Robust estimation for copula Parameter in SCOMDY models

In this study, we study the robust estimation for the copula parameter in semiparametric copula‐based multivariate dynamic (SCOMDY) models proposed by Chen and Fan (2006). To this end, instead of the pseudo maximum likelihood estimator in Chen and Fan (2006), we use a minimum density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE is consistent and asymptotically normal under regularity conditions. We compare the performance between the two estimators when outliers exist through a simulation study.     

Dynamics of Model Overfitting Measured in terms of Autoregressive Roots

Abstract. One method of describing the properties of a fitted autoregressive model of order p is to show the p roots that are implied by the lag operator. Considering autoregressive models fitted to 215 US macro series, with lags chosen by either the Bayesian or Schwarz information criteria or Akaike information criteria, the roots are found to constitute a distinctive pattern. Later analysis suggests that much of this pattern occurs because of overfitting of the models. An extension of the results shows that they have some practical multivariate time‐series modelling implications.     

The Slow Convergence of Ordinary Least Squares Estimators of α, β and Portfolio Weights under Long‐Memory Stochastic Volatility

We consider inference for the market model coefficients based on simple linear regression under a long memory stochastic volatility generating mechanism for the returns. We obtain limit theorems for the ordinary least squares (OLS) estimators of α and β in this framework. These theorems imply that the convergence rate of the OLS estimators is typically slower than if both the regressor and the predictor have long memory in volatility, where T is the sample size. The traditional standard errors of the OLS‐estimated intercept () and slope (), which disregard long memory in volatility, are typically too optimistic, and therefore the traditional t‐statistic for testing, say, α = 0 or β = 1, will diverge under the null hypothesis. We also obtain limit theorems (which imply slow convergence) for the estimated weights of the minimum variance portfolio and the optimal portfolio in the same framework. In addition, we propose and study the performance of a subsampling‐based approach to hypothesis testing for α and β. We conclude by noting that analogous results hold under more general conditions on long‐memory volatility models and state these general conditions which cover certain fractionally integrated exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models.     

Time‐series models with an EGB2 conditional distribution

A time‐series model in which the signal is buried in noise that is non‐Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation‐driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum‐likelihood (ML) estimator. Score‐driven models of this kind can also be based on conditional t distributions, but whereas these models carry out what, in the robustness literature, is called a soft form of trimming, the EGB2 distribution leads to a soft form of Winsorizing. An exponential general autoregressive conditional heteroscedastic (EGARCH) model based on the EGB2 distribution is also developed. This model complements the score‐driven EGARCH model with a conditional t distribution. Finally, dynamic location and scale models are combined and applied to data on the UK rate of inflation.     

Using the HEGY Procedure When Not All Roots Are Present

Abstract. Empirical studies have shown little evidence to support the presence of all unit roots present in the Δ₄ filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo [Journal of Econometrics (1990) Vol. 44, pp. 215–238] (HEGY) procedure when the roots under the null are not all present. We exploit the vector of quarters representation and cointegration relationship between the quarters when factors (1 − L), (1 + L), (1 + L²), (1 − L²) and (1 + L + L² + L³) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency π/2 and two combinations of the previous cases. We show both theoretically and through a Monte Carlo analysis that the t‐ratios t and t and the F‐type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is (are) present, although this is not the case for the t‐ratio tests associated with unit roots at frequency π/2.     

Some new operational modes and parameters of stress relaxation for the viscoelastic characterization of solid polymers. I. The “virtual modulus” mode

A new operational (functional) parameter, the so‐called virtual modulus, ē(t), is introduced. By this, an attempt was made for the approximation of the function of the real modulus E(t), which, as known, is valid only for instantaneous loading, namely, for zero loading times. Thus, through a simple theoretical modeling and an algorithmic approach, the determination of E(t), from ē(t), sets sail, at the end, to the solution of a Volterra integral equation of the second type, which, in turn, sets sail to the solution of a differential equation. By the aid of numerical integration and also of some experimental evidence, it seems that this solution is valid only for loading times approximately above 0.2 s, thus obtaining, in fact, a “pseudomodulus” of relaxation. To assess the validity of this pseudomodulus, the well‐known Kohlrausch–Williams–Watt (KWW) and the power‐law models were used as some crude “criteria.” By means of best fit, it appeared, at the first instance, that the so‐calculated pseudomodulus better obeys the power‐law model than it does the KWW model. This is a certain contradiction with the so‐called apparent modulus, which was obtained from experiment with a finite loading time superior to 1 s. Two other criteria that were used have shown a satisfactory proof of the validity of this modeling. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 121–137, 2003     

Dimensionless Empirical Model to Correlate Pharmaceutical Compound Solubility in Supercritical Carbon Dioxide

The accurate experimental determination of pharmaceutical compound solubilities at various temperature and pressure ranges in supercritical carbon dioxide (ScCO₂) is a challenging and time‐consuming task. Therefore, prediction or correlations of solute solubilities are essential for implementation of ScCO₂ technologies to pharmaceutical industries. Solubilities of 41 pharmaceutical compounds in ScCO₂ are correlated by an empirical model, which is developed based on the degree of freedom analysis. Its correlating ability is compared with existing solubility models elaborated by other authors and evaluated in terms of global mean absolute relative deviation, sum of squares due to error, root mean square deviation, R², and Adj. R². The proposed model is found to correlate better than existing models.     

