Sea surface target detection based on complex ARMA-GARCH processes

In financial applications, it is common practice to fit return series by AutoRegressive Moving-Average (ARMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. In this paper, we develop a complex-valued ARMA-GARCH model for the sea clutter modeling application. Compared with the AR-GARCH model, the additionally introduced MA terms make the proposed model capable of considering the dependence of conditional variances of adjacent echo measurements as model coefficients, improving the modeling precision by taking advantage of the strong correlations between adjacent measurements. Based on the complex-valued ARMA-GARCH process for sea clutter modeling, we further develop a sea surface target detection algorithm. By analyzing a large number of the practical sea clutter data, we evaluate its performance and show that the proposed sea surface target detector offers a noticeable improvement for the probability of detection, comparing with the state-of-the-art AR-GARCH detector.     

A Soft Voice Activity Detection Using GARCH Filter and Variance Gamma Distribution

This paper presents a robust algorithm for a voice activity detector (VAD) based on generalized autoregressive conditional heteroscedasticity (GARCH) filter, variance gamma distribution (VGD), and adaptive threshold function. GARCH models are new statistical methods that are used especially in economic time series. There is a consensus that speech signals exhibit variances that change through time. GARCH models are a popular choice to model these changing variances. A speech signal is assumed to have a VGD because the VGD has heavier tails than the Gaussian distribution (GD). The distribution of noise signal is assumed to be Gaussian. In proposed method, heteroscedasticity will be modeled by GARCH, and then the parameters of the distributions will be estimated recursively. Finally, hard detection is the result of comparing a multiple observation likelihood ratio test (MOLRT) with an adaptive threshold function. The simulation results show that the proposed VAD is able to operate down to -5 dB and in nonstationary environments     

Radar detection algorithm for GARCH clutter model

We propose a GARCH model to represent the clutter in radar applications. We fit this model to real sea clutter data and we show that it represents adequately the statistics of the data. Then, we develop a detection test based on this model. Using synthetic and real radar data, we evaluate its performance and we show that the proposed detector offers higher probability of detection for a specified value of probability of false alarm than tests based on Gaussian and Weibull models, especially for low signal to clutter ratios.     

Intra-daily information of range-based volatility for MEM-GARCH

Conventional GARCH modeling formulates an additive-error mean equation for daily return and an autoregressive moving-average specification for its conditional variance, without much consideration on the effects of intra-daily data. Using Engle’s multiplicative-error model (MEM) formulation, range-based volatility is proposed as an intraday proxy for several GARCH frameworks. The performances of these different approaches for two 8-year market data sets: the S&P 500 and the NASDAQ composite index, are studied and compared. The impact of significant changes in intraday data has been found to reflect in the MEM-GARCH volatility. For some frameworks it is also possible to use lagged values of range-based volatility to delay the intraday effects in the conditional variance estimation.     

Knowledge-based target detection in compound Gaussian clutter with inverse Gaussian texture

This paper addresses the problem of adaptive detection of radar targets embedded in heterogeneous compound-Gaussian clutter environments. Based on the Bayesian theory, a priori knowledge of clutter is utilized to improve detection performance. The clutter texture is modeled by the inverse Gaussian distribution to describe the heavy-tailed clutter. Furthermore, clutter's heterogeneity results in insufficient secondary data, and the inverse complex Wishart distribution is exploited to model the speckle covariance matrix. Based on a priori distributions of clutter, a novel detector without using secondary data is derived via the generalized likelihood ratio test (GLRT). Monte Carlo experiments are performed to evaluate the detection performance of the proposed detector. Experimental results illustrate that the proposed detector outperforms its competitors in scenarios with limited secondary data.     

一种基于自适应背景杂波模型的宽幅SAR图像CFAR舰船检测算法

利用海洋宽幅SAR图像进行大范围海域舰船检测在海洋监视、军事侦察等方面具有重要应用。由于海况的复杂性,宽幅SAR图像背景杂波特性随海域不同而变化。采用双参数CFAR检测算法和基于K分布CFAR检测算法在处理宽幅SAR图像时,由于在待检测的所有区域采用同种背景杂波模型,导致使用的杂波模型在不适应区域失配,使CFAR检测性能下降。针对这个问题,提出了一种基于自适应背景杂波模型的CFAR宽幅SAR图像舰船检测算法,该算法通过背景窗口的多尺度统计方差判断目标所处的杂波环境,自适应选择对应的背景杂波分布模型,最后根据已知的恒虚警率及选择的杂波概率密度函数进行CFAR检测。对20多幅宽幅SAR图像进行了试验,实验结果表明:该算法在检测精度上有明显的改善。     

Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis

Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the Gram-Charlier (GC) density and the skewed-t density. The Gram-Charlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen’s skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate.     

