Forecasting unstable processes

Previous analysis on forecasting theory either assume knowing the true parameters or assume the stationarity of the series. Not much are known on the forecasting theory for nonstationary process with estimated parameters. This paper investigates the recursive least square forecast for stationary and nonstationary processes with unit roots. We first prove that the accumulated forecast mean square error can be decomposed into two components, one of which arises from estimation uncertainty and the other from the disturbance term. The former, of the order of $\log(T)$, is of second order importance to the latter term, of the order T. However, since the latter is common for all predictors, it is the former that determines the property of each predictor. Our theorem implies that the improvement of forecasting precision is of the order of $\log(T)$ when existence of unit root is properly detected and taken into account. Also, our theorem leads to a new proof of strong consistency of predictive least squares in model selection and a new test of unit root where no regression is needed. The simulation results confirm our theoretical findings. In addition, we find that while mis-specification of AR order and under-specification of the number of unit root have marginal impact on forecasting precision, over-specification of the number of unit root strongly deteriorates the quality of long term forecast. As for the empirical study using Taiwanese data, the results are mixed. Adaptive forecast and imposing unit root improve forecast precision for some cases but deteriorate forecasting precision for other cases.Comment: Published at http://dx.doi.org/10.1214/074921706000000969 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Radial Angular Momentum Transfer and Magnetic Barrier for Short-Type Gamma-Ray Burst Central Engine Activity

Soft extended emission (EE) following initial hard spikes up to 100 seconds was observed with {\em Swift}/BAT for about half of short-type gamma-ray bursts (SGRBs). This challenges the conversional central engine models of SGRBs, i.e., compact star merger models. In the framework of the black hole-neutron star merger models, we study the roles of the radial angular momentum transfer in the disk and the magnetic barrier around the black hole for the activity of SGRB central engines. We show that the radial angular momentum transfer may significantly prolong the lifetime of the accretion process and multiple episodes may be switched by the magnetic barrier. Our numerical calculations based on the models of the neutrino-dominated accretion flows suggest that the disk mass is critical for producing the observed EE. In case of the mass being $\sim 0.8M_{\odot}$, our model can reproduce the observed timescale and luminosity of both the main and EE episodes in a reasonable parameter set. The predicted luminosity of the EE component is lower than the observed EE with about one order of magnitude and the timescale is shorter than 20 seconds if the disk mass being $\sim 0.2M_{\odot}$. {\em Swift}/BAT-like instruments may be not sensitive enough to detect the EE component in this case. We argue that the EE component would be a probe for merger process and disk formation for compact star mergers.Comment: 9 pages, 3 figures, accepted for publication in Ap

Imputing unknown competitor marketing activity with a Hidden Markov Chain

We demonstrate on a case study with two competing products at a bank how one can use a Hidden Markov Chain (HMC) to estimate missing information on a competitor's marketing activity. The idea is that given time series with sales volumes for products A and B and marketing expenditures for product A, as well as suitable predictors of sales for products A and B, we can infer at each point in time whether it is likely or not that marketing activities took place for product B. The method is successful in identifying the presence or absence of marketing activity for product B about 84% of the time. We allude to the issue of whether, if one can infer marketing activity about product B from knowledge of marketing activity for product A and of sales volumes of both products, the reverse might be possible and one might be able to impute marketing activity for product A from knowledge of that of product B. This leads to a concept of symmetric imputation of competing marketing activity. The exposition in this paper aims to be accessible and relevant to practitioners

In-Process Global Interpretation for Graph Learning via Distribution Matching

Graphs neural networks (GNNs) have emerged as a powerful graph learning model due to their superior capacity in capturing critical graph patterns. To gain insights about the model mechanism for interpretable graph learning, previous efforts focus on post-hoc local interpretation by extracting the data pattern that a pre-trained GNN model uses to make an individual prediction. However, recent works show that post-hoc methods are highly sensitive to model initialization and local interpretation can only explain the model prediction specific to a particular instance. In this work, we address these limitations by answering an important question that is not yet studied: how to provide global interpretation of the model training procedure? We formulate this problem as in-process global interpretation, which targets on distilling high-level and human-intelligible patterns that dominate the training procedure of GNNs. We further propose Graph Distribution Matching (GDM) to synthesize interpretive graphs by matching the distribution of the original and interpretive graphs in the feature space of the GNN as its training proceeds. These few interpretive graphs demonstrate the most informative patterns the model captures during training. Extensive experiments on graph classification datasets demonstrate multiple advantages of the proposed method, including high explanation accuracy, time efficiency and the ability to reveal class-relevant structure.Comment: Under Revie

Exothermic isospin-violating dark matter after SuperCDMS and CDEX

We show that exothermic isospin-violating dark matter (IVDM) can make the results of the latest CDMS-Si experiment consistent with recent null experiments, such as XENON10, XENON100, LUX, CDEX, and SuperCDMS, whereas for the CoGeNT experiment, a strong tension still persists. For CDMS-Si, separate exothermic dark matter or isospin-violating dark matter cannot fully ameliorate the tensions among these experiments; the tension disappears only if exothermic scattering is combined with an isospin-violating effect of f_n/f_p=-0.7. For such exothermic IVDM to exist, at least a new vector gauge boson (dark photon or dark Z') that connects SM quarks to Majorana-type DM particles is required.Comment: 12 pages, 6 figure

Poly[[penta­aqua­(μ4-pyridine-2,4,6-tri­carboxyl­ato)(μ3-pyridine-2,4,6-tri­carboxyl­ato)disamarium(III)] mono­hydrate]

The asymmetric unit of the title compound, {[Sm2(C8H2NO6)2(H2O)5]·H2O}n, contains two independent SmIII ions, two pyridine-2,4,6-tricarboxyl­ate (ptc) ligands, five aqua ligands and one lattice water mol­ecule. One SmIII ion is nine-coordinated by one N and five O atoms from the three ptc ligands and three aqua ligands in a distorted monocapped square antiprismatic geometry, and the other is eight-coordinated by one N and five O atoms from three ptc ligands and two aqua ligands in a 4,4′-bicapped trigonal anti­prismatic geometry. The ptc ligands brigde the SmIII ions into a three-dimensional polymeric framework. Extensive O—H⋯O hydrogen bonding is observed in the crystal structure