Nonstationary Case Research Articles

Extremal charged Vaidya and its near horizon geometry

Recently [Formula: see text]-dimensional spherically symmetric charged Vaidya black hole solution has been constructed. We observe that this nonstationary solution admits extremal limit and study its near horizon geometry. We show that the symmetry of the near horizon geometry is [Formula: see text]. Our analysis shows that the theorems for the near horizon geometry of stationary extremal black holes, may be extended to nonstationary cases.

Univariate Generalized Additive Models for Simulated Stationary and Non-Stationary Generalized Pareto Distribution

Generalized additive models as a predictor in regression approaches, are made up over cubic spline basis and penalized regression splines. Despite of linear predictor in GLM, generalized additive models use a sum of smooth functions of covariates as a predictor. The data which are used in this study have generalized Pareto distribution and have been simulated by inversion method. The data are generated in two types, the stationary case and the non-stationary case. The method of root mean square of errors as a method of measurement is used for comparison between power of predictions which are based on penalized regression splines as a method in univariate generalized additive models and linear regression based on maximum likelihood estimation. The finding of this research illustrates that the amount of accuracy of estimation of parameter of location in UGAM approach as an alternative promising of modelling through each specialized GPD's models, has less RMSE in compare with MLE.

Modeling of the Dynamics of Burning a Granule of Carbonate Mineral

Thermophysical processes occurring during the thermal decarbonization of natural carbonate minerals (limestones, magnesites) have been investigated. A new model of the working process of burning a single spherical carbonate granule in the form of a system of ordinary differential equations has been proposed. This system makes it possible to generalize, in a natural manner, the model to the multidimensional and nonstationary cases where a moving mass of loose material is described. A comparison of the numerical calculations of the decarbonization dynamics and the measurement results obtained under totally controlled laboratory conditions has proved the high accuracy of the proposed model.

Moving Front Solution of the Reaction-Diffusion Problem

In this paper, we study the moving front solution of the reaction-diffusion initialboundary value problem with a small diffusion coefficient. Problems in such statements can be used to model physical processes associated with the propagation of autowave fronts, in particular, in biophysics or in combustion. The moving front solution is a function the distinctive feature of which is the presence in the domain of its definition of a subdomain where the function has a large gradient. This subdomain is called an internal transition layer. In the nonstationary case, the position of the transition layer varies with time which, as it is well known, complicates the numerical solution of the problem as well as the justification of the correctness of numerical calculations. In this case the analytical method is an essential component of the study. In the paper, asymptotic methods are applied for analytical investigation of the solution of the problem posed. In particular, an asymptotic approximation of the solution as an expansion in powers of a small parameter is constructed by the use of the Vasil’eva algorithm and the existence theorem is carried out using the asymptotic method of differential inequalities. The methods used also make it possible to obtain an equation describing the motion of the front. For this purpose a transition to local coordinates takes place in the region of the front localization. In the present paper, in comparison with earlier publications dealing with two-dimensional problems with internal transition layers the transition to local coordinates in the vicinity of the front has been modified, that led to the simplification of the algorithm of determining the equation of the curve motion.

Verifying of reciprocal relations for nonlinear quadripole in unsteady mode

This paper deals with experimental verification of reciprocal relations of nonlinear quadripole for unsteady mode in external magnetic field. We find out transients of measured voltages in the quadripole after current switch. These transients are caused by changing of current–voltage characteristics (CVC) of quadripole. We propose the reciprocal relations for linear part of full resistance matrix and its experimental verification method based on algorithm of separation of resistance matrix linear part. It is shown that the proposed reciprocal relations are valid with 10−3 relatively accuracy even for non-stationary case in external magnetic field.

Plurigaussian modeling of geological domains based on the truncation of non-stationary Gaussian random fields

The plurigaussian model is used in mining engineering, oil reservoir characterization, hydrology and environmental sciences to simulate the layout of geological domains in the subsurface, while reproducing their spatial continuity and dependence relationships. However, this model is well-established only in the stationary case, when the spatial distribution of the domains is homogeneous in space, and suffers from theoretical and practical impediments in the non-stationary case. To overcome these limitations, this paper proposes extending the model to the truncation of intrinsic random fields of order k with Gaussian generalized increments, which allows reproducing spatial trends in the distribution of the geological domains. Methodological tools and algorithms are presented to infer the model parameters and to construct realizations of the geological domains conditioned to existing data. The proposal is illustrated with the simulation of rock type domains in an ore deposit in order to demonstrate its applicability. Despite the limited number of conditioning data, the results show a remarkable agreement between the simulated domains and the lithological model interpreted by geologists, while the conventional stationary plurigaussian model turns out to be unsuccessful.

The Multivariate Bullwhip Effect

A multivariate bullwhip expression for m two-stage supply chains with an order-up-to inventory policy is developed. The demand models under consideration are differenced stationary vector time series with a Wold representation for which general forecasting formulas are available, resulting in a large class of possible models (including nonstationary ones). Examples are provided for common demand models and implemented on sales data. It is found that the multivariate approach gives rise to mechanisms for understanding and reducing the bullwhip effect through horizontal information sharing, particularly for the nonstationary demand case. In the stationary setting, a more nuanced approach to bullwhip reduction can be achieved by identifying product bundles based on the relationship between cross-correlations and lead-time.

Estimating smooth structural change in cointegration models

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to re-orient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression.

Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case

This paper is a continuation of (Bernoulli 20 (2014) 2169–2216) where we prove a characterization of the support in Hölder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable and null initial conditions. Here, we allow for non-null initial conditions and, therefore, the solution does not possess a stationary property in space. As in (Bernoulli 20 (2014) 2169–2216), the support theorem is a consequence of an approximation result, in the convergence of probability, of a sequence of evolution equations driven by a family of regularizations of the driving noise. However, the method of the proof differs from (Bernoulli 20 (2014) 2169–2216) since arguments based on the stationarity property of the solution cannot be used.

Simplified quantised kernel least mean square algorithm with fixed budget

Quantised kernel least mean square algorithm with fixed budget (QKLMS-FB) is an effective method for constraining the final network size of QKLMS at the cost of less accuracy loss. However, the significances of all centres in the dictionary are required to be calculated at each iteration, which will lead to linear increasing in the computational complexity of QKLMS-FB with the centre number. To reduce the computational cost and retain a better accuracy simultaneously, only the coefficient vector and influence factor are incorporated to measure the significance of each centre, thereby generating a novel simplified QKLMS-FB (SQKLMS-FB). In addition, the gradient descent method is applied in the SQKLMS-FB to update the coefficient of the closest centre for accuracy improvement. Simulations both in stationary and non-stationary cases validate the proposed SQKLMS-FB.

Nonparametric estimation of a scalar diffusion model from discrete time data: a survey

In view of rapid developments on nonparametric estimation of the drift and volatility functions in scalar diffusion models in financial econometrics, from discrete-time observations, we provide, in this paper, a survey of its state-of-the-art with new insights into current practices, as well as elaborating on our own recent contributions. In particular, in presenting the main principles of estimation for both stationary and nonstationary cases, we show the possibility to estimate nonparametrically the drift and volatility functions without distinguishing these two frameworks.

Influence of surface texturing on the hydrodynamic performance of a thrust bearing operating in steady-state and transient lubrication regime

This paper presents a finite element modeling of hydrodynamic thrust bearings operating both in steady-state and transient lubrication regime. The presented numerical algorithm is conservative and makes it possible to determine, with a high degree of accuracy, the operating characteristics such as the friction torque, the film pressure, the film thickness and the oil flow. For different operating conditions, it was shown that the behavior of the thrust bearing is not the same when textures are applied on the rotor or on the stator. Thus, the difference in behavior between the stationary and non-stationary case was revealed. Lastly, it was predicted that placing the textures on the rotor could, under certain conditions, improve the hydrodynamic performance of the thrust bearing.

Persistence in world energy consumption: Evidence from subsampling confidence intervals

This paper analyzes the persistence properties of energy consumption in 107 countries over the 1971–2011 period. It uses subsampling confidence interval methods that are more informative than simple unit root tests to describe the underlying process of energy consumption. Because subsampling requires fewer assumptions on the nature of the data generating process, inference is less prone to a number of potential misspecification errors. By focusing on the degree of persistence in the process describing a country's energy consumption, the analysis not only provides evidence on the stationarity or nonstationarity of the energy consumption but also gives insight into the likely success of environmentally oriented government intervention. The analysis finds that the 107 countries can be grouped into three persistence classes: those whose energy consumption is explosive (highly populated countries with high growth rates); those with nonstationary energy consumption (developing and highly oil dependent economies); and those whose energy consumption is stationary (developed and energy-rich countries). In nonstationary cases, government intervention can be effective and produce permanent improvements in energy conservation and other environmental concerns. In stationary cases energy conservation and environmentally-oriented demand-management policies can have only temporary effects and thus designed to speed re-adjustment to the longer run underlying trend.

Local composite quantile regression smoothing for Harris recurrent Markov processes

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory.

Component-wise Representations of Long-memory Models and Volatility Prediction

Extracting and forecasting the volatility of financial markets is an important empirical problem. The article provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, through a generalization of the Beveridge–Nelson decomposition, and proposes a new integrated moving average (MA) model, formulated in terms of the fractional lag operator, the FLagIMA model, which allows the series to be decomposed as the sum of a fractional noise and a white noise component. We provide an assessment of the predictive performance of the FLagIMA model in comparison with other popular predictors and two other rival specifications, the fractionally integrated first-order MA model, and a fractional equal root integrated MA model. For statistical inference we show that, under mild regularity conditions, the Whittle pseudo-maximum likelihood estimator of the model parameters is consistent and asymptotically normal, also in the nonstationary case.