Detection in sea clutter based on nonlinear ARCH model

In this paper, a complex nonlinear autoregressive conditional heteroscedasticity (CNARCH) model is proposed to model sea clutter. For heteroscedastic model, since the likelihood function is not obtained from explicit probability density function (PDF) expression, it is typically referred to as a quasi-likelihood function. The corresponding quasi-maximum likelihood estimation (QMLE) of the model parameters is derived. Furthermore, the corresponding detection algorithm is derived based on this model. We also conduct the simulations of both synthetic and practical data, demonstrate that the proposed model offers higher accuracy in detection, than the linear ARCH model, when used in the sea clutter.     

Change Point Detection in GARCH Models for Voice Activity Detection

This paper presents a robust algorithm for voice activity detection (VAD) based on change point detection in a generalized autoregressive conditional heteroscedasticity (GARCH) process. GARCH models are new statistical methods that are used especially in economic time series and are a popular choice to model speech signals and their changing variances. Change point detection is also important in economic sciences. In this paper, no distinct probability functions are assumed for speech and noise distributions. Also, to detect speech/nonspeech intervals, no likelihood ratio test (LRT) is employed. For testing parameter constancy in GARCH models, the algorithm of the Cramer-von Mises (CVM) test is described. This test is a nonparametric test and is based on the empirical quantiles. We show that VAD is related to the parameter constancy test in GARCH process, and we illustrate several examples.     

Adaptive detection of range-spread targets in compound Gaussian clutter with the square root of inverse Gaussian texture

The compound Gaussian clutter with the square root of inverse Gaussian texture component has been successfully used for modeling the heavy-tailed non-Gaussian clutter measured by high-resolution radars. In high-resolution radars, the targets may extend along multiple consecutive range cells, which are called range-spread targets. In this paper, we consider the range-spread target detection problem in the compound Gaussian clutter with the square root of inverse Gaussian texture. Three adaptive detectors are proposed based on Bayesian one-step generalized likelihood ratio test, maximum a posteriori generalized likelihood ratio test and Bayesian two-step generalized likelihood ratio test, respectively. Finally, the detection performances of the proposed detectors are evaluated by the Monte Carlo simulation. The simulation results show that the proposed detectors have better detection performance of range-spread target than the conventional generalized likelihood ratio test detector.     

Dual multivariate auto-regressive modeling in state space for temporal signal separation

Many existing independent component analysis (ICA) approaches result in deteriorated performance in temporal source separation because they have not taken into consideration of the underlying temporal structure of sources. In this paper, we model temporal sources as a general multivariate auto-regressive (AR) process whereby an underlying multivariate AR process in observation space is obtained. In this dual AR modeling, the mixing process from temporal sources to observations is the same as the mixture from the nontemporal residuals of the source AR (SAR) process to that of the observation AR (OAR) process. We can therefore avoid the source temporal effects in performing ICA by learning the demixing system on the independently distributed OAR residuals rather than the time-correlated observations. Particularly, we implement this approach by modeling each source signal as a finite mixture of generalized autoregressive conditional heteroskedastic (GARCH) process. The adaptive algorithms are proposed to extract the OAR residuals appropriately online, together with learning the demixing system via a nontemporal ICA algorithm. The experiments have shown its superior performance on temporal source separation.     

Nonlinear spatial-temporal prediction based on optimal fusion

The problem of spatial-temporal signal processing and modeling has been of great interest in recent years. A new spatial-temporal prediction method is presented in this paper. An optimal fusion scheme based on fourth-order statistic is first employed to combine the received signals at different spatial domains. The fused signal is then used to construct a spatial-temporal predictor by a support vector machine. It is shown theoretically that the proposed method has an improved performance even in non-Gaussian environments. To demonstrate the practicality of this spatial-temporal predictor, we apply it to model real-life radar sea scattered signals. Experimental results show that the proposed method can provide a more accurate model for sea clutter than the conventional methods.     

