Browsing by Subject "Monte Carlo Simulations"

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Open Access
Joint test for structural model specification
(2006) Yüksel, Serkan
Aim of this thesis is to propose a test statistic that can test for true structural model in time series. Main concern of the thesis is to suggest a test statistic, which has joint null of unit root and no structural break (difference stationary model). When joint null hypothesis is rejected, source of deviation from the null model may be structural break or (and) stationarity. Sources of the deviation correspond to different structural models: Pure stationary model, trendbreak stationary model and trend-break with unit root model. The thesis suggests a test statistic that can discriminate null model from alternative models and more importantly, one alternative model from another. The test statistic that is proposed in the thesis is able to detect specific source of deviation from the null model. By doing so, we can determine the true structure model in time series. The thesis compares power properties of the test statistic that is proposed with the most favorable test in the literature. Simulation results indicate the power dominance over the test statistics in the literature. Moreover, we are able to specify true alternative model.
Open Access
Non-equilibrium steady state phase transitions of various statistical models
(2013) Renklioğlu, Başak
Non-equilibrium phase transitions of a number of systems are investigated by several methods. These systems are in contact with thermal baths with different temperatures and taken to be driven to the non-equilibrium limits by spin exchange (Kawasaki) dynamics. First of all, the criticality of the two-finite temperature spin-1/2 Ising model with a conserved order parameter on a square lattice is studied through a real space renormalization group transformation. The dynamics of the nonequilibrium system are characterized by means of different temperatures (Tx and Ty), and also different time-scale constants, (αx and αy) for spin exchanges in the x and y directions. Based on the RG flows, the critical surface of the system is obtained as a function of these exchange parameters. This is the first study in which the full critical surface displaying various universality classes of this system is reported. Secondly, steady state phase transitions of the eight-vertex model, formulated by two interlaced two-dimensional Ising models on square lattices, are studied through four independent Monte Carlo simulations, each with 60 × 106 Monte Carlo steps on N × N lattices with N = 32, 40, 80, 100. To obtain an isotropic system, the spin exchanges are considered to occur within the sublattices. We observe non-universal behavior for non-equilibrium transitions around the equilibrium transitions, and Ising like behavior when one of the bath temperature becomes very large.