Wavelet based time-varying vector autoregressive modelling

Vector autoregressive (VAR) modelling is one of the most popular approaches in multivariate time series analysis. The parameters interpretation is simple, and provide an intuitive identification of relationships and Granger causality among time series. However, the VAR modelling requires stationarity conditions which could not be valid in many practical applications. Locally stationary or time dependent modelling seem attractive generalizations, and several univariate approaches have already been proposed. In this paper we propose an estimation procedure for time-varying vector autoregressive processes, based on wavelet expansions of autoregressive coefficients. The asymptotic properties of the estimator are derived and illustrated by computer intensive simulations. We also present an application to brain connectivity identification using functional magnetic resonance imaging (fMRI) data sets.     

基于时变自回归模型的FAJD盲源分离算法

为实现多高斯源和相关源信号的盲分离,在快速近似联合对角化(FAJD)算法的基础上,将故障诊断领域的时变自回归理论成功地应用于相关源信号的盲分离和多高斯源信号的盲分离.首先采用时变自回归模型(TVAR)对源信号建模,并通过白化预处理使得建模后的源信号具有可联合对角化的结构;然后,通过基函数加权和的方法将时变参数近似为已知基函数的加权和的形式,将其变成时不变的参数,再通过递推最小二乘法求解出模型系数矩阵组;最后,将所求出的系数矩阵组作为快速近似联合对角化的目标矩阵组,通过FAJD算法实现混合信号的分离.Matlab仿真实验验证了所提出的算法对于相关源信号和多高斯源信号的分离是行之有效的.由于算法中TVAR模型的优良特性,此算法非常适用于混合通信信号的盲分离.     

基于支持向量回归的多时间序列自回归方法

能耗时间序列涉及多种能源,且各种能源间关系复杂,主要通过多个独立的单时间序列进行预报,这种方式忽略了多时间序列之间的依赖性。为了充分利用多时间序列之间的关联信息以提高预报的准确性,根据机器学习中的向量值函数学习和多任务学习理论,采用支持向量回归(SVR)算法建立了多时间序列的向量值自回归方法和多任务自回归方法。实验结果证明,与多个独立的单时间序列模型相比,通过这种方法建立的多时间序列自回归模型在焦化工序能耗预报中表现出了更好的性能。     

On a constrained mixture vector autoregressive model

A mixture vector autoregressive model has recently been introduced to the literature. Although this model is a promising candidate for nonlinear multiple time series modeling, high dimensionality of the parameters and lack of method for computing the standard errors of estimates limit its application to real data. The contribution of this paper is threefold. First, a form of parameter constraints is introduced with an efficient EM algorithm for estimation. Second, an accurate method for computing standard errors is presented for the model with and without parameter constraints. Lastly, a hypothesis-testing approach based on likelihood ratio tests is proposed, which aids in the selection of unnecessary parameters and leads to the greater efficiency at the estimation. A case study employing U.S. Treasury constant maturity rates illustrates the applicability of the mixture vector autoregressive model with parameter constraints, and the importance of using a reliable method to compute standard errors.     

Functional coefficient autoregressive models for vector time series

We extend the functional coefficient autoregressive (FCAR) model to the multivariate nonlinear time series framework. We show how to estimate parameters of the model using kernel regression techniques, discuss properties of the estimators, and provide a bootstrap test for determining the presence of nonlinearity in a vector time series. The power of the test is examined through extensive simulations. For illustration, we apply the methods to a series of annual temperatures and tree ring widths. Computational issues are also briefly discussed.     

Subset selection for vector autoregressive processes using Lasso

A subset selection method is proposed for vector autoregressive (VAR) processes using the Lasso [Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58, 267-288] technique. Simply speaking, Lasso is a shrinkage method in a regression setup which selects the model and estimates the parameters simultaneously. Compared to the conventional information-based methods such as AIC and BIC, the Lasso approach avoids computationally intensive and exhaustive search. On the other hand, compared to the existing subset selection methods with parameter constraints such as the top-down and bottom-up strategies, the Lasso method is computationally efficient and its result is robust to the order of series included in the autoregressive model. We derive the asymptotic theorem for the Lasso estimator under VAR processes. Simulation results demonstrate that the Lasso method performs better than several conventional subset selection methods for small samples in terms of prediction mean squared errors and estimation errors under various settings. The methodology is applied to modeling U.S. macroeconomic data for illustration.     

Functional coefficient autoregressive models for vector time series

We extend the functional coefficient autoregressive (FCAR) model to the multivariate nonlinear time series framework. We show how to estimate parameters of the model using kernel regression techniques, discuss properties of the estimators, and provide a bootstrap test for determining the presence of nonlinearity in a vector time series. The power of the test is examined through extensive simulations. For illustration, we apply the methods to a series of annual temperatures and tree ring widths. Computational issues are also briefly discussed.     

