Detecting Tail Risk Differences in Multivariate Time Series

We derive functional central limit theory for tail index estimates in multivariate time series under mild conditions on the extremal dependence between the components. We use this result to also derive convergence results for extreme value‐at‐risk and extreme expected shortfall estimates. This allows us to construct tests for equality of ‘tail risk’ in multivariate data, which can be useful in a number of empirical contexts. In constructing test statistics, we avoid estimating long‐run variances by using self‐normalization. Size and power of the tests for equal ‘tail risk’ are assessed in simulations. An empirical application to exchange returns illustrates the practical usefulness of the tests.     

Testing Non‐Correlation and Non‐Causality between Multivariate ARMA Time Series

Abstract. Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378–85] developed an approach to the problem of testing non‐correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long distributed lag when individual lag coefficients are relatively small. As a remedy, Koch and Yang [Journal of the American Statistical Association (1986) Vol. 8, pp. 533–44] proposed an alternative method that performs better than Haugh's under such dependencies. A multivariate extension of Haugh's procedure was proposed by El Himdi and Roy [The Canadian Journal of Statistics (1997) Vol. 25, pp. 233–56], but suffers the same weaknesses as the original univariate method. We develop here an asymptotic test generalizing Koch and Yang's method to the multivariate case. Our method includes El Himdi and Roy's as a special case. Based on the same idea, we also suggest a generalization of the El Himdi and Roy procedure for testing causality in the sense of Granger [Econometrica (1969) Vol. 37, pp. 424–38] between two multivariate series. A Monte Carlo study is conducted, which indicates that our approach performs better than El Himdi and Roy's for a wide range of models. Both procedures are applied to the problem of testing the absence of correlation between Canadian and US economic indicators, and to a brief study of causality between money and income in Canada.     

Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series

We derive tests of stationarity for univariate time series by combining change‐point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a general procedure for combining dependent tests based on resampling. After proving the asymptotic validity of the combining procedure under the conjunction of null hypotheses and investigating its consistency, we study rank‐based tests of stationarity by combining cumulative sum change‐point tests based on the contemporary empirical distribution function and on the empirical autocopula at a given lag. Extensions based on tests solely focusing on second‐order characteristics are proposed next. The finite‐sample behaviors of all the derived statistical procedures for assessing stationarity are investigated in large‐scale Monte Carlo experiments, and illustrations on two real datasets are provided. Extensions to multi‐variate time series are briefly discussed as well.     

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is in-troduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to re-trieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.     

Testing for Change in Long‐Memory Stochastic Volatility Time Series

In this article, change‐point problems for long‐memory stochastic volatility (LMSV) models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting behavior of CUSUM‐ and Wilcoxon‐type test statistics is derived. In this context, a limit theorem for the two‐parameter empirical process of LMSV time series is proved. In particular, it is shown that the asymptotic distribution of CUSUM test statistics may not be affected by long memory, unlike Wilcoxon test statistics which are typically influenced by long‐range dependence. To avoid the estimation of nuisance parameters in applications, the usage of self‐normalized test statistics is proposed. The theoretical results are accompanied by an analysis of Standard & Poor's 500 daily closing indices with respect to structural changes and by simulation studies which characterize the finite sample behavior of the considered testing procedures when testing for changes in mean and in variance.     

Asymptotics for the Conditional‐Sum‐of‐Squares Estimator in Multivariate Fractional Time‐Series Models

This article proves consistency and asymptotic normality for the conditional‐sum‐of‐squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time‐series models. The model is parametric and quite general and, in particular, encompasses the multivariate non‐cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where uniform convergence fails is handled using a truncation argument.     

