Image data compression using autoregressive time series models

A two-dimensional image model is formulated using a seasonal autoregressive time series. With appropriate use of initial conditions, the method of least squares is used to obtain estimates of the model parameters. The model is then used to regenerate the original image. Results obtained indicate this method could be used to code textures for low bit rates or be used in an application of generating compressed background scenes. A differential pulse code modulation (DPCM) scheme is also demonstrated as a means of archival storage of images along with a new quantization technique for DPCM. This quantization technique is compared with standard quantization methods.     

Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model

Recent developments in multivariate volatility modeling suggest that the conditional correlation matrix can be described by a time series recursion, where the total number of parameters grows by the power-of-two of the dimension of financial returns. The power of two computational requirement makes high-dimensional multivariate volatility modeling very time consuming. In this paper, we propose two simplified specifications in a multivariate autoregressive conditional heteroscedasticity model. The first specification computes an unconditional correlation matrix from standardized residuals of the model. The second specification restricts the sum of the weights in a time-varying conditional correlation equation to be one. Applying a Bayesian sampling scheme allows the number of parameters to be reduced from the power of two of the dimension to the linear order of the dimension only and simultaneously provides us a framework for model comparison. We test our simplified specifications using simulated and real data from three sectoral indices in Hong Kong, three market indices and four exchange rates. The results suggest that our simplified specifications are more effective than the original formulation.     

Analytical Score for Multivariate GARCH Models

Multivariate GARCH models constitute the workhorse of empiricalapplications in several fields, a notable example being financialeconometrics. Unfortunately, ML (or quasi-ML) estimation of such models,although relatively straightforward in theory, is often made difficult bythe fact that available software relies on numerical methods for computingthe first derivatives of the log-likelihood; the fact that these modelsoften include a large number of parameters makes it impractical toestimate even medium-sized models. In this paper, closed-form expressionsfor the score of the BEKK model of Engle and Kroner (1995) are obtained,and strategies for efficient computation are discussed.     

A kernel-based parametric method for conditional density estimation

A conditional density function, which describes the relationship between response and explanatory variables, plays an important role in many analysis problems. In this paper, we propose a new kernel-based parametric method to estimate conditional density. An exponential function is employed to approximate the unknown density, and its parameters are computed from the given explanatory variable via a nonlinear mapping using kernel principal component analysis (KPCA). We develop a new kernel function, which is a variant to polynomial kernels, to be used in KPCA. The proposed method is compared with the Nadaraya-Watson estimator through numerical simulation and practical data. Experimental results show that the proposed method outperforms the Nadaraya-Watson estimator in terms of revised mean integrated squared error (RMISE). Therefore, the proposed method is an effective method for estimating the conditional densities.     

On pseudo maximum likelihood estimation for multivariate time series models with conditional heteroskedasticity

We consider a general multivariate conditional heteroskedastic model under a conditional distribution that is not necessarily normal. This model contains autoregressive conditional heteroskedastic (ARCH) models as a special class. We use the pseudo maximum likelihood estimation method and derive a new estimator of the asymptotic variance matrix for the pseudo maximum likelihood estimator. We also study four special cases in this class, which are conditional heteroskedastic autoregressive moving-average models, regression models with ARCH errors, models with constant conditional correlations, and ARCH in mean models.     

Joint order and parameter estimation of multivariate autoregressive models using multi-model partitioning theory

In this paper the multi-model partitioning theory is used for simultaneous order and parameter estimation of multivariate autoregressive models. Simulation experiments show that the proposed method successfully selects the correct model order and estimates the parameters accurately, in very few steps, even with a small sample size. They also show that the proposed method performs equally well when the complexity of the model is increased. The results are compared to those obtained using well-established order selection criteria. Finally, it is shown that the method is also successful in tracking model order changes, in real time.     

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.     

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.     