Support vector regression based shear strength modelling of deep beams

Support vector regression based modelling approach was used to predict the shear strength of reinforced and prestressed concrete deep beams. To compare its performance, a back-propagation neural network and the three empirical relations was used with reinforced concrete deep beams. For prestressed deep beams, one empirical relation was used. Results suggest an improved performance by the SVR in terms of prediction capabilities in comparison to the empirical relations and back propagation neural network. Parametric studies with SVR suggest the importance of concrete cylinder strength and ratio of shear span to effective depth of beam on strength prediction of deep beams.     

Wavelet support vector machine

An admissible support vector (SV) kernel (the wavelet kernel), by which we can construct a wavelet support vector machine (SVM), is presented. The wavelet kernel is a kind of multidimensional wavelet function that can approximate arbitrary nonlinear functions. The existence of wavelet kernels is proven by results of theoretic analysis. Computer simulations show the feasibility and validity of wavelet support vector machines (WSVMs) in regression and pattern recognition.     

Wavelet twin support vector machine

Twin support vector machine (TWSVM) is a research hot spot in the field of machine learning in recent years. Although its performance is better than traditional support vector machine (SVM), the kernel selection problem still affects the performance of TWSVM directly. Wavelet analysis has the characteristics of multivariate interpolation and sparse change, and it is suitable for the analysis of local signals and the detection of transient signals. The wavelet kernel function based on wavelet analysis can approximate any nonlinear functions. Based on the wavelet kernel features and the kernel function selection problem, wavelet twin support vector machine (WTWSVM) is proposed by this paper. It introduces the wavelet kernel function into TWSVM to make the combination of wavelet analysis techniques and TWSVM come true. The experimental results indicate that WTWSVM is feasible, and it improves the classification accuracy and generalization ability of TWSVM significantly.     

Efficient construction of canonical ladder forms for vector autoregressive processes

The paper treats the problem of constructing canonical ladder realizations for vector autoregressive (AR) processes specified by their characteristic matrix polynomials. The difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector AR process is a nontrivial function of the forward matrix polynomial. The construction calls for solving a discrete Lyapunov equation in block-controller form. Two efficient procedures for solving this equation are presented, both requiring a number of operations that is proportional to at most the square of the model order. Applications of the new procedures to stability, tests, simulation of AR processes, and model reduction are described.     

The role of vector autoregressive modeling in predictor-based subspace identification

Subspace identification for closed loop systems has been recently studied by several authors. A class of new and consistent closed-loop subspace algorithms is based on identification of a predictor model, in a way similar as prediction error methods (PEM) do. Experimental evidence suggests that these methods have a behavior which is very close to PEM in certain examples. The asymptotical statistical properties of one of these methods have been studied recently allowing to show (i) its relation with CCA and (ii) that Cramér-Rao lower bound is not reached in general. Very little, however, is known concerning their relative performance.In this paper we shall discuss the link between these “predictor-based” methods; to this purpose we exploit the role which Vector Auto Regressive with eXogenous input models play in all these algorithms. The results of this paper provide a unifying framework under which all these algorithms can be viewed; also the link with VARX modeling have important implications as to computational complexity is concerned, leading to very computationally attractive implementations.We also hope that this framework, and in particular the relation with VARX modeling followed by model reduction will turn out to be useful in future developments of subspace identification, such as the quest for efficient procedures and the statistical analysis with finite-data.     

Generalized method of moments estimation for cointegrated vector autoregressive models

In this study, a generalized method of moments (GMM) for the estimation of nonstationary vector autoregressive models with cointegration is considered. Two iterative methods are considered: a simultaneous estimation method and a switching estimation method. The asymptotic properties of the GMM estimators of these methods are found to be the same as those of the Gaussian reduced-rank estimator. Through Monte Carlo simulation, the small-sample properties of the GMM estimators are studied and compared with those of the Gaussian reduced-rank estimator and the maximum likelihood estimator considered by other researchers. In the case of small samples, the GMM estimators are more robust to deviations from normality assumptions, particularly to outliers.     

A self-organising mixture autoregressive network for FX time series modelling and prediction

Nowadays a great deal of effort has been made in order to gain advantages in foreign exchange (FX) rates predictions. However, most existing techniques seldom excel the simple random walk model in practical applications. This paper describes a self-organising network formed on the basis of a mixture of adaptive autoregressive models. The proposed network, termed self-organising mixture autoregressive (SOMAR) model, can be used to describe and model nonstationary, nonlinear time series by means of a number of underlying local regressive models. An autocorrelation coefficient-based measure is proposed as the similarity measure for assigning input samples to the underlying local models. Experiments on both benchmark time series and several FX rates have been conducted. The results show that the proposed method consistently outperforms other local time series modelling techniques on a range of performance measures including the mean-square-error, correct trend predication percentage, accumulated profit and model variance.     

