Non-stationary Parameters Research Articles

Inventory Optimization for Perishables Subject to Supply Disruptions

We study a retailer selling perishable products with fixed lifetime. Retailer's supply system is subject to random disruptions. Assuming a base-stock policy, deterministic demand and stationary parameters, we derive an expression for the expected cost function which consists of holding, backordering and perishing costs. After analyzing the properties of this function, we determine the closed form expression for the optimal base-stock level. This is the first paper to study the effects of supply disruptions on perishable-product inventory systems. Our analysis suggests that the optimal base-stock level depends on the lifetime but not on the unit perishing cost. We show that, for items with short lifetime, the choice of the base-stock level has a bigger impact on the cost than for items with a longer lifetime. We also show that if the retailer can manage to make the system safer, it is possible to operate with the same expected cost even with products with shorter lifetime. When it comes to disruption management, we conclude that companies should concentrate more on reducing the duration of supply disruptions instead of trying to prevent them. Finally, we show how to use our model for systems with stochastic demand and non-stationary parameters.

Sensitivity Analysis in Markov Decision Processes with Uncertain Reward Parameters

Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be performed directly for a Markov decision process with uncertain reward parameters using the Bellman equations. In particular, we consider problems involving (i) a single stationary parameter, (ii) multiple stationary parameters, and (iii) multiple nonstationary parameters. We illustrate the applicability of this work through a capacitated stochastic lot-sizing problem.

Sensitivity Analysis in Markov Decision Processes with Uncertain Reward Parameters

Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be performed directly for a Markov decision process with uncertain reward parameters using the Bellman equations. In particular, we consider problems involving (i) a single stationary parameter, (ii) multiple stationary parameters, and (iii) multiple nonstationary parameters. We illustrate the applicability of this work through a capacitated stochastic lot-sizing problem.

Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis

Abstract. The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks – a recently developed approach – are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.

Spectral tempering to model non-stationary covariance of nitrous oxide emissions from soil using continuous or categorical explanatory variables at a landscape scale

The rate of nitrous oxide emissions was measured from 276 soil cores on a 7.5-km transect, and then a subset of these data was used to compute geostatistical models in which land categories (land-use and soil type) were fixed effects. In one model the random effects were assumed to be second-order stationary. In the other models non-stationary random variation was modelled independently for the autocorrelation and variance of the spatially correlated component of emission rate, and for the nugget variance. This was done with the method of spectral tempering. Non-stationary variance parameters were modelled as functions of discrete or continuous auxiliary variables. Models in which spectral tempering was applied using quadratic functions of soil pH fitted the data significantly better than a stationary model and gave better estimates of the prediction error variances. A significantly better fit was also obtained using splines on location to model non-stationarity, but mapped soil associations did not provide a basis for a significantly better variance model. Computational difficulties with spectral tempering are identified and strategies to overcome them are discussed.

Statistical downscaling of extreme precipitation events using extreme value theory

Present day weather forecast models usually cannot provide realistic descriptions of local and particularly extreme weather conditions. However, for lead times of about 0–5 days, they provide reliable forecasts of the atmospheric circulation that encompasses the sub-scale processes leading to extremes. Hence, forecasts of extreme events can only be achieved through a combination of dynamical and statistical analysis methods, where a stable and significant statistical model based on a-priori physical reasoning establishes a-posterior a statistical-dynamical model between the local extremes and the large scale circulation. Here we present the development and application of such a statistical model calibration on the basis of extreme value theory, in order to derive probabilistic forecasts for (extreme) local precipitation. Besides a semi-parametric approach (censored quantile regression, QR) to derive conditional quantile estimates, we use a Poisson point process representation (PP) with non-stationary parameters but a constant threshold, and a peak-over-threshold representation (POT) using the non-stationary generalized Pareto distribution and a variable threshold. The variable threshold is conditioned on the numerical model output and defined as the 0.95 conditional quantile. The performance of the different approaches is compared using the quantile verification score. The downscaling applies to ERA40 re-analysis, in order to derive estimates of the conditional quantiles of daily precipitation accumulations at German weather stations. In terms of the verification score, the differences between the downscaling approaches are marginal. However, the uncertainty of the quantile estimates is larger for the semi-parametric QR approach, particularly for the high quantiles. A constant shape parameter is to be preferred for a stable statistical downscaling model.