The Effect of the Estimation on Goodness‐of‐Fit Tests in Time Series Models

Abstract. We analyze, by simulation, the finite‐sample properties of goodness‐of‐fit tests based on residual autocorrelation coefficients (simple and partial) obtained using different estimators frequently used in the analysis of autoregressive moving‐average time‐series models. The estimators considered are unconditional least squares, maximum likelihood and conditional least squares. The results suggest that although the tests based on these estimators are asymptotically equivalent for particular models and parameter values, their sampling properties for samples of the size commonly found in economic applications can differ substantially, because of differences in both finite‐sample estimation efficiencies and residual regeneration methods.     

An Asymptotic F Test for Uncorrelatedness in the Presence of Time Series Dependence

We propose a simple asymptotically F-distributed Portmanteau test for zero autocorrelations in an otherwise dependent time series. By employing the orthonormal series variance estimator of the variance matrix of sample autocovariances, our test statistic follows an F distribution asymptotically under fixed-smoothing asymptotics. The asymptotic F theory accounts for the estimation error in the underlying variance estimator, which the asymptotic chi-squared theory ignores. Monte Carlo simulations reveal that the F approximation is much more accurate than the corresponding chi-squared approximation in finite samples. The asymptotic F test is as easy to use as the chi-squared test: there is no need to obtain critical values by simulations. Furthermore, it has more accurate empirical sizes and substantial power advantages, comparing to other competitors.     

Time‐Dependent Dual‐Frequency Coherence in Multivariate Non‐Stationary Time Series

Coherence is one common metric for cross‐dependence in multichannel signals. However, standard coherence does not sufficiently model many biological signals with complex dependence structures such as cross‐oscillatory interactions between a low‐frequency component in one signal and a high‐frequency component in another. The notion of cross‐dependence between low‐ and high‐frequency components, as defined in classical harmonizable processes, is still inadequate because it assumes time invariance and thus cannot capture cross‐frequency interactions that evolve over time. We construct a novel framework for modeling and estimating these dependencies under the replicated time series setting. Under this framework, we establish the novel concept of evolutionary dual‐frequency coherence and develop time‐localized estimators based on dual‐frequency local periodograms. The proposed nonparametric estimation procedure does not suffer from model misspecification. It uses the localized fast Fourier transform and hence is able to handle massive data. When applied to electroencephalogram data recorded in a motor intention experiment, the proposed method uncovers new and interesting cross‐oscillatory interactions that have been overlooked by the standard approaches.     

Inference for the Fourth‐Order Innovation Cumulant in Linear Time Series

The rescaled fourth‐order cumulant of the unobserved innovations of linear time series is an important parameter in statistical inference. This article deals with the problem of estimating this parameter. An existing nonparametric estimator is first discussed, and its asymptotic properties are derived. It is shown how the autocorrelation structure of the underlying process affects the behaviour of the estimator. Based on our findings and on an important invariance property of the parameter of interest with respect to linear filtering, a pre‐whitening‐based nonparametric estimator of the same parameter is proposed. The estimator is obtained using the filtered time series only; that is, an inversion of the pre‐whitening procedure is not required. The asymptotic properties of the new estimator are investigated, and its superiority is established for large classes of stochastic processes. It is shown that for the particular estimation problem considered, pre‐whitening can reduce the variance and the bias of the estimator. The finite sample performance of both estimators is investigated by means of simulations. The new estimator allows for a simple modification of the multiplicative frequency domain bootstrap, which extends its considerable range of validity. Furthermore, the problem of testing hypotheses about the rescaled fourth‐order cumulant of the unobserved innovations is also considered. In this context, a simple test for Gaussianity is proposed. Some real‐life data applications are presented.     

New image analysis methods for the study of mixing patterns in stirred tanks

A method of treating data acquired with the planar laser‐induced fluorescence technique has been developed to visualize the topology of two‐dimensional concentration fields and to describe the dynamics of the coherent mixing structures identified. This method is based on a conditional binary transformation of the local concentration data, combined with a joint probability calculation. The methodology has been used to investigate the mixing in a stirred tank, at two injection port locations (in the bulk and in the impeller stream region). With bulk injection, a “folding phenomenon” of the coherent mixing structure was detected. Away from this port, large‐scale spatially periodic motion was identified, with a characteristic time of oscillation of the order of 2 to 3 s. With injection in the impeller stream region, no spatial instabilities of the coherent structure were detected. Local oscillations of the coherent mixing structure were found both on short and long time‐scales (i.e., ?1 and ?80 s).     