A novel feasibility analysis method for black‐box processes using a radial basis function adaptive sampling approach

Feasibility analysis is used to determine the feasible region of a multivariate process. This can be difficult when the process models include black‐box constraints or the simulation is computationally expensive. To address such difficulties, surrogate models can be built as an inexpensive approximation to the original model and help identify the feasible region. An adaptive sampling method is used to efficiently sample new points toward feasible region boundaries and regions where prediction uncertainty is high. In this article, cubic Radial Basis Function (RBF) is used as the surrogate model. An error indicator for cubic RBF is proposed to indicate the prediction uncertainty and is used in adaptive sampling. In all case studies, the proposed RBF‐based method shows better performance than a previously published Kriging‐based method. © 2016 American Institute of Chemical Engineers AIChE J, 63: 532–550, 2017     

A Shrinked Forecast in Stationary Processes Favouring Percentage Error

Abstract. In stationary time‐series forecasting, the commonly used criterion for selecting a proper forecast is the mean square error (MSE), which is minimized by the conditional expectation of future observation given the entire past known as a minimum MSE forecast. In this paper, mean square percentage error (MSPE) instead of is used to forecast autoregressive moving average (ARMA)(p,q) series. The suggested forecast takes the form of or (CV_t+1 is the coefficient of variation for one step ahead) times the minimum MSE forecast, which performs better not only in MSPE, but also in mean absolute percentage error (MAPE) than the ordinary MSE forecast in simulation studies. A real data example also supported this result. We conclude that, if percentage error is a prime concern, this shrinked version of MSE forecast performs better than the ordinary forecast in the stationary ARMA(p,q) model.     

Nonlinear viscoelasticity of “hard elastic” polypropylene fibers

“Hard elastic” polypropylene fibers respond nonlinearly to stress at all strains. Low tenacities at break (less than 1 g/denier), low moduli of elasticity (slopes of stress-strain curves from 2.8 to 28 g/denier), and large breaking extensions (over 800 percent) are characteristic of “hard elastic” fibers. Behavior in simple extension, cyclic extension, and stress relaxation can be represented by a quasi-linear viscoelastic model which uses a continuous relaxation spectrum and a quasilinear relation between stress history T(t)and strain history λ(t): where T^e[λ(t)] is the elastic response. When creep data are available, this model should provide a unified representation of experimental observations.     

Residuals‐based tests for the null of no‐cointegration: an Analytical comparison

Abstract. This article studies the asymptotic distribution of five residuals‐based tests for the null of no‐cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares (GLS)‐detrended variables. The local asymptotic power of the tests is shown to be a function of Brownian motion and Ornstein–Uhlenbeck processes, depending on a single nuisance parameter, which is determined by the correlation at frequency zero of the errors of the cointegration regression with the shocks to the right‐hand side variables. The tests are compared in terms of power in large and small samples. It is shown that, while no significant improvement can be achieved by using unit root tests other than the OLS detrended t‐test originally proposed by Engle and Granger (1987), the power of GLS residuals tests can be higher than the power of system tests for some values of the nuisance parameter.     

A Precursor Approach to Electrospun Polyaniline Nanofibers for Gas Sensors

Polyaniline (PANI) has served as one of the most promising conducting materials in a variety of fields including sensors, actuators, and electrodes. Fabrication of 1D PANI fibers using electrospinning methods has gained a significant amount of attention. Due to the extremely poor solubility of PANI in common organic solvents, fabrication of electrospun PANI fiber has been carried out either by using corrosive solvents such as H₂SO₄ or by electrospinning in the presence of other matrix polymers. Herein, a new approach to the fabrication of PANI fibers using tert‐butyloxycarbonyl‐protected PANI (t‐Boc PANI) as the conducting polymer precursor is reported. The t‐Boc PANI is soluble in common organic solvents (e.g., chloroform and tetrahydrofuran), and electrospinning of t‐Boc PANI in those solvents affords nano/micrometer‐sized t‐Boc PANI fibers. Treatment of the electrospun t‐Boc PANI fibers with HCl results in the removal of the acid labile t‐Boc group and the generation of conducting (≈20 S cm^?1) PANI fibers. The HCl‐doped PANI fibers are successfully used in the detection of gaseous ammonia with a detection limit of 10 ppm.

