DETECTING CHANGES IN GARCH(1,1) PROCESSES WITHOUT ASSUMING STATIONARITY

Date-stamping multiple bubble regimes

Limit theory for moderate deviation from Integrated GARCH processes

The parameters of the robot have been changed due to the rising of machine temperature and the external environment variances during the continuous moving of the robot, which greatly enlarge the error of the robot coordinate measurement system, therefore the changes of the parameters must be compensated. This paper compares two techniques used in robot parameters rapid calibration: based on measurement space fixed-point real-time robot parameters rapid calibration technology and based on space constant distance real-time robot parameters rapid calibration technology. Both of the techniques realize with the same method. First, we should solve out the robot model parameters in reversal after changing based on the relationship of the robot motion model, parameters and fixed-point coordinate (constant distance).Then figure out the measuring results variation caused by the change of robot parameters by forward calculation with these parameters. At last, amend the final measuring results to realize real-time robot parameters rapid calibration. Experiments prove that techniques based on meas urement space fixed-point real-time robot parameters rapid calibration can improve system accuracy from 0.5mm to 0.2mm above E while those based on space constant distance real-time robot parameters rapid calibration can reduce the system error from 0.5mm to 0.18mm. So, the accuracy compensate ability of the latter one is slightly higher than that of the former one by 0.02mm . Key words : Robot, on-line measurement, parameter calibration, compensation

A demographic transition is a change in the pattern of growth of a population. Human history records several kinds of such transitions, e.g., from stability to growth or between different kinds of growth. Culture is often implied as the main fuel of demographic transitions, but theorizing is so far limited to verbal arguments. Here we study two simple formal models in which population size and the amount of culture in a population influence each other’s dynamics. The first model has two regimes: an equilibrium regime in which both population size and amount of culture reach stable values, and an explosive regime in which both variables increase exponentially without bound. A transition between these regimes is caused by changes in parameters that describe the accuracy of cultural transmission and the interaction between demography and culture. The second model suggests that a transition from extensive to intensive accumulation of culture may derive from a qualitative change in how individuals cooperate to create culture.

Numerous studies of nonlinear dynamical systems have revealed a wide variety of dynamic behaviors. Nonlinear effects that occur when the initial conditions and parameters change can appear in different and sometimes unexpected ways. This work focuses on studying how complex dynamics arise in nonlinear systems. A bilinear oscillator is used as an example to show how the behavior of the system changes as its parameters vary. The study is based on a systems approach and uses the method of complete bifurcation groups. To investigate nonlinear effects, analog simulation or the direct scanning method is usually employed. However, these methods are somewhat limited in their ability to predict many dynamic characteristics, including bifurcations that lead to unstable, rare, and chaotic solutions. The paper is devoted to the parametrical analysis of periodic and chaotic oscillations in non-linear dynamic systems. The description of the regular approach to construction of bifurcation diagrams is offered to your attention. This approach allows building complete bifurcation diagrams constructing into consideration regimes the analysis of which is inaccessible by traditional methods. For example, regimes with a very small area of existence are identified as rare attractors. Such approach is used in a method of complete bifurcation groups and realized in software SPRING that developing in the Riga Technical University under guidance of Professor Mikhail Zakrzhevsky. The description of this approach and results of its application are presented in this report. The object of the research is a dynamical system whose behavior is described by the second order ordinary differential equation or a system of such equations. The dynamical system state at any time moment is characterized by the values of its phase coordinates and behavior – by variation of the phase coordinates in time. The behavior of a determinate dynamical system is uniquely defined by its initial state and the fixed parameters. The initial state is given by the values of the phase coordinates at the start. In the system behavior we can distinguish a transient process, which ends by a stationary state or regime. The stationary regime can be periodic with a period equal to the mapping period, subharmonic with a period multiple to the mapping period, almost periodic and chaotic. This method is effective for scientific research because it allows a systematic study of the main scenarios of birth and conditions for the formation of chaotic and rare attractors, which depend on parameters defined by engineering systems. Applications of this method include the simulation and analysis of nonlinear dynamic systems, the prediction of technical disasters, and the development of new vibration technologies and other technical systems.