Efficient Construction of Robust Hedging Strategies Under Jump Models

Markets where asset prices follow processes with jumps are incomplete and any portfolio hedging against large movements in the price of the underlying asset must include other instruments. The standard approach in literature is to minimize the price variance of the hedging portfolio under a certain choice for the jump size distribution. This paper generalizes the hedging strategy of Kennedy, Forsyth, and Vetzal (2009) to minimize the weighted variance of hedging portfolio price and Greeks (sensitivities of portfolio values to changes in the state variables or models parameters). The new approach yields improved hedging portfolios over long horizons (i.e. semi-static and static hedging) and for non-stationary model parameters (e.g. stochastic volatility or jump arrival rate). From the computational perspective, this paper develops a new Fourier transform-based numerical method for computing the Greeks of European options with arbitrary payoffs by extending the work of Jackson, Jaimungal, and Surkov (2008). The new computational method allows to rapidly compute the hedging portfolio weights of the generalized hedging approach. We demonstrate the precision and efficiency of the new numerical scheme and perform a comparative analysis of various hedging approaches.

Hybrid Particle Swarm Optimization and Unscented Filtering Technique for Estimation of Non-stationary Signal Parameters

This paper proposes an adaptive unscented Kalman filter for parameter estimation of non-stationary signals, like amplitude and frequency, in the presence of significant noise and harmonics. This paper proposes an iterative update equation for model and measurement error covariances Q and R to improve tracking of the filter in the presence of high noise. The initial choice of the model and measurement error covariances Q and R, along with the UKF parameters, are crucial in noise rejection. This paper utilizes a modified particle swarm optimization (MPSO) algorithm for the initial choice of the error covariances and UKF parameters. Various simulation results for time varying signals reveal significant improvement in noise rejection and accuracy in obtaining the frequency and amplitude of the signal.

Nonstationary monotone iterative methods for nonlinear partial differential equations

A simple technique is given in this paper for the construction and analysis of monotone iterative methods for a class of nonlinear partial differential equations. With the help of the special nonlinear property we can construct nonstationary parameters which can speed up the iterative process in solving the nonlinear system. Picard, Gauss–Seidel, and Jacobi monotone iterative methods are presented and analyzed for the adaptive solutions. The adaptive meshes are generated by the 1-irregular mesh refinement scheme which together with the M -matrix of the finite element stiffness matrix lead to existence–uniqueness–comparison theorems with simple upper and lower solutions as initial iterates. Some numerical examples, including a test problem with known analytical solution, are presented to demonstrate the accuracy and efficiency of the adaptive and monotone properties. Numerical results of simulations on a MOSFET with the gate length down to 34 nm are also given.

Signal Processing by Energy Normalization Method Based on Wavelet Packet

Fault diagnosis is a key technology to ensure safe and reliable operation of large electromechanical equipments. Fault feature extraction is important in fault diagnosis process. For non-stationary vibration signal, energy normalization method based on wavelet packet is used to make signal processing with signals decomposed into different frequency bands to perform energy normalization process in corresponding frequency band so as to extract fault feature. Flue Gas Turbine is chosen as research object and analysis shows that energy normalization processing method based on wavelet packet can effectively extract non-stationary signal characteristic parameters and make effective nondestructive testing analysis of equipments condition.

