NONLINEAR TIME SERIES REGRESSION FOR A CLASS OF AMPLITUDE MODULATED CONSINUSOIDS

Abstract. A central limit theorem is proved for estimates of the unknown parameters in a time series which is a sum of amplitude modulated consinusoids observed subject to error. The amplitude function depends upon unknown parameters as well as the length of the series. The frequency for each cosinusoid is also assumed to be unknown. Estimates and standard errors are obtained through nonlinear least squares in the frequency domain.     

ATesting for the Onset of Trend, Using Wavelets

This paper develops a test for the onset of a time trend, using a wavelet-type estimator. The series level is a nonlinear function of time, with a slope that is zero initially, but non-negative and non-decreasing, or non-positive and non-increasing, beyond the onset point, permitting divergence. The series level is otherwise unspecified, and to estimate it we regress the data series on wavelet scaling functions of time, with a coefficient restriction that makes the fitted level constant until some point in the sample. Since the true onset point is unknown, we examine several such restrictions, yielding candidate onset points at equally spaced positions in the sample. We base our test on some F -type statistics, which compare the performance of successive fitted levels. To exploit the asymmetry of the true level under the alternative, we use a weighted sum of F stastistics, with linearly increasing weight at points further in the sample. This test statistic has a nonstandard distribution, which we tabulate. Asymptotically, we show that linear weighting gives better local power than equal weighting. A simulation study confirms the power advantage of our test.     

化工过程基于广义非线性状态观测器的不可测输入和不确定模型参数软仪表(英文)

Chemical processes are usually nonlinear singular systems. In this study, a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes, which are augmented as state variables. Based on the observability of the singular system, this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters. When the observability is satisfied, the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer. The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation. With the catalyst circulation rate as the only unknown input without model error, one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst cir- culation rate. However, when uncertain model parameters also exist, additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.     

Structural parameter identifiability analysis for dynamic reaction networks

A fundamental problem in model identification is to investigate whether unknown parameters in a given model structure potentially can be uniquely recovered from experimental data. This issue of global or structural identifiability is essential during nonlinear first principles model development where for a given set of measured variables it is desirable to investigate which parameters may be estimated prior to spending computational effort on the actual estimation. This contribution addresses the structural parameter identifiability problem for the typical case of reaction network models. The proposed analysis is performed in two phases. The first phase determines the structurally identifiable reaction rates based on reaction network stoichiometry. The second phase assesses the structural parameter identifiability of the specific kinetic rate expressions using a generating series expansion method based on Lie derivatives. The proposed systematic two phase methodology is illustrated on a mass action based model for an enzymatically catalyzed reaction pathway network where only a limited set of variables is measured. The methodology clearly pinpoints the structurally identifiable parameters in dependence of the given measurements and input perturbations.     

A GOODNESS-OF-FIT TEST FOR AUTOREGRESSIVE MOVING-AVERAGE MODELS BASED ON THE STANDARDIZED SAMPLE SPECTRAL DISTRIBUTION OF THE RESIDUALS

Abstract. A stochastic process derived from the standardized sample spectral density of the residuals of a causal and invertible ARMA( p, q ) model is introduced to construct a goodness-of-fit procedure. The test statistics considered have a proper limiting distribution which is free of unknown parameters and which, unlike some well-known goodness-of-fit statistics based on the residuals, does not depend on the sample size.     

PARAMETER ESTIMATION OF MONOD KINETICS WITHOUT BIOMASS DATA AND INITIAL SUBSTRATE CONCENTRATION

The uniqueness of the parameters in a Monod kinetics model estimated from substrate depletion and product growth data were analyzed using nonlinear regression. The initial substrate and biomass concentrations were considered as unknown (unmeasured) parameters. Simulated data containing known measurement errors were generated first using specified parameters and then these data were used for the analysis. Sensitivity coefficients were determined by differentiating the original differential equations of the Monod kinetics. A procedure for determining the scale factors for the parameters (used in the nonlinear regression method) has also been developed. The number of parameters that can be determined uniquely depends on the region of substrate depletion (first order, mixed order or zero order). The availability of product data leads to additional estimation of parameters in the mixed order region. The number of parameters that could be estimated are identified qualitatively by the sensitivity coefficient analysis and quantitatively by analyzing the orthonormal eigenvectors of the Gauss-Newton matrix in the nonlinear regression algorithm. Experimental data on aerobic and anareobic substrate depletion were used to estimate the parameters and validate the analysis.     

