A NOTE ON NON-STATIONARITY AND CANONICAL ANALYSIS OF MULTIPLE TIME SERIES MODELS

Abstract. Box and Tiao (1977) established the correspondence between non-stationary roots and canonical correlations of an AR(1) process. In this paper, we give an alternative, more direct, proof of the correspondence and extend a special case of that result to AR( p ) processes. The usefulness of these results for multiple time series modelling is also briefly discussed.     

A UNIFIED APPROACH TO THE STUDY OF SUMS, PRODUCTS, TIME-AGGREGATION AND OTHER FUNCTIONS OF ARMA PROCESSES

Abstract. Conditions under which sums, products and time-aggregation of ARMA processes follow ARMA models are derived from a single theorem. This characterizes these processes in terms of difference equations satisfied by their autocovariance function. From this we obtain necessary and sufficient conditions for a function of a Gaussian ARMA process and the product of two possibly dependent Gaussian ARMA processes to be ARMA. We show that the sum and product of two ARMA processes related by a Box and Jenkins transfer function model belong to the ARMA family.     

Decomposition of Time Series Dynamic Linear Models

This paper derives the admissible decompositions for a time series dynamic linear model, assuming only that the model is observable. The decompositions depend on factorizations of the characteristic polynomial of the state evolution matrix G into relatively prime factors. This generalizes the method of West (1997 ) which considers one decomposition in the particular case where G is diagonalizable. Conditions are derived for a decomposition to be independent. These results show that no autoregressive process of order d has an independent decomposition for any integer d . Two illustrations of this procedure are discussed in detail.     

STOCHASTIC MODELING AND ANALYSIS OF A TURBULENT FLOW SYSTEM

A stochastic model is developed to describe the axial movement of an element or particle in a turbulent flow system, where diffusion or local transition is not the major mechanism dictating particle motion. The model is a generalization of the diffusion equation for particle movement and includes both diffusion and random displacements. From this model, one can determine the residence time distribution and estimate the parameters characterizing the flow system.     

ON THE DIFFERENT FORMS OF MOMENTUM EQUATIONS AND ON THE INTRA- AND INTERPHASE INTERACTION IN THE HYDROMECHANICS OF A MONODISPERSED MIXTURE

Many different forms of the phasic conservation equations of two-phase flow have been presented in the literature. Unfortunately, there is still a lot of controversy as to "best" form for two-fluid modeling. In addition, while there have been many attempts to constitute the intraphase and interfacial closure laws to achieve closure, ill-posed models are still the rule rather than the exception. The purpose of the paper is to show how various popular forms of the two-fluid model are relaled, and to summarize the current state-of-the art in the modeling of interfacial and intraphase closure laws. Moreover, new closure laws are proposed which attempt to account for the effect of dispersed phase (i.e., inter-partical) interactions. It is hoped that this paper will help stimulate multiphase flow researchers to redouble this effort to achieve accurate, properly closed, two-fluid models which can used for the mechanistic predictions of multidimensional two-phase flows.     

ON THE DIFFERENT FORMS OF MOMENTUM EQUATIONS AND ON THE INTRA- AND INTERPHASE INTERACTION IN THE HYDROMECHANICS OF A MONODISPERSED MIXTURE

Many different forms of the phasic conservation equations of two-phase flow have been presented in the literature. Unfortunately, there is still a lot of controversy as to "best" form for two-fluid modeling. In addition, while there have been many attempts to constitute the intraphase and interfacial closure laws to achieve closure, ill-posed models are still the rule rather than the exception. The purpose of the paper is to show how various popular forms of the two-fluid model are relaled, and to summarize the current state-of-the art in the modeling of interfacial and intraphase closure laws. Moreover, new closure laws are proposed which attempt to account for the effect of dispersed phase (i.e., inter-partical) interactions. It is hoped that this paper will help stimulate multiphase flow researchers to redouble this effort to achieve accurate, properly closed, two-fluid models which can used for the mechanistic predictions of multidimensional two-phase flows.     

A BAYESIAN APPROACH TO ESTIMATING AND FORECASTING ADDITIVE NONPARAMETRIC AUTOREGRESSIVE MODELS

Abstract. We present a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines. Our approach is robust to innovation outliers; it can handle missing observations and produce multistep ahead forecasts. The computation is carried out using Markov chain Monte Carlo and requires O( nM ) operations where n is the sample size and M is the number of Markov chain iterations. This makes it the first exact algorithm for spline smoothing of an additive autoregressive model which can handle large data sets. The properties of the estimates and forecasts are studied empirically using simulated and real data sets.     