Mixture cure models for multivariate survival data

Mixture cure models (MCMs) have been widely used to analyze survival data with a cure fraction. The MCMs postulate that a fraction of the patients are cured from the disease and that the failure time for the uncured patients follows a proper survival distribution, referred to as latency distribution. The MCMs have been extended to bivariate survival data by modeling the marginal distributions. In this paper, the marginal MCM is extended to multivariate survival data. The new model is applicable to the survival data with varied cluster size and interval censoring. The proposed model allows covariates to be incorporated into both the cure fraction and the latency distribution for the uncured patients. The primary interest is to estimate the marginal parameters in the mean structure, where the correlation structure is treated as nuisance parameters. The marginal parameters are estimated consistently by treating the observations within the cluster as independent. The variances of the parameters are estimated by the one-step jackknife method. The proposed method does not depend on the specification of correlation structure. Simulation studies show that the new method works well when the marginal model is correct. The performance of the MCM is also examined when the clustered survival times share common random effect. The MCM is applied to the data from a smoking cessation study.     

Detection of chatter vibration in a drilling process using multivariate control charts

Time series analysis and multivariate control charts are used to devise a real-time monitoring strategy in a drilling process. The process is used to produce holes with high length-to-diameter ratio, good surface finish and straightness. It is subject to dynamic disturbances that are classified as either chatter vibration or spiralling. A new nonparametric control chart for multivariate processes is proposed. It is used to detect chatter vibration which is dominated by single frequencies. The results showed that the proposed monitoring strategy can detect chatter vibration and that some alarm signals are related to changing physical conditions of the process.     

基于储备池主成分分析的多元时间序列预测研究

提出一种基于回声状态网络储备池的非线性ＰＣＡ 方法,并将其应用于多元时间序列的预测中．由于多维输入变量间的相关性会影响建模效果,通过储备池将输入在原空间的非线性特征转化成高维空间的线性特征．在其中运用线性ＰＣＡ 技术寻找输入在储备池空间的最大方差方向,提取有效的多元变量综合信息．经储备池主成分分析处理后的输入与预测点呈动态线性映射,可使用线性方法建模．仿真结果表明了该方法的有效性．     

Estimating multidimensional probability fields using the Field Estimator for Arbitrary Spaces (FiEstAS) with applications to astrophysics

The Field Estimator for Arbitrary Spaces (FiEstAS) computes the continuous probability density field underlying a given discrete data sample in multiple, non-commensurate dimensions. The algorithm works by constructing a metric-independent tessellation of the data space based on a recursive binary splitting. Individual, data-driven bandwidths are assigned to each point, scaled so that a constant “mass” M₀ is enclosed. Kernel density estimation may then be performed for different kernel shapes, and a combination of balloon and sample point estimators is proposed as a compromise between resolution and variance. A bias correction is evaluated for the particular (yet common) case where the density is computed exactly at the locations of the data points rather than at an uncorrelated set of locations. By default, the algorithm combines a top-hat kernel with M₀=2.0 with the balloon estimator and applies the corresponding bias correction. These settings are shown to yield reasonable results for a simple test case, a two-dimensional ring, that illustrates the performance for oblique distributions, as well as for a six-dimensional Hernquist sphere, a fairly realistic model of the dynamical structure of stellar bulges in galaxies and dark matter haloes in cosmological N-body simulations. Results for different parameter settings are discussed in order to provide a guideline to select an optimal configuration in other cases. Source code is available upon request.     

一类非线性周期时间序列模型

为了描述周期时间序列中的偏倚和多峰等非线性特征,结合有限混合模型方法,提出混合周期自回归滑动平均时间序列模型（MPARMA）,给出了MPARMA模型的平稳性条件,讨论了期望最大化（EM）算法的应用,通过PM10浓度序列分析,评估了MPARMA模型的表现。     

Unsupervised learning algorithm for time series using bivariate AR(1) model

Currently, there is an increased interest in time series clustering research, particularly for finding useful similar time series in various applied areas such as speech recognition, environmental research, finance and medical imaging. Clustering and classification of time series has the potential to analyze large volumes of data. Most of the traditional time series clustering and classification algorithms deal only with univariate time series data. In this paper, we develop an unsupervised learning algorithm for bivariate time series. The initial clusters are found using K-means algorithm and the model parameters are estimated using the EM algorithm. The learning algorithm is developed by utilizing component maximum likelihood and Bayesian Information Criteria (BIC). The performance of the developed algorithm is evaluated using real time data collected from a pollution centre. A comparative study of the proposed algorithm is made with the existing data mining algorithm that uses univariate autoregressive process of order 1 (AR(1)) model. It is observed that the proposed algorithm out performs the existing algorithms.     