Inference in Autoregression under Heteroskedasticity

Abstract. A scalar pth‐order autoregression (AR(p)) is considered with heteroskedasticity of the unknown form delivered by a transition function of time. A limit theory is developed and three heteroskedasticity‐robust test statistics are proposed for inference, one of which is based on the nonparametric estimation of the variance function. The performance of the resulting testing procedures in finite samples is compared in simulations and some suggestions for practical application are given.     

New Improved Tests for Cointegration with Structural Breaks

Abstract. This article proposes Lagrange multiplier‐based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small‐sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests.     

Nonlinear process identification in the presence of multiple correlated hidden scheduling variables with missing data

Identification of nonlinear processes in the presence of noise corrupted and correlated multiple scheduling variables with missing data is concerned. The dynamics of the hidden scheduling variables are represented by a state‐space model with unknown parameters. To assure generality, it is assumed that the multiple correlated scheduling variables are corrupted with unknown disturbances and the identification dataset is incomplete with missing data. A multiple model approach is proposed to formulate the identification problem of nonlinear systems under the framework of the expectation‐maximization algorithm. The parameters of the local process models and scheduling variable models as well as the hyperparameters of the weighting function are simultaneously estimated. The particle smoothing technique is adopted to handle the computation of expectation functions. The efficiency of the proposed method is demonstrated through several simulated examples. Through an experimental study on a pilot‐scale multitank system, the practical advantages are further illustrated. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3270–3287, 2015     

Real time change-point detection in a nonlinear quantile model

Most studies in real-time change-point detection either focus on the linear model or use the cumulative sum (CUSUM) method under classical assumptions on model errors. This article considers the sequential change-point detection in a nonlinear quantile model. A test statistic based on the CUSUM of the quantile process subgradient is proposed and studied. Under the null hypothesis that the model does not change, the asymptotic distribution of the test statistic is determined. Under the alternative hypothesis that at some unknown observation there is a change in the model, the proposed test statistic converges in probability to ∞. These results allow building the critical regions on open-end and on closed-end procedures. Simulation results, using a Monte Carlo technique, investigate the performance of the test statistic, especially for heavy-tailed error distributions. We also compare it with the classical CUSUM test statistic. An example on real data is also given.     

Recursive adjustment,unit root tests and structural breaks

In this paper, we introduce unit root tests for time series with a potential structural break computed from test regressions in which the deterministic components have been recursively adjusted. We present finite sample critical values as well as Monte Carlo results on the size and power performance of the new procedures, and compare these with other available tests in the literature, such as OLS and quasi‐differenced based tests (see, for instance, Perron, (1997) Perron and Rodriguez, (2003) and Carrion‐i‐Silvestre et al. (2009) ). The small sample behaviour of the tests is evaluated in a known and an unknown break date context allowing for negligible and non‐negligible initial conditions. In the unknown break date case, two break date estimation procedures are considered, one based on the minimum unit root t‐statistic and the other based on the minimum sum of squared residuals obtained from a regression on a set of deterministic variables. The size and power performance of the recursive adjustment based procedure in the unknown break date case is encouraging. A further result of this paper relates to the aditional finite sample evidence on the performance of quasi‐differenced unit root tests, complementing the results in Perron and Rodriguez (2003) .     

A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks

Abstract. Macroeconomic variables have been shown to display a wide variety of structural breaks of unknown number, duration and form. This poses a challenge since improperly modelled breaks can result in a seriously misspecified model. In this paper, we develop a new test for stationarity that approximates the unknown form of structural breaks using a selected frequency component from a Fourier approximation. Our proposed test performs quite well when breaks are gradual, and shows reasonable power. The appropriate use of the test is illustrated by examining real exchange rates in the post‐Bretton Woods period.     

TESTING THE ORDER OF DIFFERENCING IN TIME SERIES REGRESSION

Abstract. In this paper we develop a test procedure for detecting overdifferencing or a moving-average unit root in time series regression models with Gaussian autoregressive moving-average errors. In addition to an intercept term the regressors consist of stable or asymptotically stationary variables and non-stationary trending variables generated by an integrated process of order 1. The test of the paper is based on the theory of locally best invariant unbiased tests. Its limiting distribution is derived under the null hypothesis and found to be non-standard but free of unknown nuisance parameters. Asymptotic critical values, which depend on the number of integrated regressors, are obtained by simulation. A limited simulation study is carried out to illustrate the finite sample properties of the test.     

