Spectral Analysis of Multi-dimensional Self-similar Markov Processes

In this paper we consider a discrete scale invariant (DSI) process $\{X(t), t\in {\bf R^+}\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\alpha^k, k\in {\bf W}$ where $\alpha$ is obtained by the equality $l=\alpha^T$ and ${\bf W}=\{0, 1,...\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\cdot)$ with parameter space $\{\alpha^k, k\in {\bf W}\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We assume that the process $\{X(t), t\in {\bf R^+}\}$ is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally we find the spectral density matrix of such DT-SIM process and show that its associated $T$-dimensional self-similar Markov process is fully specified by $\{R_{j}^H(1),R_{j}^H(0),j=0, 1,..., T-1\}$ where $R_j^H(\tau)$ is the covariance function of $j$th and $(j+\tau)$th observations of the process.Comment: 16 page

Detecting intraday periodicities with application to high frequency exchange rates

Many recent papers have documented periodicities in returns, return volatility, bid–ask spreads and trading volume, in both equity and foreign exchange markets. We propose and employ a new test for detecting subtle periodicities in time series data based on a signal coherence function. The technique is applied to a set of seven half-hourly exchange rate series. Overall, we find the signal coherence to be maximal at the 8-h and 12-h frequencies. Retaining only the most coherent frequencies for each series, we implement a trading rule that is based on these observed periodicities. Our results demonstrate in all cases except one that, in gross terms, the rules can generate returns that are considerably greater than those of a buy-and-hold strategy, although they cannot retain their profitability net of transactions costs. We conjecture that this methodology could constitute an important tool for financial market researchers which will enable them to detect, quantify and rank the various periodic components in financial data better

The Design Optimization and Experimental Investigation of the 4.4 μm Raman Laser Basedon Hydrogen-filled Revolver Silica Fiber

Optical properties of hollow-core revolver fibers are numerically investigated depending on various parameters: the hollow-core diameter, the capillary wall thickness, the values of the minimum gap between the capillaries, the number of capillaries in the cladding and the type of glass (silica and chalcogenide). Preliminary, similar calculations are made for simple models of hollow-core fibers. Based on the obtained results, the optimal design of the revolver fiber for Raman laser frequency conversion (1.56 μm → 4.4 μm in 1H2) was determined. As a result, efficient ns-pulsed 4.42 μm Raman laser based on 1H2-filled revolver silica fiber is realized. Quantum efficiency as high as 36 % is achieved and output average power as high as 250 mW is demonstrated

Fast optical variability of SS 433

We study the optical variability of the peculiar Galactic source SS 433 using the observations made with the Russian Turkish 1.5-m telescope (RTT150). A simple technique which allows to obtain high-quality photometric measurements with 0.3-1 s time resolution using ordinary CCD is described in detail. Using the test observations of nonvariable stars, we show that the atmospheric turbulence introduces no significant distortions into the measured light curves. Therefore, the data obtained in this way are well suited for studying the aperiodic variability of various objects. The large amount of SS 433 optical light curve measurements obtained in this way allowed us to obtain the power spectra of its flux variability with a record sensitivity up to frequencies of ~0.5 Hz and to detect its break at frequency =~2.4e-3 Hz. We suggest that this break in the power spectrum results from the smoothing of the optical flux variability due to a finite size of the emitting region. Based on our measurement of the break frequency in the power spectrum, we estimated the size of the accretion-disk photosphere as 2e12 cm. We show that the amplitude of the variability in SS 433 decreases sharply during accretion-disk eclipses, but it does not disappear completely. This suggests that the size of the variable optical emission source is comparable to that of the normal star whose size is therefore R_O \approx 2e12 cm \approx 30 R_sun. The decrease in flux variability amplitude during eclipses suggests the presence of a nonvariable optical emission component with a magnitude m_R=~13.2.Comment: 12 pages, 11 figures. Accepted for publication in Astronomy Letters. The original version in Russian is available at http://hea.iki.rssi.ru/rtt150/ru/ss433_pazh10/pss433_fast.pd

Where is SUSY?

The direct searches for Superymmetry at colliders can be complemented by direct searches for dark matter (DM) in underground experiments, if one assumes the Lightest Supersymmetric Particle (LSP) provides the dark matter of the universe. It will be shown that within the Constrained minimal Supersymmetric Model (CMSSM) the direct searches for DM are complementary to direct LHC searches for SUSY and Higgs particles using analytical formulae. A combined excluded region from LHC, WMAP and XENON100 will be provided, showing that within the CMSSM gluinos below 1 TeV and LSP masses below 160 GeV are excluded (m_{1/2} > 400 GeV) independent of the squark masses.Comment: 16 pages, 10 figure

The High Resolution X-ray Spectrum of SS 433 using the Chandra HETGS

We present observations of SS 433 using the Chandra High Energy Transmission Grating Spectrometer. Many emission lines of highly ionized elements are detected with the relativistic blue and red Doppler shifts. The lines are measurably broadened to 1700 km/s (FWHM) and the widths do not depend significantly on the characteristic emission temperature, suggesting that the emission occurs in a freely expanding region of constant collimation with opening angle of 1.23 +/- 0.06 deg. The blue shifts of lines from low temperature gas are the same as those of high temperature gas within our uncertainties, again indicating that the hottest gas we observe to emit emission lines is already at terminal velocity. Fits to the emission line fluxes give a range of temperatures in the jet from 5e6 to 1e8 K. We derive the emission measure as a function of temperature for a four component model that fits the line flux data. Using the density sensitive Si XIII triplet, the characteristic electron density is 1e14 cm^{-3}, where the gas temperature is about 1.3e7 K. Based on an adiabatic expansion model of the jet, the electron densities drop from ~2e15 to 4e13 cm^{-3} at distances of 2e10 to 2e11 cm from the apex of the jet cone. The jet mass outflow rate is 1.5e-7 Msun / yr. The kinetic power is 3.2e38 erg/s, which is x1000 larger than the unabsorbed 2-10 keV X-ray luminosity. The bremsstrahlung emission associated with the lines can account for the entire continuum; we see no direct evidence for an accretion disk. The image from zeroth order shows extended emission at a scale of ~2", aligned in the general direction of the radio jets.Comment: 28 pages, 12 figures (1, 4, 5, and 6 are color), to appear in the Astrophysical Journa

Unit roots in periodic autoregressions

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model

Adiabatic compression and indirect detection of supersymmetric dark matter

Recent developments in the modelling of the dark matter distribution in our Galaxy point out the necessity to consider some physical processes to satisfy observational data. In particular, models with adiabatic compression, which include the effect of the baryonic gas in the halo, increase significantly the dark matter density in the central region of the Milky Way. On the other hand, the non-universality in scalar and gaugino sectors of supergravity models can also increase significantly the neutralino annihilation cross section. We show that the combination of both effects gives rise to a gamma-ray flux arising from the Galactic Center largely reachable by future experiments like GLAST. We also analyse in this framework the EGRET excess data above 1 GeV, as well as the recent data from CANGAROO and HESS. The analysis has been carried out imposing the most recent experimental constraints, such as the lower bound on the Higgs mass, the \bsg branching ratio, and the muon $g-2$. In addition, the recently improved upper bound on $B(B_s \to \mu^+ \mu^-)$ has also been taken into account. The astrophysical (WMAP) bounds on the dark matter density have also been imposed on the theoretical computation of the relic neutralino density through thermal production.Comment: 32 pages, 11 figures, final version to appear in JCA