     

One‐Step C‐Terminal Deprotection and Activation of Peptides with Peptide Amidase from Stenotrophomonas maltophilia in Neat Organic Solvent

Chemoenzymatic peptide synthesis is a rapidly developing technology for cost effective peptide production on a large scale. As an alternative to the traditional C→N strategy, which employs expensive N‐protected building blocks in each step, we have investigated an N→C extension route that is based on activation of a peptide C‐terminal amide protecting group to the corresponding methyl ester. We found that this conversion is efficiently catalysed by Stenotrophomonas maltophilia peptide amidase in neat organic media. The system excludes the possibility of internal peptide cleavage as the enzyme lacks intrinsic protease activity. The produced peptide methyl ester was used for peptide chain extension in a kinetically controlled reaction by a thermostable protease.

     

Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

Finite Sample Theory of QMLE in ARCH Models with Dynamics in the Mean Equation

Abstract. We provide simulation and theoretical results concerning the finite‐sample theory of quasi‐maximum‐likelihood estimators in autoregressive conditional heteroskedastic (ARCH) models when we include dynamics in the mean equation. In the setting of the AR(q)–ARCH(p), we find that in some cases bias correction is necessary even for sample sizes of 100, especially when the ARCH order increases. We warn about the existence of important biases and potentially low power of the t‐tests in these cases. We also propose ways to deal with them. We also find simulation evidence that when conditional heteroskedasticity increases, the mean‐squared error of the maximum‐likelihood estimator of the AR(1) parameter in the mean equation of an AR(1)‐ARCH(1) model is reduced. Finally, we generalize the Lumsdaine [J. Bus. Econ. Stat. 13 (1995) pp. 1–10] invariance properties for the biases in these situations.     

Hyper‐spherical and elliptical stochastic cycles

A univariate first‐order stochastic cycle can be represented as an element of a bivariate first‐order vector autoregressive process, or VAR(1), where the transition matrix is associated with a rotation along a circle in the plane, and the reduced form is ARMA(2,1). This paper generalizes this representation in two directions. According to the first, the cyclical dynamics originate from the motion of a point along an ellipse. The reduced form is also ARMA(2,1), but the model can account for certain types of asymmetries. The second deals with the multivariate case: the cyclical dynamics result from the projection along one of the coordinate axis of a point moving in along an hyper‐sphere. This is described by a VAR(1) process whose transition matrix is obtained by a sequence of n‐dimensional Givens rotations. The reduced form of an element of the system is shown to be ARMA(n, n ? 1). The properties of the resulting models are analysed in the frequency domain, and we show that this generalization can account for a multimodal spectral density. The illustrations show that the proposed generalizations can be fitted successfully to some well‐known case studies of the time series literature.     

Asymptotic Distribution of the Bias Corrected Least Squares Estimators in Measurement Error Linear Regression Models Under Long Memory

This article derives the consistency and asymptotic distribution of the bias corrected least squares estimators (LSEs) of the regression parameters in linear regression models when covariates have measurement error (ME) and errors and covariates form mutually independent long memory moving average processes. In the structural ME linear regression model, the nature of the asymptotic distribution of suitably standardized bias corrected LSEs depends on the range of the values of where d _X ,d _u , and d _ε are the LM parameters of the covariate, ME and regression error processes respectively. This limiting distribution is Gaussian when and non‐Gaussian in the case . In the former case some consistent estimators of the asymptotic variances of these estimators and a log(n)‐consistent estimator of an underlying LM parameter are also provided. They are useful in the construction of the large sample confidence intervals for regression parameters. The article also discusses the asymptotic distribution of these estimators in some functional ME linear regression models, where the unobservable covariate is non‐random. In these models, the limiting distribution of the bias corrected LSEs is always a Gaussian distribution determined by the range of the values of d _ε ? d _u .     

Median‐unbiased Estimation and Exact Inference Methods for First‐order Autoregressive Models with Conditional Heteroscedasticity of Unknown Form

Abstract. Consider the first‐order autoregressive model y_t = φy_t?1 + ?_t, t = 1,…, T, with arbitrary initial non‐zero value y₀. Assuming that the error terms ?_t are independently distributed according to median‐zero distributions [ Zieliński (1999) Journal of Time Series Analysis, Vol. 20, p. 477] shows that the estimator conjectured by Hurwicz (1950) Statistical Inference in Dynamic Economic Models. New York, NY: Wiley – the median of the consecutive ratios y_t/y_t?1– is an exactly median‐unbiased estimator of the autoregressive parameter φ. This paper shows that the Hurwicz estimator remains median‐unbiased under more general distributional assumptions, without assuming statistical independence. In particular, no restrictions are placed on the degree of heterogeneity and dependence of the conditional variance process. A computationally efficient method is also proposed to build exact confidence intervals for the autoregressive parameter which are valid in finite samples for any value of φ on the real line.     

Simplified theory for linear rheology of monodisperse linear polymers

A new version of the tube theory based on the de Gennes–Doi–Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero‐shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman–McLeish model combines self‐consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman–McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed‐form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero‐shear viscosity (η₀). Results of the computations of the zero‐shear viscosity and of the slope of η₀ versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of η₀ versus molecular weight. The possibility of inferring monomer chemistry–dependent parameters from the zero‐shear viscosity remains a difficult task because of the introduction of a constraint‐release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 569–586, 2004