炭/炭复合材料试样加工对其力学性能测试结果的影响

针对同批炭/炭复合材料力学性能测试结果相差较大的情况,从取样、试样加工过程和工艺试验研究入手,通过分析其力学性能测试结果,对加工参数、加工方法对炭/炭复合材料力学性能测试的影响程度进行了研究,结合对所加工试样的表观质量分析,系统地探讨各种参数的影响,给出适合炭/炭复合材料试样加工的最优切削参数,并给出试样界面尺寸的公差控制范围,有效地降低了炭/炭复合材料试样力学性能测试的偏差。     

NORMING RATES AND LIMIT THEORY FOR SOME TIME‐VARYING COEFFICIENT AUTOREGRESSIONS

A time‐varying autoregression is considered with a similarity‐based coefficient and possible drift. It is shown that the random‐walk model has a natural interpretation as the leading term in a small‐sigma expansion of a similarity model with an exponential similarity function as its AR coefficient. Consistency of the quasi‐maximum likelihood estimator of the parameters in this model is established, the behaviours of the score and Hessian functions are analysed and test statistics are suggested. A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian function standardization. A large family of unit root models with stationary and explosive alternatives is characterized within the similarity class through the asymptotic negligibility of a certain quadratic form that appears in the score function. A variant of the stochastic unit root model within the class is studied, and a large‐sample limit theory provided, which leads to a new nonlinear diffusion process limit showing the form of the drift and conditional volatility induced by sustained stochastic departures from unity. The findings provide a composite case for time‐varying coefficient dynamic modelling. Some simulations and a brief empirical application to data on international Exchange Traded Funds are included. Copyright © 2014 Wiley Publishing Ltd     

A GENERALIZED VARIANCE RATIO TEST OF ARIMA (p, 1, q) MODEL SPECIFICATION

Abstract. The variance ratio test is often used as a check of the hypothesis that a time series is generated by a random walk. A natural extension of the test is developed to cover the case where the assumed model is ARIMA(p, 1, q), with unknown parameters. Small sample properties of the generalized test are investigated, and the test is applied to a frequently analysed data set on US quarterly real gross national product. In effect, we are testing for low frequency misspecification in assumed autoregressive moving-average (ARMA) models for a differenced series.     

Detecting misspecifications in autoregressive conditional duration models and non‐negative time‐series processes

We develop a general theory to test correct specification of multiplicative error models of non‐negative time‐series processes, which include the popular autoregressive conditional duration (ACD) models. Both linear and nonlinear conditional expectation models are covered, and standardized innovations can have time‐varying conditional dispersion and higher‐order conditional moments of unknown form. No specific estimation method is required, and the tests have a convenient null asymptotic N(0,1) distribution. To reduce the impact of parameter estimation uncertainty in finite samples, we adopt Wooldridge's (1990a) device to our context and justify its validity. Simulation studies show that in the context of testing ACD models, finite sample correction gives better sizes in finite samples and are robust to parameter estimation uncertainty. And, it is important to take into account time‐varying conditional dispersion and higher‐order conditional moments in standardized innovations; failure to do so can cause strong overrejection of a correctly specified ACD model. The proposed tests have reasonable power against a variety of popular linear and nonlinear ACD alternatives.     

基于S3C2410的嵌入式弧焊电源测试平台设计

基于三星公司的S3C2410处理器设计了一款弧焊电源测试平台,利用该平台实现对弧焊电源电参数的测量,评估被测弧焊电源的质量和产品性能。该系统适合交、直流弧焊电源测试,可以进行静态工作点的测试和电流、电压及功率等电参数的测量。     

Temperature regulation of a class of continuous chemical reactor based on a nonlinear Luenberger-like observer

In this paper is studied the temperature regulation problem of a continuous stirred tank reactor with two consecutive and oscillatory exothermic reactions in which the heat of the reactions is unknown. A strategy to estimate the reactions' heat from measurements of reactor temperature is proposed. This strategy is coupled with a linearizing-like feedback regulatory control. Practical convergence of this control scheme is proved when the uncertainty observer satisfies the high gain assumption. The performance of the uncertainty observer and the closed loop behavior is illustrated by means of numerical simulations. ©1997 SCI