FORECASTING TIME SERIES:A COMPARATIVE ANALYSIS OF ALTERNATIVE CLASSES OF TIME SERIES MODELS

Abstract. Performance of the state dependent model developed by Priestley is evaluated relative to that of bilinear and standard linear models using two well-known time series. The results indicate the use of broader classes of time series models beyond the conventional ARMA class is likely to lead to significant reductions in forecasting error. However, there are difficult problems relating to the identification of the order of the model, estimation of the parameters, and determination of the correct nonlinear model.     

ON THE AUTOCORRELATION STRUCTURE AND IDENTIFICATION OF SOME BILINEAR TIME SERIES

Abstract. For the bilinear time series X _t =β X _t-k e _t-l + e _v , k ≥ l , formulas for the first k -1 autocorrelations of X ² _t are obtained. These results fill in a gap in Granger and Andersen (1978). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if ß is not too small, k and l may be identified using the autocorrelations of X ² _t . Application to more general situations is also briefly discussed.     

LOGSPLINE ESTIMATION OF A POSSIBLY MIXED SPECTRAL DISTRIBUTION

Abstract. Cubic splines and indicator functions are used to estimate the spectral density function and line spectrum, respectively, for a stationary time series. A fully automatic procedure involving maximum likelihood, stepwise addition and deletion of basis functions, and the Bayes information criterion (BIC) is used to select the final model.     

STATE-DEPENDENT MODELS: A GENERAL APPROACH TO NON-LINEAR TIME SERIES ANALYSIS

Abstract. We construct a general class of non-linear models, called 'state-dependent models', which have a very flexible non-linear structure and which contain, as special cases, bilinear, threshold autoregressive, and exponential autoregressive models. We describe a sequential type of recursive algorithm for identifying state-dependent models, and show how such models may be used for forecasting and for indicating specific types of non-linear behaviour.     

ESTIMATION AND TESTING OF A MULTIVARIATE EXPONENTIAL SMOOTHING MODEL

Abstract. The form of the spectral likelihood function of a multivariate stochastic process permits straightforward construction of a scoring algorithm for maximum likelihood estimation using first derivatives only and a score test statistic for hypothesis testing. These techniques are applied to the analysis of a multivariate exponential smoothing model for which the homogeneity hypothesis is also discussed.     

A Structural‐Factor Approach to Modeling High‐Dimensional Time Series and Space‐Time Data

This article considers a structural‐factor approach to modeling high‐dimensional time series and space‐time data by decomposing individual series into trend, seasonal, and irregular components. For ease in analyzing many time series, we employ a time polynomial for the trend, a linear combination of trigonometric series for the seasonal component, and a new factor model for the irregular components. The new factor model simplifies the modeling process and achieves parsimony in parameterization. We propose a Bayesian information criterion to consistently select the order of the polynomial trend and the number of trigonometric functions, and use a test statistic to determine the number of common factors. The convergence rates for the estimators of the trend and seasonal components and the limiting distribution of the test statistic are established under the setting that the number of time series tends to infinity with the sample size, but at a slower rate. We study the finite‐sample performance of the proposed analysis via simulation, and analyze two real examples. The first example considers modeling weekly PM_2.5 data of 15 monitoring stations in the southern region of Taiwan and the second example consists of monthly value‐weighted returns of 12 industrial portfolios.     

食品冷冻干燥过程的模型及影响因素

在合理简化的基础上,得到了只需较少参数的冷冻干燥过程一维数学模型。通过对胡萝卜和土豆食品的冷冻干燥实验,研究了加热方式、加热搁板温度和干燥室真空度对干燥时间的影响,模型的数值解与实验值吻合良好。     

a rview of: UNIFIED ANALYSIS AND SOLUTIONS OF HEAT AND MASS DIFFUSION

ABSTRACT

The objective of this study is the formulation of a finite element model that could be used to analyze the stress crack formation in a viscoelastic sphere resulting from temperature and moisture gradients during the drying process. Numerical solutions to the simultaneous moisture and heat diffusion equations describing moisture removal and heat intake process for the sphere are obtained. The distribution and gradients of temperature and moisture developed inside the sphere during drying are established. The calculated temperature and moisture gradients are used in a finite element analysis of the thermo-hydro viscoelastic boundary value problem to simulate the stresses in the body.