Diagnostics for conditional heteroscedasticity models: some simulation results

In this paper, we study the size and power of various diagnostic statistics for univariate conditional heteroscedasticity models. These test statistics include the residual-based tests recently derived by Tse, Li and Mak, and Wooldridge, respectively. Monte-Carlo experiments with 1000 replications are conducted to generate conditional variances which follow the autoregressive conditional heteroscedasticity (ARCH)/GARCH processes. We use quasi-maximum likelihood estimation (MLE) method to obtain estimates of parameters under different ARCH/ generalized ARCH (GARCH) models. It is found that the Tse and Li–Mak diagnostics are more powerful.     

Bayesian estimation of the Gaussian mixture GARCH model

Bayesian inference and prediction for a generalized autoregressive conditional heteroskedastic (GARCH) model where the innovations are assumed to follow a mixture of two Gaussian distributions is performed. The mixture GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. Bayesian prediction of the Value at Risk is also addressed providing point estimates and predictive intervals. The method is illustrated using the Swiss Market Index.     

Signal detection using the radial basis function coupled maplattice

From observation sea clutter, radar echoes from a sea surface, is chaotic rather than random. We propose the use of a spatial temporal predictor to reconstruct the chaotic dynamic of sea clutter because electromagnetic wave scattering is a spatial temporal phenomenon which is physically modeled by partial differential equations. The spatial temporal predictor used here is called radial basis function coupled map lattice (RBF-CML) which uses linear combination to fuse either measurements in different spatial domains for an RBF prediction or predictions from several RBF nets operated on different spatial regions. Using real-life radar data, it is shown that the RBF-CML is an effective method to reconstruct the sea clutter dynamic. The RBF-CML predictor is then applied to detect small targets in sea clutter using the constant false alarm rate (CFAR) principle. The spatial temporal approach is shown, both theoretically and experimentally, to be superior to a conventional CFAR detector.     

基于NSCT 的自适应乘性水印局部最优非线性盲检测算法

图像水印算法研究是多媒体技术领域中的重要议题。比较并结合当前两类主流的 图像水印算法,提出了一种基于非下采样Contourlet 变换的自适应乘性水印算法。借鉴Barni 的“pixel-wise masking”模型和冗余小波域掩盖效应建模的做法,建立非下采样Contourlet 变换域 掩盖效应计算模型。用广义高斯分布模型和Cauchy 分布模型描述非下采样Contourlet 变换系数 的统计特性,将水印的检测问题表述为一个复合假设检验。通过理论推导分别建立了乘性水印 的两种局部最优非线性盲检测器及检测门限的自适应确定方法。实验结果表明,非下采样 Contourlet 变换域掩盖效应计算模型使得水印嵌入算法具有良好的视觉不可见性,两种检测器在 无原始图像和自适应嵌入强度系数参与检测的情况下均能准确地检测到水印信息的存在。实验 结果同时显示,基于Cauchy 分布的盲检测器在检测效果和检测时间方面优于基于广义高斯分 布的盲检测器。     

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg–Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN’s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.     

雷达模拟器中海杂波模拟的一种新方法

海杂波的建模方法已趋于成熟,而如何在光栅显示器上快速逼真地模拟海杂波是当前模拟器面临的一个重要问题。在成熟的海杂波模型基础上,用ZMNL快速模拟杂波序列,并通过距离和近程增益调制可快速逼真地模拟海杂波。     

A generalized Dynamic Conditional Correlation model for portfolio risk evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339–350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537–572]. The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123–130] and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.     

Hidden messages in heavy-tails: DCT-domain watermark detection using alpha-stable models

This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alpha-stable family, are in many cases more accurate modeling tools for the DCT coefficients of JPEG-analyzed images than families with exponential tails such as the generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alpha-stable family. The Cauchy distribution is chosen because it is the only non-Gaussian symmetric alpha-stable distribution that exists in closed form and also because it leads to the design of a nearly optimum detector with robust detection performance. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector by performing experiments with various test images.