Testing for parameter constancy in general causal time‐series models

We consider a process belonging to a large class of causal models including AR(∞), ARCH(∞), TARCH(∞),… processes. We assume that the model depends on a parameter and consider the problem of testing for change in the parameter. Two statistics and are constructed using quasi‐likelihood estimator of the parameter. Under the null hypothesis that there is no change, it is shown that each of these two statistics weakly converges to the supremum of the sum of the squares of independent Brownian bridges. Under the alternative of a change in the parameter, we show that the test statistic diverges to infinity. Some simulation results for AR(1), ARCH(1), GARCH(1,1) and TARCH(1) models are reported to show the applicability and the performance of our procedure with comparisons to some other approaches.     

Regression‐based analysis of multivariate non‐Gaussian datasets for diagnosing abnormal situations in chemical processes

This article presents a regression‐based monitoring approach for diagnosing abnormal conditions in complex chemical process systems. Such systems typically yield process variables that may be both Gaussian and non‐Gaussian distributed. The proposed approach utilizes the statistical local approach to monitor parametric changes of the latent variable model that is identified by a revised non‐Gaussian regression algorithm. Based on a numerical example and recorded data from a fluidized bed reactor, the article shows that the proposed approach is more sensitive when compared to existing work in this area. A detailed analysis of both application studies highlights that the introduced non‐Gaussian monitoring scheme extracts latent components that provide a better approximation of non‐Gaussian source signal and/or is more sensitive in detecting process abnormities. © 2013 American Institute of Chemical Engineers AIChE J, 60: 148–159, 2014     

Scalable inference for space‐time Gaussian Cox processes

The log‐Gaussian Cox process is a flexible and popular stochastic process for modeling point patterns exhibiting spatial and space‐time dependence. Model fitting requires approximation of stochastic integrals which is implemented through discretization over the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally burdensome because of the cost of matrix decompositions and storage, such as the Cholesky, for high dimensional covariance matrices associated with latent Gaussian variables. This article addresses these computational bottlenecks by combining two recent developments: (i) a data augmentation strategy that has been proposed for space‐time Gaussian Cox processes that is based on exact Bayesian inference and does not require fine grid approximations for infinite dimensional integrals, and (ii) a recently developed family of sparsity‐inducing Gaussian processes, called nearest‐neighbor Gaussian processes, to avoid expensive matrix computations. Our inference is delivered within the fully model‐based Bayesian paradigm and does not sacrifice the richness of traditional log‐Gaussian Cox processes. We apply our method to crime event data in San Francisco and investigate the recovery of the intensity surface.     

Inference for non‐stationary time‐series autoregression

The article considers simultaneous inference for a class of non‐stationary autoregressive models where the model parameters are allowed to vary smoothly over time. Simultaneous confidence tubes with asymptotically correct coverage probabilities are constructed to assess the overall patterns and magnitudes of the parameter functions over time. Simulation studies are conducted, and a real time‐series dataset is analyzed to demonstrate the usefulness of the proposed methodology.     

A bootstrap test for additive outliers in non‐stationary time series

In this paper we propose a new procedure for detecting additive outliers in a univariate time series based on a bootstrap implementation of the test of Perron and Rodríguez (2003, Journal of Time Series Analysis 24, 193‐220). This procedure is used to test the null hypothesis that a time series is uncontaminated by additive outliers against the alternative that one or more additive outliers are present. We demonstrate that the existing tests of, inter alia, Vogelsang (1999, Journal of Time Series Analysis 20, 237–52) Perron and Rodríguez (2003) and Burridge and Taylor (2006, Journal of Time Series Analysis 27, 685–701) are unable to strike a balance between size and power when the order of integration of a time series is unknown and the time series is driven by innovations drawn from an unknown distribution. We show that the proposed bootstrap testing procedure is able to control size to such an extent that its size properties are comparable with the robust test of Burridge and Taylor (2006) when the distribution of the innovations is not assumed known, whilst maintaining power in the Gaussian environment close to that of the test of Perron and Rodríguez (2003).     

Convolution‐closed models for count time series with applications

There has recently been an upsurge of interest in time series models for count data. Many papers focus on the model with first‐order (Markov) dependence and Poisson innovations. Our paper considers practical models that can capture higher‐order dependence based on the work of Joe (1996). In this framework we are able to model both equidispersed and overdispersed marginal distributions of data. The latter is approached using generalized Poisson innovations. Central to the models is the use of the property of closure under convolution of certain families of random variables. The models can be thought of as stationary Markov chains of finite order. Parameter estimation is undertaken by maximum likelihood, inference procedures are considered and means of assessing model adequacy employed. Applications to two new data sets are provided.     

