Unit Root Testing with Slowly Varying Trends

A unit root test is proposed for time series with a general nonlinear deterministic trend component. It is shown that asymptotically the pooled OLS estimator of overlapping blocks filters out any trend component that satisfies some Lipschitz condition. Under both fixed-$b$ and small-$b$ block asymptotics, the limiting distribution of the t-statistic for the unit root hypothesis is derived. Nuisance parameter corrections provide heteroskedasticity-robust tests, and serial correlation is accounted for by pre-whitening. A Monte Carlo study that considers slowly varying trends yields both good size and improved power results for the proposed tests when compared to conventional unit root tests

Properties of the Power Envelope for Tests Against Both Stationary and Explosive Alternatives: The Effect of Trends

This paper details a precise analytic e¤ect that inclusion of a linear trend has on the power of Neyman-Pearson point optimal unit root tests and thence the power envelope. Both stationary and explosive alternatives are considered. The envelope can be characterized by probabilities for two, related, sums of chi-square random variables. A stochastic expansion, in powers of the local-to-unity parameter, of the di¤erence between these loses its leading term when a linear trend is included. This implies that the power envelope converges to size at a faster rate, which can then be exploited to prove that the power envelope must necessarily be lower. This e¤ect is shown to be, analytically, greater asymptotically than in small samples and numerically far greater for explosive than for stationary alternatives. Only a linear trend has a speci…c rate e¤ect on the power envelope, however other deterministic variables will have some e¤ect. The methods of the paper lead to a simple direct measure of this e¤ect which is then informative about power, in practice

The role of information in nonstationary regression

The role of standard likelihood based measures of information and efficiency is unclear when regressions involve nonstationary data. Typically the standardized score is not asymptotically Gaussian and the standardized Hessian has a stochastic, rather than deterministic limit. Here we consider a time series regression involving a deterministic covariate which can be evaporating, slowly evolving or nonstationary. It is shown that conditional information, or equivalently, profile Kullback-Leibler and Fisher Information remain informative about both the accuracy, i.e. asymptotic variance, of profile maximum likelihood estimators, as well as the power of point optimal invariant tests for a unit root. Specifically these information measures indicate fractional, rather than linear trends may minimize inferential accuracy. Such is confirmed in numerical experiment

XMM-Newton detection of two clusters of galaxies with strong SPT Sunyaev-Zel'dovich effect signatures

We report on the discovery of two galaxy clusters, SPT-CL J2332-5358 and SPT-CL J2342-5411, in X-rays. These clusters were also independently detected through their Sunyaev-Zel'dovich effect by the South Pole Telescope, and confirmed in the optical band by the Blanco Cosmology Survey. They are thus the first clusters detected under survey conditions by all major cluster search approaches. The X-ray detection is made within the frame of the XMM-BCS cluster survey utilizing a novel XMM-Newton mosaic mode of observations. The present study makes the first scientific use of this operation mode. We estimate the X-ray spectroscopic temperature of SPT-CL J2332-5358 (at redshift z=0.32) to T = 9.3 (+3.3/-1.9) keV, implying a high mass, M_{500} = 8.8 +/- 3.8 \times 10^{14} M_{sun}. For SPT-CL J2342-5411, at z=1.08, the available X-ray data doesn't allow us to directly estimate the temperature with good confidence. However, using our measured luminosity and scaling relations we estimate that T = 4.5 +/- 1.3 keV and M_{500} = 1.9 +/- 0.8 \times 10^{14} M_{sun}. We find a good agreement between the X-ray masses and those estimated from the Sunyaev-Zel'dovich effect.Comment: Submitted to A&A, 8 pages, 5 figures, 1 tabl

Age Determination of Six Intermediate-age SMC Star Clusters with HST/ACS

We present a photometric analysis of the star clusters Lindsay 1, Kron 3, NGC339, NGC416, Lindsay 38, and NGC419 in the Small Magellanic Cloud (SMC), observed with the Hubble Space Telescope Advanced Camera for Surveys (ACS) in the F555W and F814W filters. Our color magnitude diagrams (CMDs) extend ~3.5 mag deeper than the main-sequence turnoff points, deeper than any previous data. Cluster ages were derived using three different isochrone models: Padova, Teramo, and Dartmouth, which are all available in the ACS photometric system. Fitting observed ridgelines for each cluster, we provide a homogeneous and unique set of low-metallicity, single-age fiducial isochrones. The cluster CMDs are best approximated by the Dartmouth isochrones for all clusters, except for NGC419 where the Padova isochrones provided the best fit. The CMD of NGC419 shows several main-sequence turn-offs, which belong to the cluster and to the SMC field. We thus derive an age range of 1.2-1.6 Gyr for NGC419. Interestingly, our intermediate-age star clusters have a metallicity spread of ~0.6 dex, which demonstrates that the SMC does not have a smooth, monotonic age-metallicity relation. We find an indication for centrally concentrated blue straggler star candidates in NGC416, while for the other clusters these are not present. Using the red clump magnitudes, we find that the closest cluster, NGC419 (~50kpc), and the farthest cluster, Lindsay 38 (~67kpc), have a relative distance of ~17kpc, which confirms the large depth of the SMC.Comment: 25 pages, 45 Figure