The model is used to solve a sample problem of drying a soybean kernel. The simulated drying curve for the soybean model is obtained and compared favorably with the experimental results reported in the literature. Tangential stress, as a criteria for failure, is shown to change from compressive to tensile stress as it approaches the surface. It reaches its peak value at the surface in one hour and then decays slowly. The effect of different drying conditions is studied and the results are discussed.     

A+A~2/O工艺脱氮除磷参数调控及运行效果分析

结合广州市猎德污水处理厂A+A2/O工艺的实际运行情况,对其脱氮除磷参数调控和运行效果进行了分析。首先考察了冬天低温条件下的脱氮除磷效果,然后经过不同混合液体积回流比和污泥体积回流比的运行分析,得到适合工艺运行的最佳值,分别为100%和100%,还对其它参数调控进行了简要介绍,最后对工艺整体运行效果进行了分析,得到良好的结果。证明A+A2/O工艺具有良好的脱氮除磷效果。     

A note on non‐parametric testing for Gaussian innovations in AR–ARCH models

In this paper, we consider autoregressive models with conditional autoregressive variance, including the case of homoscedastic AR models and the case of ARCH models. Our aim is to test the hypothesis of normality for the innovations in a completely non‐parametric way, that is, without imposing parametric assumptions on the conditional mean and volatility functions. To this end, the Cramér–von Mises test based on the empirical distribution function of non‐parametrically estimated residuals is shown to be asymptotically distribution‐free. We demonstrate its good performance for finite sample sizes in a small simulation study. AMS 2010 Classification: Primary 62 M10, Secondary 62 G10     

SIMULTANEOUS DEVELOPMENT OF VELOCITY AND TEMPERATURE PROFILES IN THE ENTRANCE REGION OF A PARALLEL PLATE CHANNEL: LAMINAR FLOW WITH UNIFORM WALL HEAT FLUX

Available boundary layer type solutions to the combined hydrodynamic and thermal entrance region problem are known to exhibit a discontinuity in the gradients of the velocity and temperature distributions in the entrance region. A new solution is presented which alleviates this shortcoming. The new solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Das (1982) to hydrodynamically developing flow in a channel. This concept is extended to the combined entry length problem by dividing the thermal entrance length into two lengthwise regions, a thermal inlet region and a thermally filled region. In the former, the effect of heat transfer between fluid and wall is confined within the thermal boundary layer developing along the wall. At the end of the thermal inlet region, the thermal boundary layers meet at the duct axis but the temperature profile is not yet developed. In the thermally filled region, the heat effects propagate throughout the entire cross section and the temperature profile undergoes adjustment in a fully thermal region to finally attain the fully developed form. A thermal shape factor is also introduced in the thermally filled region which ensures that all thermal quantities attain their fully developed values asymptotically. The new model is used to obtain solutions to the combined entry length problem for laminar flow through a parallel plate channel under the constant wall heat flux boundary condition. The analysis gives considerably better results for the local Nusselt number and thermal entrance length than previously available.     

AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A NON-FRACTAL APPROACH

Aggregation and breakage of solid particles or aggregates suspended in liquid can be found in numerous industrial processes. It is crucially important to predict the evolution of aggregates at any moment during the process. This aim can be achieved by modeling based on solid phase population balances. A lumped discrete population balance model has been selected for the verification of the experimental data. The experiments have been carried out in a laboratory-scale vibrating mixer equipped with a disc-type reciprocating impeller. A reasonably good agreement between the computational and experimental results of PSD data has been obtained. Dependencies between aggregation and breakage rate coefficients and the average energy dissipation rate in the mixer have been shown.     

AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A NON-FRACTAL APPROACH

Aggregation and breakage of solid particles or aggregates suspended in liquid can be found in numerous industrial processes. It is crucially important to predict the evolution of aggregates at any moment during the process. This aim can be achieved by modeling based on solid phase population balances. A lumped discrete population balance model has been selected for the verification of the experimental data. The experiments have been carried out in a laboratory-scale vibrating mixer equipped with a disc-type reciprocating impeller. A reasonably good agreement between the computational and experimental results of PSD data has been obtained. Dependencies between aggregation and breakage rate coefficients and the average energy dissipation rate in the mixer have been shown.