A similarity‐based approach to time‐varying coefficient non‐stationary autoregression

We suggest in this article a similarity‐based approach to time‐varying coefficient non‐stationary autoregression. In a given sample, the model can display characteristics consistent with stationary, unit root and explosive behaviour, depending on the similarity between the dependent variable and its past values. We establish consistency of the quasi‐maximum likelihood estimator of the model, with a general norming factor. Asymptotic score‐based hypothesis tests are derived. The model is applied to a data set comprised of dual stocks traded in NASDAQ and the Tokyo Stock Exchange.     

The Calculation of Some Limiting Distributions Arising in Near‐Integrated Models with GLS Detrending

Many unit root test statistics are based on detrended data, with the method of generalized least squares (GLS) detrending being popular in the setting of a near‐integrated model. This article determines the properties of some associated limiting distributions when the GLS detrending is based on a linear time trend. A fundamental result for the moment generating function of two key functionals of the relevant stochastic process is provided and used to compute probability density functions and cumulative distribution functions, as well as means and variances, of the limiting distributions of some statistics of interest. The exact moments and percentiles of some of these distributions are compared with those obtained by simulations, and it is found that, even with a large number of replications and a large sample size, the errors resulting from the simulation methods are not negligible. Some further applications, including a comparison of limiting power functions of different unit root test statistics and the consideration of a more complicated statistic, are also provided.     

Moving ion fronts in mixed ionic‐electronic conducting polymer films

The aim of this paper is to analyze moving front dynamics of ions and holes in a planar, mixed ionic‐electronic conducting polymer film. As cations invade the film, holes evacuate; thus, an ionic current is converted to an electronic signal. Recent experiments show that the location of the advancing ion front increases as the square‐root of time, a scaling typically associated with diffusive transport, which is surprising given the large driving voltages utilized. Ionic and electronic transport is modeled via the drift‐diffusion equations. A similarity transformation reduces the governing partial differential equations to ordinary differential equations that are solved numerically. The similarity transformation elucidates the origin of the square‐root‐of‐time front scaling. The similarity solution is then compared to the numerical solution of the full drift‐diffusion equations, finding excellent agreement. When compared with experimental data, our model captures the front location; however, qualitative differences between the ion profiles are observed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1447–1454, 2015     

Boundary Limit Theory for Functional Local to Unity Regression

This article studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multidirectional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its t‐statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the article.     

Asymptotic Theory and Unified Confidence Region for an Autoregressive Model

Although some unified inferences for the coefficient in an AR(1) model have been proposed in the literature, it remains open as to how to construct a unified confidence region for the intercept and the coefficient jointly without a prior on whether the sequence is stationary or unit root or near unit root or moderate deviations from a unit root or explosive and whether the sequence has a zero or nonzero constant intercept. After deriving the joint limit of the least squares estimator for all of these cases, this article proposes a unified empirical likelihood confidence region by first splitting the data into two parts and then constructing some weighted score equations. The good finite sample performance of the proposed method is demonstrated via a simulation study. Real data applications are provided as well.     

A Goodness‐of‐Fit Test for Integer‐Valued Autoregressive Processes

For autoregressive count data time series, a goodness‐of‐fit test based on the empirical joint probability generating function is considered. The underlying process is contained in a general class of Markovian models satisfying a drift condition. Asymptotic theory for the test statistic is provided, including a functional central limit theorem for the non‐parametric estimation of the stationary distribution and a parametric bootstrap method. Connections between the new approach and existing tests for count data time series based on moment estimators appear in limiting scenarios. Finally, the test is applied to a real data set.     

Long-Memory Errors in Time Series Regressions with a Unit Root

This paper is concerned with estimation and inference in univariate time series regression with a unit root when the error sequence exhibits long-range temporal dependence. We consider generating mechanisms for the unit root process which include models with or without a drift term and we study the limit behavior of least squares statistics in regression models without drift and trend, with drift but no time trend, and with drift and time trend. We derive the limit distribution and rate of convergence of the ordinary least squares (OLS) estimator of the unit root, the intercept and the time trend in the three regression models and for the two different data-generating processes. The limiting distributions for the OLS estimator differ from those obtained under the hypothesis of weakly dependent errors not only in terms of the limiting process involved but also in terms of functional form. Further, we characterize the asymptotic behavior of both the t statistics for testing the unit root hypothesis and the t statistic for the intercept and time trend coefficients. We find that t ratios either diverge to infinity or collapse to zero. The limiting behavior of Phillips's Z _α and Z _t semiparametric corrections is also analyzed and found to be similar to that of standard Dickey– Fuller tests. Our results indicate that misspecification of the temporal dependence features of the error sequence produces major effects on the asymptotic distribution of estimators and t ratios and suggest that alternative approaches might be more suited to testing for a unit root in time series regression.     

Time‐Transformed Unit Root Tests for Models with Non‐Stationary Volatility

Abstract. Conventional unit root tests are known to be unreliable in the presence of permanent volatility shifts. In this paper, we propose a new approach to unit root testing which is valid in the presence of a quite general class of permanent variance changes which includes single and multiple (abrupt and smooth transition) volatility change processes as special cases. The new tests are based on a time transformation of the series of interest which automatically corrects their form for the presence of non‐stationary volatility without the need to specify any parametric model for the volatility process. Despite their generality, the new tests perform well even in small samples. We also propose a class of tests for the null hypothesis of stationary volatility in (near‐) integrated time‐series processes.     

Improved Void Fraction Correlation for Two‐Phase Flow in Large‐Diameter Annuli

A flow pattern‐independent void fraction correlation for gas‐liquid two‐phase flow in vertical large‐diameter annuli is established. Two equations are proposed for the parameters of a drift flux model‐based correlation: the distribution parameter and the drift flux velocity. These equations are expressed as a function of two‐phase flow variables including void fraction, fluid properties, pipe geometry, and phase flow rates. Experiments were performed to study the void fraction of vertical air‐water two‐phase flow in large‐diameter annuli. The obtained experimental data along with the literature data of Caetano are used to verify the performance of the proposed void fraction correlation. The accuracy of this correlation is compared with nineteen frequently used correlations in literature. The proposed correlation was found to predict the void fraction consistently with a better accuracy.     

Dickey–Fuller, Lagrange Multiplier and Combined Tests for a Unit Root in Autoregressive Time Series

In this paper we investigate (augmented) Dickey–Fuller (DF) and Lagrange multiplier (LM) type unit root tests for autoregressive time series through comprehensive Monte Carlo simulations. We consider two sorts of null and alternative hypotheses: a unit root without drift versus level stationarity and a unit root with drift versus trend stationarity. The DF-type coef ficient tests are found to show the best overall performance in both cases, at least if the sample size is sufficiently large. How ever, it is also found that the DF and LM tests are roughly complementary with regard to their finite-sample power. We therefore consider combining these two types of unit root tests to obtain ( ad hoc 'but') 'robust' test procedures. Critical values for the proposed tests are provided     

Quasi‐Bayesian Estimation of Time‐Varying Volatility in DSGE Models

We propose a novel quasi‐Bayesian Metropolis‐within‐Gibbs algorithm that can be used to estimate drifts in the shock volatilities of a linearized dynamic stochastic general equilibrium (DSGE) model. The resulting volatility estimates differ from the existing approaches in two ways. First, the time variation enters non‐parametrically, so that our approach ensures consistent estimation in a wide class of processes, thereby eliminating the need to specify the volatility law of motion and alleviating the risk of invalid inference due to mis‐specification. Second, the conditional quasi‐posterior of the drifting volatilities is available in closed form, which makes inference straightforward and simplifies existing algorithms. We apply our estimation procedure to a standard DSGE model and find that the estimated volatility paths are smoother compared to alternative stochastic volatility estimates. Moreover, we demonstrate that our procedure can deliver statistically significant improvements to the density forecasts of the DSGE model compared to alternative methods.     

