Weak Convergence of Multivariate Fractional Processes - (Now published in Stochastic Processes and their Applications, 80 (1999), pp.103-120.)

Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent interest on approximations for partial sums of stationary linear vector sequences. A functional central limit theorem for smoothed processes is analyzed under more general assumptions.Nonstationary fractional integration, functional central limit theorem

Narrow-Band Analysis of Nonstationary Processes

The behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behaviour of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.Nonstationary processes, long-range dependence, least squares estimation, narrow-band estimation, cointegration analysis.

Finite Sample Improvement in Statistical Inference with I(1) Processes

Robinson and Marinucci (1998) investigated the asymptotic behaviour of a narrow-band semiparametric procedure termed Frequency Domain Least Squares (FDLS) in the broad context of fractional cointegration analysis. Here we restrict to the standard case when the data are I(1) and the cointegrating errors are I(0), proving that modifications of the Fully-Modified Ordinary Least Squares (FM-OLS) procedure of Phillips and Hansen (1990) which use the FDLS idea have the same asymptotically desirable properties as FM-OLS, and, on the basis of a Monte Carlo study, find evidence that they have superior finite-sample properties; the new procedures are also shown to compare satisfactorily with parametric estimates.Fully-modified ordinary least squares, finite sample improvements, statistical inference with I(1) processes, Monte Carlo study, parametric estimates.

The Averaged Periodogram for Nonstationary Vector Time Series

Averaged periodogram; nonstationary processes; fractional Brownian motion.Averaged periodogram, nonstationary processes, fractional Brownian motion.

Alternative Forms of Fractional Brownian Motion - (Now published in Journal of Statistical Planning and Inference, 80 (1999), pp.111-122.)

It is pointed out that two contradictory definitions of fractional Brownian motion are well established, one prevailing in the probabilistic literature, the other in the econometric literature. Each is associated with a different definition of nonstationary fractional time series. These various definitions have occasionally led to some confusion. The paper discusses the definitions and attempts a clarification.Frational Brownian motion, nonstationary time series, long-range dependence

Semiparametric Fractional Cointegration Analysis

Fractional cointegration is viewed from a semiparametric viewpoint as a narrow-band phenomenon at frequency zero. We study a narrow-band frequency domain least squares estimate of the cointegrating vector, and related semiparametric methods of inference for testing the memory of observables and the presence of fractional cointegration. These procedures are employed in analysing empirical macroeconomic series; their usefulness and feasibility in finite samples is supported by results of a Monte Carlo experiment.Semiparametric analysis, fractional cointegration.

Narrow-band analysis of nonstationary processes.

The behavior of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behavior of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.

The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

Suitable classification of mortars from ancient roman and renaissance frescoes using thermal analysis and chemometrics

Background Literature on mortars has mainly focused on the identification and characterization of their components in order to assign them to a specific historical period, after accurate classification. For this purpose, different analytical techniques have been proposed. Aim of the present study was to verify whether the combination of thermal analysis and chemometric methods could be used to obtain a fast but correct classification of ancient mortar samples of different ages (Roman era and Renaissance). Results Ancient Roman frescoes from Museo Nazionale Romano (Terme di Diocleziano, Rome, Italy) and Renaissance frescoes from Sistine Chapel and Old Vatican Rooms (Vatican City) were analyzed by thermogravimetry (TG) and differential thermal analysis (DTA). Principal Component analysis (PCA) on the main thermal data evidenced the presence of two clusters, ascribable to the two different ages. Inspection of the loadings allowed to interpret the observed differences in terms of the experimental variables. Conclusions PCA allowed differentiating the two kinds of mortars (Roman and Renaissance frescoes), and evidenced how the ancient Roman samples are richer in binder (calcium carbonate) and contain less filler (aggregate) than the Renaissance ones. It was also demonstrated how the coupling of thermoanalytical techniques and chemometric processing proves to be particularly advantageous when a rapid and correct differentiation and classification of cultural heritage samples of various kinds or ages has to be carried out

X-ray observations of the Compton-thick Seyfert 2 galaxy, NGC 5643

We present results from a ~55 ks long XMM-Newton observation of the obscured AGN, NGC 5643, performed in July 2009. A previous, shorter (about 10 ks) XMM-Newton observation in February 2003 had left two major issues open, the nature of the hard X-ray emission (Compton-thin vs Compton-thick) and of the soft X-ray excess (photoionized vs collisionally ionized matter). The new observation shows that the source is Compton-thick and that the dominant contribution to the soft X-ray emission is by photoionized matter (even if it is still unclear whether collisionally ionized matter may contribute as well). We also studied three bright X-ray sources that are in the field of NGC 5643. The ULX NGC 5643 X-1 was confirmed to be very luminous, even if more than a factor 2 fainter than in 2003. We then provided the first high quality spectrum of the cluster of galaxies Abell 3602. The last source, CXOJ143244.5-442020, is likely an unobscured AGN, possibly belonging to Abell 3602.Comment: 6 pages. Accepted for publication in A&