Numerical Distribution Functions for Seasonal Unit Root Tests

When working with time series data observed at intervals smaller than a year, it is often necessary to test for the presence of seasonal unit roots. One of the most widely used methods for testing seasonal unit roots is that of HEGY, which provides test statistics with non-standard distributions. This paper describes a generalisation of this method for any periodicity and uses a response surface regressions approach to calculate the critical values and P values of the HEGY statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and some new tables of critical values for daily, hourly and half-hourly data are presented.seasonality, unit roots, surface response analysis

A Hardware Efficient Random Number Generator for Nonuniform Distributions with Arbitrary Precision

Nonuniform random numbers are key for many technical applications, and designing efficient hardware implementations of non-uniform random number generators is a very active research field. However, most state-of-the-art architectures are either tailored to specific distributions or use up a lot of hardware resources. At ReConFig 2010, we have presented a new design that saves up to 48% of area compared to state-of-the-art inversion-based implementation, usable for arbitrary distributions and precision. In this paper, we introduce a more flexible version together with a refined segmentation scheme that allows to further reduce the approximation error significantly. We provide a free software tool allowing users to implement their own distributions easily, and we have tested our random number generator thoroughly by statistic analysis and two application tests

Numerical Distribution Functions for Seasonal Unit Root Tests

When working with time series data observed at intervals smaller than a year, it is often necessary to test for the presence of seasonal unit roots. One of the most widely used methods for testing seasonal unit roots is that of HEGY, which provides test statistics with non-standard distributions. This paper describes a generalisation of this method for any periodicity and uses a response surface regressions approach to calculate the critical values and P values of the HEGY statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and some new tables of critical values for daily, hourly and half-hourly data are presented.Financial support from research project ECO2010-15332 from Ministerio de Ciencia e Innovación, and Econometrics Research Group IT-334-07 from the Basque Government are gratefully acknowledged. The SGI/IZO-SGIker UPV/EHU is gratefully aknowledged for its generous allocation of computational resource

Mixtures of strongly interacting bosons in optical lattices

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of K induces a significant loss of coherence in Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.Comment: 10 pages, 3 figures; some changes in the text and abstract have been introduced; coherence now given in terms of visibility; a couple of new reference adde

Design Exploration of an FPGA-Based Multivariate Gaussian Random Number Generator

Monte Carlo simulation is one of the most widely used techniques for computationally intensive simulations in a variety of applications including mathematical analysis and modeling and statistical physics. A multivariate Gaussian random number generator (MVGRNG) is one of the main building blocks of such a system. Field Programmable Gate Arrays (FPGAs) are gaining increased popularity as an alternative means to the traditional general purpose processors targeting the acceleration of the computationally expensive random number generator block due to their fine grain parallelism and reconfigurability properties and lower power consumption. As well as the ability to achieve hardware designs with high throughput it is also desirable to produce designs with the flexibility to control the resource usage in order to meet given resource constraints. This work proposes a novel approach for mapping a MVGRNG onto an FPGA by optimizing the computational path in terms of hardware resource usage subject to an acceptable error in the approximation of the distribution of interest. An analysis on the impact of the error due to truncation/rounding operation along the computational path is performed and an analytical expression of the error inserted into the system is presented. Extra dimensionality is added to the feature of the proposed algorithm by introducing a novel methodology to map many multivariate Gaussian random number generators onto a single FPGA. The effective resource sharing techniques introduced in this thesis allows further reduction in hardware resource usage. The use of MVGNRG can be found in a wide range of application, especially in financial applications which involve many correlated assets. In this work it is demonstrated that the choice of the objective function employed for the hardware optimization of the MVRNG core has a considerable impact on the final performance of the application of interest. Two of the most important financial applications, Value-at-Risk estimation and option pricing are considered in this work