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

GRISOTTO: A greedy approach to improve combinatorial algorithms for motif discovery with prior knowledge

<p>Abstract</p> <p>Background</p> <p>Position-specific priors (PSP) have been used with success to boost EM and Gibbs sampler-based motif discovery algorithms. PSP information has been computed from different sources, including orthologous conservation, DNA duplex stability, and nucleosome positioning. The use of prior information has not yet been used in the context of combinatorial algorithms. Moreover, priors have been used only independently, and the gain of combining priors from different sources has not yet been studied.</p> <p>Results</p> <p>We extend RISOTTO, a combinatorial algorithm for motif discovery, by post-processing its output with a greedy procedure that uses prior information. PSP's from different sources are combined into a scoring criterion that guides the greedy search procedure. The resulting method, called GRISOTTO, was evaluated over 156 yeast TF ChIP-chip sequence-sets commonly used to benchmark prior-based motif discovery algorithms. Results show that GRISOTTO is at least as accurate as other twelve state-of-the-art approaches for the same task, even without combining priors. Furthermore, by considering combined priors, GRISOTTO is considerably more accurate than the state-of-the-art approaches for the same task. We also show that PSP's improve GRISOTTO ability to retrieve motifs from mouse ChiP-seq data, indicating that the proposed algorithm can be applied to data from a different technology and for a higher eukaryote.</p> <p>Conclusions</p> <p>The conclusions of this work are twofold. First, post-processing the output of combinatorial algorithms by incorporating prior information leads to a very efficient and effective motif discovery method. Second, combining priors from different sources is even more beneficial than considering them separately.</p

Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change

Wavelet‐Based Wavenumber Spectral Estimate of Eddy Kinetic Energy: Idealized Quasi‐Geostrophic Flow

International audienceA wavelet-based method is re-introduced in an oceanographic and spectral context to estimate wavenumber spectrum and spectral flux of kinetic energy and enstrophy. We apply this to a numerical simulation of idealized, doubly periodic quasi-geostrophic flows, that is, the flow is constrained by the Coriolis force and vertical stratification. The double periodicity allows for a straightforward Fourier analysis as the baseline method. Our wavelet spectra agree well with the canonical Fourier approach but with the additional strengths of negating the necessity for the data to be periodic and being able to extract local anisotropies in the flow. Caution is warranted, however, when computing higher-order quantities, such as spectral flux

Wavelet-Based Wavenumber Spectral Estimate of Eddy Kinetic Energy: Idealized Quasi-Geostrophic Flow

A wavelet-based method is re-introduced in an oceanographic and spectral context to estimate wavenumber spectrum and spectral flux of kinetic energy and enstrophy. We apply this to a numerical simulation of idealized, doubly periodic quasi-geostrophic flows, that is, the flow is constrained by the Coriolis force and vertical stratification. The double periodicity allows for a straightforward Fourier analysis as the baseline method. Our wavelet spectra agree well with the canonical Fourier approach but with the additional strengths of negating the necessity for the data to be periodic and being able to extract local anisotropies in the flow. Caution is warranted, however, when computing higher-order quantities, such as spectral flux. Key Points A wavelet-based spectral method to estimate eddy variability is described Wavenumber spectra of eddies are estimated for a doubly periodic quasi-geostrophic flow The wavelet and Fourier approach agree well in their estimates of spectra and spectral flux Plain Language Summary Chaotic flows such as the ocean currents, atmospheric winds, and turbulence in general are fundamentally impossible to analytically predict, namely, to formulate a mathematical general solution. Nevertheless, the interest in describing such chaotic flows can be found in examples as old as Leonardo da Vinci's sketch of turbulence. While we cannot obtain an analytical description of turbulence, we can extract statistical information from turbulent flows and a common descriptor has been the wavenumber spectrum. The spectrum reveals at each spatial scale, the level of variability the flow carries. Here, we re-introduce an alternative method in estimating the spectrum based on wavelet functions