Diffuse light and building history of the galaxy cluster Abell 2667

We have searched for diffuse intracluster light in the galaxy cluster Abell 2667 (z=0.233) from HST images in three filters. We have applied to these images an iterative multi-scale wavelet analysis and reconstruction technique, which allows to subtract stars and galaxies from the original images. We detect a zone of diffuse emission south west of the cluster center (DS1), and a second faint object (ComDif), within DS1. Another diffuse source (DS2) may be detected, at lower confidence level, north east of the center. These sources of diffuse light contribute to 10-15% of the total visible light in the cluster. Whether they are independent entities or are part of the very elliptical external envelope of the central galaxy remains unclear. VLT VIMOS integral field spectroscopy reveals a faint continuum at the positions of DS1 and ComDif but do not allow to compute a redshift. A hierarchical substructure detection method reveals the presence of several galaxy pairs and groups defining a similar direction as the one drawn by the DS1-central galaxy-DS2 axis. The analysis of archive XMM-Newton and Chandra observations shows X-ray emission elongated in the same direction. The X-ray temperature map shows the presence of a cool core, a broad cool zone stretching from north to south and hotter regions towards the north east, south west and north west. This possibly suggests shock fronts along these directions produced by infalling material. These various data are consistent with a picture in which diffuse sources are concentrations of tidal debris and harassed matter expelled from infalling galaxies by tidal stripping and undergoing an accretion process onto the central cluster galaxy; as such, they are expected to be found along the main infall directions.Comment: Accepted for publication in Astronomy and Astrophysic

A Rich Cluster of Galaxies Near the Quasar B2 1335+28 at z=1.1: Color Distribution and Star-Formation Properties

We previously reported a significant clustering of red galaxies (R-K=3.5--6) around the radio-loud quasar B2 1335+28 at z=1.086. In this paper, we establish the existence of a rich cluster at the quasar redshift, and study the properties of the cluster galaxies through further detailed analysis of the photometric data. The color distribution of the galaxies in the cluster is quite broad and the fraction of blue galaxies (\sim 70%) is much larger than in intermediate-redshift clusters. Using evolutionary synthesis models, we show that this color distribution can be explained by galaxies with various amounts of star-formation activity mixed with the old stellar populations. Notably, there are about a dozen galaxies which show very red optical-NIR colors but also show significant UV excess with respect to passive-evolution models. They can be interpreted as old early-type galaxies with a small amount of star formation. The fact that the UV-excess red galaxies are more abundant than the quiescent red ones suggests that a large fraction of old galaxies in this cluster are still forming stars to some extent. However, a sequence of quiescent red galaxies is clearly identified on the R-K versus K color-magnitude (C-M) diagram. The slope and zero point of their C-M relation appear to be consistent with those expected for the precursors of the C-M relation of present-day cluster ellipticals when observed at z=1.1. We estimate the Abell richness class of the cluster to be R \sim 1. New X-ray data presented here place an upper limit of L_x < 2 10^{44} erg s^{-1} for the cluster luminosity. Inspections of the wider optical images reveal some lumpy structure, suggesting that the whole system is still dynamically young.Comment: 54 pages including 13 Postscript figures, 1 jpg figure, and 1 table, uses aasms4.sty and epsf.sty. Accepted for publication in ApJ: Replaced as the older verison was missed to include the figure 2c, 2d, and figure

Properties of Galaxies in and around Voids

Two surveys for intrinsically faint galaxies towards nearby voids have been conducted at the MPI f\"ur Astronomie, Heidelberg. One selected targets from a new diameter limited ($\Phi \ge 5''$) catalog with morphological criteria while the other used digitized objective prism Schmidt plates to select mainly HII dwarf galaxies. For some 450 galaxies, redshifts and other optical data were obtained. We studied the spatial distribution of the sample objects, their luminosity function, and their intrinsic properties. Most of the galaxies belong to already well known sheets and filaments. But we found about a dozen highly isolated galaxies in each sample (nearest neighborhood distance $\ge 3 h_{75}^{-1} Mpc$). These tend to populate additional structures and are not distributed homogeneously throughout the voids. As our results on 'void galaxies' still suffer from small sample statistics, I also tried to combine similar existing surveys of nearby voids to get further hints on the larger structure and on the luminosity function of the isolated galaxies. No differences in the luminosity function of sheet and void galaxies could be found. The optical and infrared properties of both samples are in the normal range for samples dominated by late-type dwarfs. Follow-up HI studies show that the isolated dwarfs in both samples have unusual high amount of neutral gas for a given luminosity.Comment: 10 pages, 4 figures, latex, to appear in the proceedings of the 'Ringberg workshop on Large Scale Structure', hold Sep. 23-28, 199

The US stock market leads the Federal funds rate and Treasury bond yields

Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variations and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.Comment: 12 pages, 7 figures, 1 tabl

The magnetic nature of disk accretion onto black holes

Although disk accretion onto compact objects - white dwarfs, neutron stars, and black holes - is central to much of high energy astrophysics, the mechanisms which enable this process have remained observationally elusive. Accretion disks must transfer angular momentum for matter to travel radially inward onto the compact object. Internal viscosity from magnetic processes and disk winds can in principle both transfer angular momentum, but hitherto we lacked evidence that either occurs. Here we report that an X-ray-absorbing wind discovered in an observation of the stellar-mass black hole binary GRO J1655-40 must be powered by a magnetic process that can also drive accretion through the disk. Detailed spectral analysis and modeling of the wind shows that it can only be powered by pressure generated by magnetic viscosity internal to the disk or magnetocentrifugal forces. This result demonstrates that disk accretion onto black holes is a fundamentally magnetic process.Comment: 15 pages, 2 color figures, accepted for publication in Nature. Supplemental materials may be obtained by clicking http://www.astro.lsa.umich.edu/~jonmm/nature1655.p