Time-dependent ARMA modeling of genomic sequences

BackgroundOver the past decade, many investigators have used sophisticated time series tools for the analysis of genomic sequences. Specifically, the correlation of the nucleotide chain has been studied by examining the properties of the power spectrum. The main limitation of the power spectrum is that it is restricted to stationary time series. However, it has been observed over the past decade that genomic sequences exhibit non-stationary statistical behavior. Standard statistical tests have been used to verify that the genomic sequences are indeed not stationary. More recent analysis of genomic data has relied on time-varying power spectral methods to capture the statistical characteristics of genomic sequences. Techniques such as the evolutionary spectrum and evolutionary periodogram have been successful in extracting the time-varying correlation structure. The main difficulty in using time-varying spectral methods is that they are extremely unstable. Large deviations in the correlation structure results from very minor perturbations in the genomic data and experimental procedure. A fundamental new approach is needed in order to provide a stable platform for the non-stationary statistical analysis of genomic sequences.ResultsIn this paper, we propose to model non-stationary genomic sequences by a time-dependent autoregressive moving average (TD-ARMA) process. The model is based on a classical ARMA process whose coefficients are allowed to vary with time. A series expansion of the time-varying coefficients is used to form a generalized Yule-Walker-type system of equations. A recursive least-squares algorithm is subsequently used to estimate the time-dependent coefficients of the model. The non-stationary parameters estimated are used as a basis for statistical inference and biophysical interpretation of genomic data. In particular, we rely on the TD-ARMA model of genomic sequences to investigate the statistical properties and differentiate between coding and non-coding regions in the nucleotide chain. Specifically, we define a quantitative measure of randomness to assess how far a process deviates from white noise. Our simulation results on various gene sequences show that both the coding and non-coding regions are non-random. However, coding sequences are "whiter" than non-coding sequences as attested by a higher index of randomness.ConclusionWe demonstrate that the proposed TD-ARMA model can be used to provide a stable time series tool for the analysis of non-stationary genomic sequences. The estimated time-varying coefficients are used to define an index of randomness, in order to assess the statistical correlations in coding and non-coding DNA sequences. It turns out that the statistical differences between coding and non-coding sequences are more subtle than previously thought using stationary analysis tools: Both coding and non-coding sequences exhibit statistical correlations, with the coding regions being "whiter" than the non-coding regions. These results corroborate the evolutionary periodogram analysis of genomic sequences and revoke the stationary analysis' conclusion that coding DNA behaves like random sequences.

Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters

Stability conditions for a nonstationary automatic-control system of variable structure in sliding mode are established. The controller of the system has feedback-switched filters functioning together with the shaper and actuator. The nonstationary parameters of the system vary within given ranges, at a finite rate, under appropriate control laws, with adjustment for the error signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach to stability analysis is based on the existence conditions for the sliding mode at the switching boundary in the phase space. The general stability and instability criteria are applied to nonstationary automatic filtered-control systems of variable structure of the third order

Technical stability of stationary automatic control systems of variable structure with switched filters

Sufficient conditions for the technical stability in measure of a nonstationary control system with variable structure are established. The controller of the system has feedback-switched filters functioning together with shaper and actuator. It is assumed that the nonstationary parameters of the system vary within given ranges, at a finite rate, with appropriate control laws, with adjustment against mismatch signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach for analysis of technical stability does not involve sliding mode conditions. Criteria of technical instability in measure for the control system under consideration are formulated using the properties of systems of comparison from below. The general criteria of technical stability and instability are applied to nonstationary filtered-control systems of variable structure of the third order. The comparison method based on normalized Lyapunov functions is used

Evolution of nonequilibrium aerosol parameters in crown-streamer discharge plasma

Nonstationary parameters of an aerosol formed from unsaturated vapors of styrene and n-hexane in a pulsed crown-streamer discharge in air or argon at atmospheric pressure have been studied. In the initial stage of aerosol formation, the concentration of aerosol particles was on the order of 107 cm−3. The characteristic time of nonequilibrium hexane aerosol degradation in the experimental chamber amounted to several hours. The aerosol particle size distribution function has a bimodal shape. Within the first seconds upon aerosol formation, the maximum particle size does not exceed 0.6 μm, whereas in several hours, the boundary of the particle size spectrum reaches the micron range.