Asymptotic results for Fourier‐PARMA time series

Periodically stationary times series are useful to model physical systems whose mean behavior and covariance structure varies with the season. The Periodic Auto‐Regressive Moving Average (PARMA) process provides a powerful tool for modelling periodically stationary series. Since the process is non‐stationary, the innovations algorithm is useful to obtain parameter estimates. Fitting a PARMA model to high‐resolution data, such as weekly or daily time series, is problematic because of the large number of parameters. To obtain a more parsimonious model, the discrete Fourier transform (DFT) can be used to represent the model parameters. This article proves asymptotic results for the DFT coefficients, which allow identification of the statistically significant frequencies to be included in the PARMA model.     

Estimation of regression and dynamic dependence paremeters for non‐stationary multinomial time series

In a time‐series regression setup, multinomial responses along with time dependent observable covariates are usually modelled by certain suitable dynamic multinomial logistic probabilities. Frequently, the time‐dependent covariates are treated as a realization of an exogenous random process and one is interested in the estimation of both the regression and the dynamic dependence parameters conditional on this realization of the covariate process. There exists a partial likelihood estimation approach able to deal with the general dependence structures arising from the influence of both past covariates and past multinomial responses on the covariates at a given time by sequentially conditioning on the history of the joint process (response and covariates), but it provides standard errors for the estimators based on the observed information matrix, because such a matrix happens to be the Fisher information matrix obtained by conditioning on the whole history of the joint process. This limitation of the partial likelihood approach holds even if the covariate history is not influeced by lagged response outcomes. In this article, a general formulation of the auto‐covariance structure of a multinomial time series is presented and used to derive an explicit expression for the Fisher information matrix conditional on the covariate history, providing the possibility of computing the variance of the maximum likelihood estimators given a realization of the covariate process for the multinomial‐logistic model. The difference between the standard errors of the parameter estimators under these two conditioning schemes (covariates Vs. joint history) is illustrated through an intensive simulation study based on the premise of an exogenous covariate process.     

Structural breaks in time series

This paper gives an account of some of the recent work on structural breaks in time series models. In particular, we show how procedures based on the popular cumulative sum, CUSUM, statistics can be modified to work also for data exhibiting serial dependence. Both structural breaks in the unconditional and conditional mean as well as in the variance and covariance/correlation structure are covered. CUSUM procedures are nonparametric by design. If the data allows for parametric modeling, we demonstrate how likelihood approaches may be utilized to recover structural breaks. The estimation of multiple structural breaks is discussed. Furthermore, we cover how one can disentangle structural breaks (in the mean and/or the variance) on one hand and long memory or unit roots on the other. Several new lines of research are briefly mentioned.     

Optimal convergence rates in non‐parametric regression with fractional time series errors

Consider the estimation of g^(ν), the νth derivative of the mean function, in a fixed‐design non‐parametric regression model with stationary time series errors ξ_i. We assume that , ξ_i are obtained by applying an invertible linear filter to iid innovations, and the spectral density of ξ_i has the form as λ → 0 with constants c_f > 0 and α ∈ (?1,1). Under regularity conditions, the optimal convergence rate of is shown to be with r = (1 ? α)(k ? ν)/(2k+1 ? α). This rate is achieved by local polynomial fitting. Moreover, in spite of including long memory and antipersistence, the required conditions on the innovation distribution turn out to be the same as in non‐parametric regression with iid errors.     

Estimation for non‐negative time series with heavy‐tail innovations

For moving average processes where the coefficients are non‐negative and the innovations are positive random variables with a regularly varying tail at infinity, we provide estimates for the coefficients based on the ratio of two sample values chosen with respect to an extreme value criteria. We then apply this result to obtain estimates for the parameters of non‐negative ARMA models. Weak convergence results for the joint distribution of our estimates are established and a simulation study is provided to examine the small sample size behaviour of these estimates.     

Testing for cycles in multiple time series

In practice, it is often impossible to assess the validity of the smoothness assumptions crucial to standard tests for singularities in the spectrum. We therefore propose new tests which are completely insensitive to sharp peaks in the absolutely continuous part of the spectrum. Using Neyman Pearson tests of Bayesian mixtures we first derive admissible tests under simplifying assumptions and then show that under realistic assumptions our test statistics remain the same. The tests are designed to have high power especially against alternatives containing oscillations which are positively correlated with each other. Motivated by a biological dataset with non‐sinusoidal oscillations, we finally extend our approach by including higher harmonics.     

Embedding a Gaussian discrete‐time autoregressive moving average process in a Gaussian continuous‐time autoregressive moving average process

Abstract. Embedding a discrete‐time autoregressive moving average (DARMA) process in a continuous‐time ARMA (CARMA) process has been discussed by many authors. These authors have considered the relationship between the autocovariance structures of continuous‐time and related discrete‐time processes. In this article, we treat the problem from a slightly different point of view. We define embedding in a more rigid way by taking account of the probability structure. We consider Gaussian processes. First we summarize the necessary and sufficient condition for a DARMA process to be able to be embedded in a CARMA process. Secondly, we show a concrete condition such that a DARMA process can be embeddable in a CARMA process. This condition is new and general. Thirdly, we show some special cases including new examples. We show how we can examine embeddability for these special cases.     