Random function based spectral representation of stationary and non-stationary stochastic processes

In conjunction with the formulation of random functions, a family of renewed spectral representation schemes is proposed. The selected random function serves as a random constraint correlating the random variables included in the spectral representation schemes. The objective stochastic process can thus be completely represented by a dimension-reduced spectral model with just few elementary random variables, through defining the high-dimensional random variables of conventional spectral representation schemes (usually hundreds of random variables) into the low-dimensional orthogonal random functions. To highlight the advantages of this scheme, orthogonal trigonometric functions with one and two random variables are constructed. Representative-point set of the dimension-reduced spectral model is derived by employing the probability-space partition techniques. The complete set with assigned probabilities of points gains a low-number-sample stochastic process. For illustrative purposes, the stochastic modeling of seismic acceleration processes is proceeded, of which the stationary and non-stationary cases are investigated. It is shown that the spectral acceleration of simulated processes matches well with the target spectrum. Stochastic seismic response analysis, moreover, and reliability assessment of a framed structure with Bouc-Wen behaviors are carried out using the probability density evolution method. Numerical results reveal the applicability and efficiency of the proposed simulation technique.

Approximation order and approximate sum rules in subdivision

Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum rules, its convergence, smoothness and approximation order. The aim of this paper is to show that, in the non-stationary case, exponential polynomials and approximate sum rules play an analogous role of polynomials and sum rules in the stationary case. Indeed, in the non-stationary univariate case we are able to show the following important facts: (i) reproduction of N exponential polynomials implies approximate sum rules of order N; (ii) generation of N exponential polynomials implies approximate sum rules of order N, under the additional assumption of asymptotical similarity and reproduction of one exponential polynomial; (iii) reproduction of an N-dimensional space of exponential polynomials and asymptotical similarity imply approximation order N; (iv) the sequence of basic limit functions of a non-stationary scheme reproducing one exponential polynomial converges uniformly to the basic limit function of the asymptotically similar stationary scheme.

System identification through nonstationary data using Time–Frequency Blind Source Separation

Classical output-only system identification (SI) methods are based on the assumption of stationarity of the system response. However, measured response of buildings and bridges is usually non-stationary due to strong winds (e.g. typhoon, and thunder storm etc.), earthquakes and time-varying vehicle motions. Accordingly, the response data may have time-varying frequency contents and/or overlapping of modal frequencies due to non-stationary colored excitation. This renders traditional methods problematic for modal separation and identification. To address these challenges, a new SI technique based on Time–Frequency Blind Source Separation (TFBSS) is proposed. By selectively utilizing “effective” information in local regions of the time–frequency plane, where only one mode contributes to energy, the proposed technique can successfully identify mode shapes and recover modal responses from the non-stationary response where the traditional SI methods often encounter difficulties. This technique can also handle response with closely spaced modes which is a well-known challenge for the identification of large-scale structures. Based on the separated modal responses, frequency and damping can be easily identified using SI methods based on a single degree of freedom (SDOF) system. In addition to the exclusive advantage of handling non-stationary data and closely spaced modes, the proposed technique also benefits from the absence of the end effects and low sensitivity to noise in modal separation. The efficacy of the proposed technique is demonstrated using several simulation based studies, and compared to the popular Second-Order Blind Identification (SOBI) scheme. It is also noted that even some non-stationary response data can be analyzed by the stationary method SOBI. This paper also delineates non-stationary cases where SOBI and the proposed scheme perform comparably and highlights cases where the proposed approach is more advantageous. Finally, the performance of the proposed method is evaluated using a full-scale non-stationary response of a tall building during an earthquake and found it to perform satisfactorily.

On the theory of nonlinear thermal conductivity

A nonlinear differential equation of thermal conductivity is derived phenomenologically from the general principles of construction of functional Q invariant to the inversion operation I(r →–r), and the temperature evolution dynamics is analyzed in the nonstationary case. The proposed method makes it possible to reveal some general regularities in the physical behavior of such systems for describing irreversible phenomena in self-organization processes. It is noted that an analogous situation may take place, for example, in strongly inhomogeneous structures with stochastic internal heat fluxes.

Asymptotic results for multivariate estimators of the mean density of random closed sets

The problem of the evaluation and estimation of the mean density of random closed sets in Rd with integer Hausdorff dimension 0 < n < d, is of great interest in many different scientific and technological fields. Among the estimators of the mean density available in literature, the so-called “Minkowski content”-based estimator reveals its benefits in applications in the non-stationary cases. We introduce here a multivariate version of such estimator, and we study its asymptotical properties by means of large and moderate deviation results. In particular we prove that the estimator is strongly consistent and asymptotically Normal. Furthermore we also provide confidence regions for the mean density of the involved random closed set in m ≥ 1 distinct points x1, . . . , xm ∈ Rd.