10,484 research outputs found

    Sign Tests for Long-memory Time Series

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    This paper proposes sign-based tests for simple and composite hypotheses on the long-memory parameter of a time series process. The tests allow for nonstationary hypothesis, such as unit root, as well as for stationary hypotheses, such as weak dependence or no integration. The proposed generalized Lagrange multiplier sign tests for simple hypotheses on the long-memory parameter are exact and locally optimal among those in their class. We also propose tests for composite hypotheses on the parameters of ARFIMA processes. The resulting tests statistics have a standard normal limiting distribution under the null hypothesis.Publicad

    A new class of distribution-free tests for time series models specification

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    The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belong to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function

    What is a quantum computer, and how do we build one?

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    The DiVincenzo criteria for implementing a quantum computer have been seminal in focussing both experimental and theoretical research in quantum information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. The question is therefore what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that according to this definition a device is a quantum computer if it obeys the following four criteria: Any quantum computer must (1) have a quantum memory; (2) facilitate a controlled quantum evolution of the quantum memory; (3) include a method for cooling the quantum memory; and (4) provide a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault-tolerantly. We discuss various existing quantum computing paradigms, and how they fit within this framework. Finally, we lay out a roadmap for selecting an avenue towards building a quantum computer. This is summarized in a decision tree intended to help experimentalists determine the most natural paradigm given a particular physical implementation

    Cellular Automata as a Model of Physical Systems

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    Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While this approach abstracts away all details of the underlying physical system, it remains faithful to the fact that there is an underlying physical reality which it describes. This imposes certain restrictions on the types of computations a CA can physically carry out, and the resources it needs to do so. In this paper we explore these and other consequences of our reformalization.Comment: To appear in the Proceedings of AUTOMATA 200

    General Focus Point in the MSSM

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    The minimal supersymmetric extension of the Standard Model (SM) is a well motivated scenario for physics beyond the SM, which allows a perturbative description of the theory up to scales of the order of the Grand Unification scale, where gauge couplings unify. The Higgs mass parameter is insensitive to the ultraviolet physics and is only sensitive to the scale of soft supersymmetry breaking parameters. Present collider bounds suggest that the characteristic values of these parameters may be significantly larger than the weak scale. Large values of the soft breaking parameters, however, induce large radiative corrections to the Higgs mass parameter and therefore the proper electroweak scale may only be obtained by a fine tuned cancellation between the square of the holomorphic \mu-parameter and the Higgs supersymmetry breaking square mass parameter. This can only be avoided if there is a correlation between the scalar and gaugino mass parameters, such that the Higgs supersymmetry breaking parameter remains of the order of the weak scale. The scale at which this happens is dubbed as focus point. In this article, we define the general conditions required for this to happen, for different values of the messenger scale at which supersymmetry breaking is transmitted to the observable sector, and for arbitrary boundary conditions of the sfermion, gaugino, and Higgs mass parameters. Specific supersymmetry breaking scenarios in which these correlations may occur are also discussed.Comment: 19 pages, 9 figures, new refs. adde

    Nonparametric Tests for Conditional Symmetry in Dynamic Models

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    This article proposes omnibus tests for conditional symmetry around a parametric function in a dynamic context. Conditional moments may not exist or may depend on the explanatory variables. Test statistics are suitable functionals of the empirical process of residuals and explanatory variables, whose limiting distribution under the null is nonpivotal. The tests are implemented with the assistance of a bootstrap method, which is justified assuming very mild regularity conditions on the specification of the center of symmetry and the underlying serial dependence structure. Finite sample properties are examined by means of a Monte Carlo experiment.Publicad

    Models of Quantum Cellular Automata

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    In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different QCA models, and compare them. One model we discuss is the traditional QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam. We discuss also Margolus QCA, also discussed by Schumacher and Werner. We introduce two new models, Coloured QCA, and Continuous-Time QCA. We also compare our models with the established models. We give proofs of computational equivalence for several of these models. We show the strengths of each model, and provide examples of how our models can be useful to come up with algorithms, and implement them in real-world physical devices

    A new class of distribution-free tests for time series models specification

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    The construction of asymptotically distribution free time series model specification tests using as statistics the estimated residual autocorrelations is considered from a general view point. We focus our attention on Box-Pierce type tests based on the sum of squares of a few estimated residual autocorrelations. This type of tests belong to the class defined by quadratic forms of weighted residual autocorrelations, where weights are suitably transformed resulting in asymptotically distribution free tests. The weights can be optimally chosen to maximize the power function when testing in the direction of local alternatives. The optimal test in this class against MA, AR or Bloomfield alternatives is a Box-Pierce type test based on the sum of squares of a few transformed residual autocorrelations. Such transformations are, in fact, the recursive residuals in the projection of the residual autocorrelations on a certain score function.Dynamic regression model, Optimal tests, Recursive residuals, Residual autocorrelation function, Specification tests, Time series models
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