Range Unit‐Root (RUR) Tests: Robust against Nonlinearities,Error Distributions,Structural Breaks and Outliers

Abstract. Since the seminal paper by Dickey and Fuller in 1979, unit‐root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long‐wave patterns observed not only in unit‐root time series but also in series following more complex data‐generating mechanisms. To this end, our testing device analyses the unit‐root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit‐root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit‐root tests on near‐unit‐root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward–backward range unit‐root (FB‐RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey–Fuller unit‐root test on exchange rate series.     

Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models

In this article, we introduce the general setting of a multivariate time series autoregressive model with stochastic time‐varying coefficients and time‐varying conditional variance of the error process. This allows modelling VAR dynamics for non‐stationary time series and estimation of time‐varying parameter processes by the well‐known rolling regression estimation techniques. We establish consistency, convergence rates, and asymptotic normality for kernel estimators of the paths of coefficient processes and provide pointwise valid standard errors. The method is applied to a popular seven‐variable dataset to analyse evidence of time variation in empirical objects of interest for the DSGE (dynamic stochastic general equilibrium) literature.     

Volume fluctuations and linear response in a simple model of compaction

By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and explicit expressions for the average and the variance are provided. Experimental and molecular dynamics results are analyzed and qualitatively compared with the model predictions. The relevance of considering open or closed systems is discussed, as well as the meaning and properties of the Edwards compactivity and the effective (configurational) temperature introduced by some authors. Finally, the linear response to a change in the vibration intensity is also investigated. A KWW decay of the volume response function is clearly identified. This seems to confirm some kind of similarity between externally excited granular systems and structural glasses.     

Large‐scale DMFC Stack Model: Feed Disturbances and Their Impact on Stack Performance

A highly scalable quasi‐3D model of a large 1‐kW class direct methanol fuel cell stack is developed. The model takes into account in‐plane heat and current transport in the bipolar plates, coupled to the through‐plane transport in the membrane‐electrode assemblies. The electro chemical model is an extension of a Perry–Newman–Cairns model with the Butler–Volmer rate of electrochemical conversion. The stack is ”cut” into a large number of elementary geometrical units and each unit is solved on a separate core using supercomputing resources. The model is used to simulate the regimes of stack operation with methanol flow failures in part of the cell. The results show that the full‐fed domain of the cell takes over part of the load of the starved domain, which homogenizes the distribution of all parameters over the defect cell surface.     

Liquid Transport in a Coalescing Froth

A previous study (Ireland and Jameson, J. Colloid Interface Sci., 314 207‐213 (2007)) demonstrated that a “drift‐flux” model could describe liquid transport in a stable rising froth with added “wash water.” In the present study, a drift‐flux model was used to describe a rising coalescing froth. This model incorporated the effect of liquid released into the froth by coalescence. Vertical profiles of liquid fraction and bubble size were obtained in a laboratory cell; a novel technique was used for measuring bubbles deep within the cell. These data were consistent with the predictions of the drift‐flux model.     

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

A two‐dimensional advection‐diffusion model accompanied with a parabolic velocity profile of Poiseuille flow is considered for the chemical species transport in a tube with a constant wall concentration. The Reynolds decomposition technique is applied to reduce it to an equivalent one‐dimensional model for advective‐dispersive transport in a tube through which the effective advection coefficient, the dispersion coefficient, and the effective Sherwood number are developed for the problem under study. The derived and the classical Taylor models are also compared in order to find the difference between the two arrangements. The reduced‐order model for the transport equation shows that the effective advection coefficient increases, whereas the dispersion coefficient in the tube decreases as compared to the classical Taylor equation. The effective Sherwood number for the steady state form of the developed model is found to be only a function of the Peclet number, which varies in the range of 3.215 ≤ Sh ≤ 4. These results find application in design of experiments and improve our understanding of mass transfer in microfluidic devices.     

Risk management for a global supply chain planning under uncertainty: Models and algorithms

In this article, we consider the risk management for mid‐term planning of a global multi‐product chemical supply chain under demand and freight rate uncertainty. A two‐stage stochastic linear programming approach is proposed within a multi‐period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi‐cut L‐shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi‐objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. © 2009 American Institute of Chemical Engineers AIChE J, 2009