On-line state and parameter estimation of EPDM polymerization reactors using a hierarchical extended Kalman filter

A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters in a first principles model of a continuous ethylene–propylene–diene polymer (EPDM) reactor. The estimator design is based on decomposing the dynamic model into two subsystems by exploiting the triangular model structure and the different sampling frequencies of on-line and laboratory measurements directly related to the state variables of each subsystem. The state variables of the first subsystem are reactant concentrations and zeroth-order moments of the molecular weight distribution (MWD). Unmeasured state variables and four kinetic parameters systematically chosen to reduce bias are estimated from frequent and undelayed on-line measurements of the ethylene, propylene, diene and total polymer concentrations. The state variables of the second subsystem are first-order moments of the MWD. Given state and parameters estimates from the first subsystem EKF, the first-order moments and three non-stationary parameters added to the model for bias reduction are estimated from infrequent and delayed laboratory measurements of the ethylene and diene contents and number average molecular weight of the polymer. Simulation tests show that the hierarchical EKF generates satisfactory estimates even in the presence of measurement noise and plant/model mismatch.

Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

Sufficient conditions of technical stability are established for nonstationary automatic-control systems of variable structure. The case is considered where for appropriate controls and for all admissible initial perturbations from a predefined measurable set of initial states, the nonstationary parameters of a process under external actions vary within given ranges. The control process depends on the mismatch signal and its derivatives up to an order that is less by one than the order of the equations of motion. The associated system of differential equations contains discontinuous time-dependent coefficients. A relationship is established between the eigenvalues of the quadratic forms of the given Lyapunov functions and the technical-stability criteria. It is shown that the technical-stability conditions do not depend on the sliding-mode conditions for variable-structure control processes

Identification of dynamic properties of boring bar vibrations in a continuous boring operation

Vibrations in internal turning operations are usually a cumbersome part of the manufacturing process. This article focuses on the boring bar vibrations. Boring bar vibrations in alloyed steel, stainless steel and cast iron have been measured in both the cutting speed direction and the cutting depth direction with the aid of accelerometers. The dynamic response of a boring bar seem to be a time varying process that exhibits non-linear behaviour. The process is influenced by non-stationary parameters that are not under the control of the operator or experimenter. The vibrations are clearly dominated by the first resonance frequency in one of the two directions of the boring bar. The problem with force modulation in rotary machinery, which appears as side band terms in the spectrum, is also addressed. Furthermore, the resonance frequencies of the boring bar are correlated to an Euler–Bernoulli beam model.

Stability of Nonstationary Automatic-Control Systems of Variable Structure in Forced Motion

Conditions of stability in sliding mode are obtained for nonstationary dynamic automatic-control processes of variable structure. The nonstationary parameters of a control process subjected to external perturbations vary in given ranges, whereas the parameters of the switching plane remain constant for the appropriately chosen parameters of discontinuous logic control laws. The corresponding system of differential equations contains coefficients that vary stepwise in time together with the parameters of the controlled process. The general stability criteria for the solutions of variable-structure systems are used to analyze the stability of motion in sliding mode of an automatic variable-structure control system of the second order.

Analysis of dynamics and object recognition performance in coupled map networks

Coupled logistic map lattices can perform object recognition by mapping class members to a point in a space defined by densities (partition cell occupancies) measured at a readout time t for the entire lattice. Each unit represents average spiking dynamics in mixed excitatory–inhibitory neuronal populations. Non-stationary parameters improve peak recognition rate and recognition time, suggesting one role for interaction of multiple time scales in neural oscillations. A hypothesis that recognition functions by modulating the approach to an invariant measure was rejected by examining the response to noise. Moderate correlation ( r=0.3) between a configuration entropy measure and recognition rate is found.

Calibrating Volatility Smile Dynamics Using an Ensemble Weighting Method

We present a novel method for calibrating pricing models to incorporate the effects of the volatility Smile and its dynamics. This is made possible by simultaneously calibrating to the Smile surface of European options as well as to prices of Barrier options which encapsulate information on the Smile dynamics. An arbitrary combination of European and simple exotics may be calibrated to without over-fitting or resorting to non-stationary model parameters. This technique has a natural analogy with classical statistical mechanics, and also allows analytic derivation of hedge ratios. Numerical implementation of the calibration method utilises Monte Carlo and PDE approaches and we present results to illustrate its practical use and effectiveness.