Prediction method of autoregressive moving average models for uncertain time series

ABSTRACT

Time series analysis is based on the continuous regularity of the development of objective things to predict the next value depending on observed values. Based on time series analysis, we present autoregressive moving average models to predict the next future value for an uncertain time series. In this paper, imprecise observations and disturbance terms are regarded as uncertain variables and assume that the latter are satisfied uncertain normal distribution. The prediction models of uncertain time series are established combining the knowledge of autoregressive model and uncertainty theory. Therefore, the interval range of the next future value is predicted based on the reliability constraint. As an illustration to compare with the numerical examples of the existing prediction method, the innovations and effectiveness of the work are further demonstrated by the computational results.     

Testing the martingale difference hypothesis using integrated regression functions

An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. A unified approach for dealing with all of these testing problems is proposed. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. In order to circumvent this problem pairwise integrated regression functions are introduced as measures of linear and nonlinear dependence. The proposed test does not require to chose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, the test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then, the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate are investigated.     

An Evolving Autoregressive Predictor for Time Series Forecasting

AR （Autoregressive） model is a common predictor that has been extensively used for time series forecasting. Many training methods can used to update AR model parameters, for instance, least square estimate and maximum likelihood estimate; however, both techniques are sensitive to noisy samples and outliers. To deal with the problems, an evolving AR predictor---EAR, is developed in this work to enhance prediction accuracy and mitigate the effect of noisy samples and outliers. The model parameters of EAR are trained with an ALSE （adaptive least square estimate） method, which can learn samples characteristics more effectively. In each training epoch, the ALSE weights the samples by their fitting accuracy. The samples with larger fitting errors will be given a larger penalty value in the cost function; however, the penalties of difficult-to-predict samples will be adaptively reduced to enhance the prediction accuracy. The effectiveness of the developed EAR predictor is verified by simulation tests. Test results show that the proposed EAR predictor can capture the dynamics of the time series effectively and predict the future trend accurately.     

Multivariate out-of-sample tests for Granger causality

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. Multivariate out-of-sample tests for Granger causality are proposed and their performance is measured by a simulation study. The results are graphically represented by size-power plots. It emerges that the multivariate regression test is the most powerful among the considered possibilities. As a real data application, it is investigated whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.     

基于特征点分段的多元时间序列相似性搜索

现有的各种多元时间序列相似性搜索方法难以准确高效地完成搜索任务。提出了一种基于特征点分段的多元时间序列相似性搜索算法,提取所定义的用于分段的特征点,分段后将原时间序列转化为模式序列,该模式序列能够很好地保留原序列的全局形状特征,再用分层匹配的方法进行相似性搜索。实验结果表明,该方法能够有效刻画序列的全局形状特征,通过分层匹配保留局部的相似性,同时提高搜索准确率。     

Dynamic network signal processing using latent threshold models

We discuss multivariate time series signal processing that exploits a recently introduced approach to dynamic sparsity modelling based on latent thresholding. This methodology induces time-varying patterns of zeros in state parameters that define both directed and undirected associations between individual time series, so generating statistical representations of the dynamic network relationships among the series. Following an overview of model contexts and Bayesian analysis for dynamic latent thresholding, we exemplify the approach in two studies: one of foreign currency exchange rate (FX) signal processing, and one in evaluating dynamics in multiple electroencephalography (EEG) signals. These studies exemplify the utility of dynamic latent threshold modelling in revealing interpretable, data-driven dynamics in patterns of network relationships in multivariate time series.