A quality relevant non‐Gaussian latent subspace projection method for chemical process monitoring and fault detection

Partial least‐squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement‐variable and quality‐variable spaces that have the maximum covariances. Therefore, PLS method relies on the second‐order statistics of covariance only but does not takes into account the higher‐order statistics that may involve certain key features of non‐Gaussian processes. Moreover, the derivations of control limits for T² and squared prediction error (SPE) indices in PLS‐based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non‐Gaussian and mutually independent by means of maximizing the high‐order statistics such as negentropy instead of the second‐order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non‐Gaussian relationships between process measurement and quality variables, a novel projection‐based monitoring method termed as quality relevant non‐Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement‐variable and quality‐variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I² and SPE statistics are developed for quality relevant fault detection of non‐Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS‐based monitoring method. © 2013 American Institute of Chemical Engineers AIChE J 60: 485–499, 2014     

Coaxial Mixer Hydrodynamics with Newtonian and non‐Newtonian Fluids

The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter‐ and co‐rotating mode were assessed with Newtonian and non‐Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co‐rotating mode were found to be a better choice for Newtonian and non‐Newtonian fluids. The hybrid impeller‐anchor combination was found to be the most efficient for mixing in counter‐rotating or co‐rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N_js) was also determined. It was found that N_js had lower values with the impellers having the best axial pumping capabilities.     

Data‐based linear Gaussian state‐space model for dynamic process monitoring

This article develops a data‐based linear Gaussian state‐space model for monitoring of dynamic processes under noisy environment. The Kalman filter is introduced for construction of the linear Gaussian state‐space model, and an iterative expectation‐maximization algorithm is used for model parameters learning. With the incorporation of the dynamic data information, a new fault detection and identification approach is proposed. The feasibility and effectiveness of the two monitoring statistics in the new method are theoretically evaluated and further confirmed through two case studies. Furthermore, detailed fault smearing effect analysis of the proposed method is provided and compared with other identification methods. Based on the simulation results of two case studies, the superiority of the proposed method is explored. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Testing for serial dependence in time series models of counts

Abstract. In analysing time series of counts, the need to test for the presence of a dependence structure routinely arises. Suitable tests for this purpose are considered in this paper. Their size and power properties are evaluated under various alternatives taken from the class of INARMA processes. We find that all the tests considered except one are robust against extra binomial variation in the data and that tests based on the sample autocorrelations and the sample partial autocorrelations can help to distinguish between integer-valued first-order and second-order autoregressive as well as first-order moving average processes.     

Volumetric Mass Transfer Coefficient in non‐Newtonian Fluids in Spout Fluid Beds

The volumetric liquid‐phase mass transfer coefficient, k_La, was determined by absorption of oxygen in air using six different carboxy‐methyl cellulose (CMC) solutions with different rheological values in three phase spout‐fluid beds operated continuously with respect to both gas and liquid. Three cylindrical columns of 7.4 cm, 11.4 cm, and 14.4 cm diameters were used. Gas velocity was varied between 0.00154–0.00563 m/s, liquid velocity between 0.0116–0.0387 m/s, surface tension between 0.00416–0.0189 N/m, static bed height between 6.0–10.8 cm, and spherical glass particles of 1.75 mm diameter were used as packing material. A single nozzle sparger of 1.0 cm diameter was used in the spouting line. The volumetric mass transfer coefficient was found to increase with gas velocity, liquid velocity, and static bed height and to decrease with the increase of the effective liquid viscosity of the CMC solution. A dimensionless correlation was developed and compared with those listed in the literature.     

A Data‐Driven Gaussian Process Regression Model for Two‐Chamber Microbial Fuel Cells

Rapidly and accurately modeling of microbial fuel cells (MFCs) plays an important role not only in thorough understanding of the effects of operating conditions on system performance, but also in the successful implementation of real‐time maximization of power output. Although the first principle electrochemical model has better generalization performance, it is often time‐consuming for model construction and is hard to real‐time application. In this study, a nonparametric Gaussian process regression (GPR) model is used to capture the nonlinear relationship between operating conditions and output voltage in the MFCs. A simple online learning strategy is proposed to recursively update the hyper‐parameters of the GPR model. The applicability and effectiveness of the proposed method is validated by both the simulation and experimental datasets from the acetate and the glucose and glutamic acid two‐chamber MFCs. The results illustrate that the online GPR model provides a promising method for capturing the complex nonlinearity phenomenon in MFCs, which can be greatly helpful for further real‐time optimization of MFCs.