Two centuries of trend following

We establish the existence of anomalous excess returns based on trend following strategies across four asset classes (commodities, currencies, stock indices, bonds) and over very long time scales. We use for our studies both futures time series, that exist since 1960, and spot time series that allow us to go back to 1800 on commodities and indices. The overall t-stat of the excess returns is $\approx 5$ since 1960 and $\approx 10$ since 1800, after accounting for the overall upward drift of these markets. The effect is very stable, both across time and asset classes. It makes the existence of trends one of the most statistically significant anomalies in financial markets. When analyzing the trend following signal further, we find a clear saturation effect for large signals, suggesting that fundamentalist traders do not attempt to resist "weak trends", but step in when their own signal becomes strong enough. Finally, we study the performance of trend following in the recent period. We find no sign of a statistical degradation of long trends, whereas shorter trends have significantly withered.Comment: 17 pages, 9 figures, 9 table

Mass-Radius Relationships for Solid Exoplanets

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial-mass planets of all compositions we considered follow a generic functional form that is not a simple power law: $\log_{10} R_s = k_1 + 1/3 \log_{10}(M_s) - k_2 M_s^{k_3}$ for up to $M_p \approx 20 M_{\oplus}$, where $M_s$ and $R_s$ are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form $\rho = \rho_0 + c P^n$. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found that: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with $\sim$~5% uncertainty water ice planets with $\gtrsim 25$ water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super Earths'' based on the clear distinction in radii between planets with significant gas envelopes and those without.Comment: ApJ, in press, 33 pages including 16 figure

Extrasolar Giant Planets under Strong Stellar Irradiation

We investigate the effects on extrasolar giant planets [EGPs] of intense irradiation by their parent stars, describing the issues involved in treating the model atmosphere problem correctly. We treat the radiative transfer in detail, allowing the flux from the parent star to interact with all relevant depths of the planetary atmosphere, with no need for a pre-assumed albedo. We present a low-resolution optical and near-IR spectrum of a close-in EGP, focusing on the differences from an isolated planet. In our dust-free planetary atmospheres we find that Rayleigh scattering increases the EGP's flux by orders of magnitude shortward of the CaII H&K doublet (393 nm), and the spectral features of the parent star are exactly reflected. In the optical and near-IR the thermal absorption of the planet takes over, but the absorption features are changed by the irradiation. The inclusion of dust increases the reflected flux in the blue; the stellar spectral lines can be seen blueward of H-beta (486 nm).Comment: 14 pages, 4 figures, LaTex, accepted in ApJ

Extreme events in multilayer, interdependent complex networks and control

This work was supported by NSF under Grant No. 1441352.Peer reviewedPublisher PD

The EXPLORE Project I: A Deep Search for Transiting Extrasolar Planets

(Abridged) We discuss the design considerations of the EXPLORE (EXtra-solar PLanet Occultation REsearch) project, a series of transiting planet searches using 4-m-class telescopes to continuously monitor a single field of stars in the Galactic Plane in each ~2 week observing campaign. We discuss the general factors which determine the efficiency and the number of planets found by a transit search, including time sampling strategy and field selection. The primary goal is to select the most promising planet candidates for radial velocity follow-up observations. We show that with very high photometric precision light curves that have frequent time sampling and at least two detected transits, it is possible to uniquely solve for the main parameters of the eclipsing system (including planet radius) based on several important assumptions about the central star. Together with a measured spectral type for the star, this unique solution for orbital parameters provides a powerful method for ruling out most contaminants to transiting planet candidates. For the EXPLORE project, radial velocity follow-up observations for companion mass determination of the best candidates are done on 8-m-class telescopes within two or three months of the photometric campaigns. This same-season follow-up is made possible by the use of efficient pipelines to produce high quality light curves within weeks of the observations. We conclude by presenting early results from our first search, EXPLORE I, in which we reached <1% rms photometric precision (measured over a full night) on ~37,000 stars to I <= 18.2.Comment: accepted by ApJ. Main points unchanged but more thorough discussion of some issues. 36 pages, including 14 figure

Photometric Light Curves and Polarization of Close-in Extrasolar Giant Planets

The close-in extrasolar giant planets [CEGPs], \ltorder 0.05 AU from their parent stars, may have a large component of optically reflected light. We present theoretical optical photometric light curves and polarization curves for the CEGP systems, from reflected planetary light. Different particle sizes of three condensates are considered. In the most reflective case, the variability is $\approx 100$ micromagnitudes, which will be easily detectable by the upcoming satellite missions MOST, COROT, and MONS, and possibly from the ground in the near future. The least reflective case is caused by small, highly absorbing grains such as solid Fe, with variation of much less than one micromagnitude. Polarization for all cases is lower than current detectability limits. We also discuss the temperature-pressure profiles and resulting emergent spectra of the CEGP atmospheres. We discuss the observational results of Tau Boo b by Cameron et al. (1999) and Charbonneau et al. (1999) in context of our model results. The predictions - the shape and magnitude of the light curves and polarization curves - are highly dependent on the size and type of condensates present in the planetary atmosphere.Comment: 33 pages, accepted by Ap

The 21 cm Signature of Cosmic String Wakes

We discuss the signature of a cosmic string wake in 21cm redshift surveys. Since 21cm surveys probe higher redshifts than optical large-scale structure surveys, the signatures of cosmic strings are more manifest in 21cm maps than they are in optical galaxy surveys. We find that, provided the tension of the cosmic string exceeds a critical value (which depends on both the redshift when the string wake is created and the redshift of observation), a cosmic string wake will generate an emission signal with a brightness temperature which approaches a limiting value which at a redshift of $z + 1 = 30$ is close to 400 mK in the limit of large string tension. The signal will have a specific signature in position space: the excess 21cm radiation will be confined to a wedge-shaped region whose tip corresponds to the position of the string, whose planar dimensions are set by the planar dimensions of the string wake, and whose thickness (in redshift direction) depends on the string tension. For wakes created at $z_i + 1 = 10^3$, then at a redshift of $z + 1 = 30$ the critical value of the string tension $\mu$ is $G \mu = 6 \times 10^{-7}$, and it decreases linearly with redshift (for wakes created at the time of equal matter and radiation, the critical value is a factor of two lower at the same redshift). For smaller tensions, cosmic strings lead to an observable absorption signal with the same wedge geometry.Comment: 11 pages, 4 figures; a couple of comments added in the discussion sectio

Looking for a varying α\alpha in the Cosmic Microwave Background

We perform a likelihood analysis of the recently released BOOMERanG and MAXIMA data, allowing for the possibility of a time-varying fine-structure constant. We find that in general this data prefers a value of $\alpha$ that was smaller in the past (which is in agreement with measurements of $\alpha$ from quasar observations). However, there are some interesting degeneracies in the problem which imply that strong statements about $\alpha$ can not be made using this method until independent accurate determinations of $\Omega_b h^2$ and $H_0$ are available. We also show that a preferred lower value of $\alpha$ comes mainly from the data points around the first Doppler peak, whereas the main effect of the high-$\ell$ data points is to increase the preferred value for $\Omega_b h^2$ (while also tightening the constraints on $\Omega_0$ and $H_0$). We comment on some implications of our results.Comment: 15 pages; submitted to Phys. Rev.