consequences regarding the cosmic ray composition and the properties of UHECR sources are briefly discussed.Comment: 9 pages, 12 figures, talk given at the 33rd International Cosmic Ray Conference, Rio de Janeiro 201

A search for point sources of EeV photons

Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10^17.3 eV to 10^18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm^-2 s^-1, and no celestial direction exceeds 0.25 eV cm^-2 s^-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.Comment: 28 pages, 10 figures, accepted for publication in The Astrophysical Journa

Reconstruction of inclined air showers detected with the Pierre Auger Observatory

We describe the method devised to reconstruct inclined cosmic-ray air showers with zenith angles greater than $60^\circ$ detected with the surface array of the Pierre Auger Observatory. The measured signals at the ground level are fitted to muon density distributions predicted with atmospheric cascade models to obtain the relative shower size as an overall normalization parameter. The method is evaluated using simulated showers to test its performance. The energy of the cosmic rays is calibrated using a sub-sample of events reconstructed with both the fluorescence and surface array techniques. The reconstruction method described here provides the basis of complementary analyses including an independent measurement of the energy spectrum of ultra-high energy cosmic rays using very inclined events collected by the Pierre Auger Observatory.Comment: 27 pages, 19 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP

The Pierre Auger Observatory III: Other Astrophysical Observations

Astrophysical observations of ultra-high-energy cosmic rays with the Pierre Auger ObservatoryComment: Contributions to the 32nd International Cosmic Ray Conference, Beijing, China, August 201

Azimuthal asymmetry in the risetime of the surface detector signals of the Pierre Auger Observatory

The azimuthal asymmetry in the risetime of signals in Auger surface detector stations is a source of information on shower development. The azimuthal asymmetry is due to a combination of the longitudinal evolution of the shower and geometrical effects related to the angles of incidence of the particles into the detectors. The magnitude of the effect depends upon the zenith angle and state of development of the shower and thus provides a novel observable, $(\sec \theta)_\mathrm{max}$, sensitive to the mass composition of cosmic rays above $3 \times 10^{18}$ eV. By comparing measurements with predictions from shower simulations, we find for both of our adopted models of hadronic physics (QGSJETII-04 and EPOS-LHC) an indication that the mean cosmic-ray mass increases slowly with energy, as has been inferred from other studies. However, the mass estimates are dependent on the shower model and on the range of distance from the shower core selected. Thus the method has uncovered further deficiencies in our understanding of shower modelling that must be resolved before the mass composition can be inferred from $(\sec \theta)_\mathrm{max}$.Comment: Replaced with published version. Added journal reference and DO