Alternating thermal analysis techniques

Given the financial and economic damage that can be caused by the collapse of an asset price bubble, it is of critical importance to rapidly detect the onset of a crash once a bubble has been identified. We develop a real‐time monitoring procedure for detecting a crash episode in a time series. We adopt an autoregressive framework, with bubble and crash regimes modelled by explosive and stationary dynamics, respectively. The first stage of our approach is to monitor for a bubble; conditional on which, we monitor for a crash in real time as new data emerges. Our crash detection procedure employs a statistic based on the different signs of the means of the first differences associated with explosive and stationary regimes, and critical values are obtained using a training period of data. We show that the procedure has desirable asymptotic properties in terms of its ability to rapidly detect a crash while never indicating a crash earlier than one occurs. Monte Carlo simulations further demonstrate that our procedure can offer a well‐controlled false positive rate during a bubble regime. Application to the US housing market demonstrates the efficacy of our procedure in rapidly detecting the house price crash of 2006.

Investigation on dielectric breakdown behavior of thermally aged cross-linked polyethylene cable insulation

Statistics are derived for testing a sequence of observations from an exponential-type distribution for no change in parameter against possible two-sided alternatives involving parameter changes at unknown points. The test statistic can be chosen to have high power against certain of a variety of alternatives. Conditions on functionals on $C\\lbrack 0,1\\rbrack$ are given under which one can assert that the large sample distribution of the test statistic under the null-hypothesis or an alternative from a range of interesting hypotheses is that of a functional on Brownian Motion. We compute and tabulate distributions for functionals defined by nonnegative weight functions of the form $\\psi(s) = as^k, k > -2$. The functionals for $-1 \\geqq k > -2$ are not continuous in the uniform topology on $C\\lbrack 0, 1\\rbrack$.

Frequency dispersion of rock properties in equations of electromagnetics

Modeling the physiological phenomena and the effects of therapy on the dynamics of tumor growth

The gain-switching properties of an InAs-InP (113)B quantum dot laser based on multi-population rate equations are examined theoretically in detail to generate shorter pulses with the application of a Gaussian pulse beam to the laser excited state. The numerical results demonstrated that as the homogeneous and the inhomogeneous broadening increase, the differential gain, the gain compression factor, and the threshold current of the excited state decrease while the threshold current of the ground state increases. It was also observed that the contribution of the excited state to gain-switched output pulses depend on not only the value of the inhomogeneous broadening but also the magnitude of the applied current. Additionally, it was found that without an optical beam, the output pulse has a long pulse width due to ground state emissions and the change in the parameters strongly affecting the output. However, under the optical beam, narrow pulses around 26 ps have high peak power owing to the excited state emission generated even at low currents and also the change in the laser parameters having a negligible effect. Finally, the gain-switching characteristics with and without a Gaussian pulse beam are shown to be similar for liner-gain and nonlinear-gain cases except that higher peak power and narrower output pulses are obtained for the linear-gain case.

Gain-switched short pulse generation from InAs-InP (1 1 3)B quantum dot laser excited state

Nonparametric simultaneous testing for structural breaks

In this paper, we propose a new approach to the empirical likelihood inference for the parameters in heteroscedastic partially linear single-index models. In the growing dimensional setting, it is proved that estimators based on semiparametric efficient score have the asymptotic consistency, and the limit distribution of the empirical log-likelihood ratio statistic for parameters $$(\beta ^{\top },\theta ^{\top })^{\top }$$ is a normal distribution. Furthermore, we show that the empirical log-likelihood ratio based on the subvector of $$\beta $$ is an asymptotic chi-square random variable, which can be used to construct the confidence interval or region for the subvector of $$\beta $$ . The proposed method can naturally be applied to deal with pure single-index models and partially linear models with high-dimensional data. The performance of the proposed method is illustrated via a real data application and numerical simulations.