Parameter Estimation of Heavy-Tailed AR Model with Missing Data via Stochastic EM

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations is preferred. Another issue that frequently occurs in time series is missing values, due to system data record failure or unexpected data loss. Although there are numerous works about Gaussian AR time series with missing values, as far as we know, there does not exist any work addressing the issue of missing data for the heavy-tailed AR model. In this paper, we consider this issue for the first time, and propose an efficient framework for parameter estimation from incomplete heavy-tailed time series based on a stochastic approximation expectation maximization (SAEM) coupled with a Markov Chain Monte Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and easy to implement. The convergence of the proposed algorithm to a stationary point of the observed data likelihood is rigorously proved. Extensive simulations and real datasets analyses demonstrate the efficacy of the proposed framework.Comment: This is a companion document to a paper that is accepted to IEEE Transaction on Signal Processing 2019, complemented with the supplementary materia

Implications of Globalization for the Output-inflation Relationship: An Assessment

During the past two decades, a growing body of research has explored the implications of increased trade and financial openness for the relationship between output and inflation. This paper reviews proposed theoretical channels through which the degree of openness might ultimately affect the output-inflation trade-off and surveys the empirical studies that have sought to determine the net effect of greater openness on this trade-off. In addition, the paper utilizes a single cross-country data set to evaluate, taking into account recent developments in the literature, the likely sign and significance of this net effect. In particular, we find current data imply that there is a negative and significant relationship between openness and the sacrifice ratio, regardless of the transmission channel that is proposed

Coulomb potentials in two and three dimensions under periodic boundary conditions

A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb's work [R. Sperb, Mol. Simulation, \textbf{22}, 199-212(1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, self-energies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.Comment: Generalization of the work done in cond-mat/0405574. To appear in J. Chem. Physics. A few typos have been correcte

Ultrasensitive interplay between ferromagnetism and superconductivity in NbGd composite thin films

A model binary hybrid system composed of a randomly distributed rare-earth ferromagnetic (Gd) part embedded in an s-wave superconducting (Nb) matrix is being manufactured to study the interplay between competing superconducting and ferromagnetic order parameters. The normal metallic to superconducting phase transition appears to be very sensitive to the magnetic counterpart and the modulation of the superconducing properties follow closely to the Abrikosov-Gorkov (AG) theory of magnetic impurity induced pair breaking mechanism. A critical concentration of Gd is obtained for the studied NbGd based composite films (CFs) above which superconductivity disappears. Besides, a magnetic ordering resembling the paramagnetic Meissner effect (PME) appears in DC magnetization measurements at temperatures close to the superconducting transition temperature. The positive magnetization related to the PME emerges upon doping Nb with Gd. The temperature dependent resistance measurements evolve in a similar fashion with the concentration of Gd as that with an external magnetic field and in both the cases, the transition curves accompany several intermediate features indicating the traces of magnetism originated either from Gd or from the external field. Finally, the signatures of magnetism appear evidently in the magnetization and transport measurements for the CFs with very low (less than 1 at. %) doping of Gd