State‐of‐the‐art and progress in the optimization‐based simultaneous design and control for chemical processes

Significant progress in the area of simultaneous design and control for chemical processes has been achieved and various methodologies have been put forward to address this issue over the last several decades. These methods can be classified in two categories (1) controllability indicator‐based frameworks that are capable of screening alternative designs, and (2) optimization‐based frameworks that integrate the process design and control system design. The major objective is to give an up‐to‐date review of the state‐of‐the‐art and progress in the challenging area of optimization‐based simultaneous design and control. First, motivations and significances of simultaneous design and control are illustrated. Second, a general classification of existing methodologies of optimization‐based simultaneous design and control is outlined. Subsequently, the mathematical formulations and relevant theoretical solution algorithms, their merits, strengths and shortcomings are highlighted. Last, based on the recent advances in this field, challenges and future research directions are discussed briefly. An attempt is made with the help of this review article to stimulate further research and disseminate the simultaneous design methods to challenging problem areas. In particular, the application of optimization‐based simultaneous design and control methods to large‐scale systems with highly inherent nonlinear dynamics often the case in industrial chemical processes remains a challenging task and yet to be solved. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1640–1659, 2012     

Structure and optical investigation of the effect of electron beam‐irradiation in poly‐allyl‐diglycol‐carbonate

The effect of electron beam irradiation on the structural and optical properties of Poly‐Allyl‐Diglycol‐Carbonate CR‐39 solid state nuclear track detector was investigated. Samples from CR‐39 detector were irradiated with electron beam with doses at levels between 10 and 140 kGy. The structural and optical modifications in the electron beam irradiated CR‐39 samples have been studied as a function of dose using different characterization techniques such as FTIR spectroscopy, Vickers hardness, refractive index and color difference measurements. The electron beam irradiation in the dose range 25–140 kGy led to a more compact structure of CR‐39 polymer, which resulted in an improvement in its hardness with an increase in the refractive index. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

A Multiscale Molecular Dynamic Analysis Reveals the Effect of Sialylation on EGFR Clustering in a CRISPR/Cas9-Derived Model

Bacterial and viral pathogens can modulate the glycosylation of key host proteins to facilitate pathogenesis by using various glycosidases, particularly sialidases. Epidermal growth factor receptor (EGFR) signaling is activated by ligand-induced receptor dimerization and oligomerization. Ligand binding induces conformational changes in EGFR, leading to clusters and aggregation. However, information on the relevance of EGFR clustering in the pattern of glycosylation during bacterial and viral invasion remains unclear. In this study, (1) we established CRISPR/Cas9-mediated GFP knock-in (EGFP-KI) HeLa cells expressing fluorescently tagged EGFR at close to endogenous levels to study EGF-induced EGFR clustering and molecular dynamics; (2) We studied the effect of sialylation on EGF-induced EGFR clustering and localization in live cells using a high content analysis platform and raster image correlation spectroscopy (RICS) coupled with a number and brightness (N&B) analysis; (3) Our data reveal that the removal of cell surface sialic acids by sialidase treatment significantly decreases EGF receptor clustering with reduced fluorescence intensity, number, and area of EGFR-GFP clusters per cell upon EGF stimulation. Sialylation appears to mediate EGF-induced EGFR clustering as demonstrated by the change of EGFR-GFP clusters in the diffusion coefficient and molecular brightness, providing new insights into the role of sialylation in EGF-induced EGFR activation; and (4) We envision that the combination of CRISPR/Cas9-mediated fluorescent tagging of endogenous proteins and fluorescence imaging techniques can be the method of choice for studying the molecular dynamics and interactions of proteins in live cells.