Assessment of anaesthetic depth by clustering analysis and autoregressive modelling of electroencephalograms

The brain activity electroencephalogram (EEG) was recorded from 30 healthy women scheduled for hysterectomy. The patients were anaesthetized with isoflurane, halothane or etomidate/fentanyl. A multiparametric method was used for extraction of amplitude and frequency information from the EEG. The method applied autoregressive modelling of the signal, segmented in 2 s fixed intervals. The features from the EEG segments were used for learning and for classification. The learning process was unsupervised and hierarchical clustering analysis was used to construct a learning set of EEG amplitude-frequency patterns for each of the three anaesthetic drugs. These EEG patterns were assigned to a colour code corresponding to similar clinical states. A common learning set could be used for all patients anaesthetized with the same drug. The classification process could be performed on-line and the results were displayed in a class probability histogram. This histogram reflected in all patients the depth of anaesthesia, when the concentration of the anaesthetic agent was adjusted either based on clinical signs or according to the protocol. This uniform display, where colours in a class probability histogram indicate the depth of anaesthesia, may in the future serve as on-line advice for the administration of anaesthetics. A comparison of multiparametric with single parametric methods, based on calculation of median, spectral edge and peak frequencies, questions the reliability of the single parametric methods in monitoring anaesthetic depth.     

Enhanced pose normalization and matching of non-rigid objects based on support vector machine modelling

The estimation of 3D surface correspondence constitutes a fundamental problem in shape matching and analysis applications. In the presence of non-rigid shape deformations, the ambiguity of surface correspondence increases together with the complexity of registration algorithms.     

The estimation of velocity vector fields from time-varying image sequences

Changes in successive images from a time-varying image sequence of a scene can be characterized by velocity vector fields. The estimate of the velocity vector field is determined as a compromise between optical flow and directional smoothness constraints. The optical flow constraints relate the values of the time-varying image function at the corresponding points of the successive images of the sequence. The directional smoothness constraints relate the values of neighboring velocity vectors. To achieve the compromise, we introduce a system of nonlinear equations of the unknown estimate of the velocity vector field using a novel variational principle applied to the weighted average of the optical flow and the directional smoothness constraints. A stable iterative method for solving this system is developed. The optical flow and the directional smoothness constraints are selectively suppressed in the neighborhoods of the occluding boundaries by implicitly adjusting their weights. These adjustments are based on the spatial variations of the estimates of the velocity vectors and the spatial variations of the time-varying image function. The system of nonlinear equations is defined in terms of the time-varying image function and its derivatives. The initial image functions are in general discontinuous and cannot be directly differentiated. These difficulties are overcome by treating the initial image functions as generalized functions and their derivatives as generalized derivatives. These generalized functions are evaluated (observed) on the parametric family of testing (smoothing) functions to obtain parametric families of secondary images, which are used in the system of nonlinear equations. The parameter specifies the degree of smoothness of each secondary image. The secondary images with progressively higher degrees of smoothness are sampled with progressively lower resolutions. Then coarse-to-fine control strategies are used to obtain the estimate.     

Bayesian forecasting with small and medium scale factor-augmented vector autoregressive DSGE models

Advanced Bayesian methods are employed in estimating dynamic stochastic general equilibrium (DSGE) models. Although policymakers and practitioners are particularly interested in DSGE models, these are typically too stylized to be taken directly to the data and often yield weak prediction results. Hybrid models can deal with some of the DSGE model misspecifications. Major advances in Bayesian estimation methodology could allow these models to outperform well-known time series models and effectively deal with more complex real-world problems as richer sources of data become available. A comparative evaluation of the out-of-sample predictive performance of many different specifications of estimated DSGE models and various classes of VAR models is performed, using datasets from the US economy. Simple and hybrid DSGE models are implemented, such as DSGE–VAR and Factor Augmented DSGEs and tested against standard, Bayesian and Factor Augmented VARs. Moreover, small scale models including the real gross domestic product, the harmonized consumer price index and the nominal short-term federal funds interest rate, are comparatively assessed against medium scale models featuring additionally sticky nominal prices, wage contracts, habit formation, variable capital utilization and investment adjustment costs. The investigated period spans 1960:Q4–2010:Q4 and forecasts are produced for the out-of-sample testing period 1997:Q1–2010:Q4. This comparative validation can be useful to monetary policy analysis and macro-forecasting with the use of advanced Bayesian methods.     

High-quality and interactive animations of 3D time-varying vector fields

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering