Rank-based estimation for all-pass time series models

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing for Noncausal Vector Autoregressive Representation

We propose a test for noncausal vector autoregressive representation generated by non-Gaussian shocks. We prove that in these models the Wold innovations are martingale difference if and only if the model is correctly specified. We propose a test based on a generalized spectral density to check for martingale difference property of the Wold innovations. Our approach does not require to identify and estimate the noncausal models. No specific estimation method is required, and the test has the appealing nuisance parameter free property. The test statistic uses all lags in the sample and it has a convenient asymptotic standard normal distribution under the null hypothesis. A Monte Carlo study is conducted to examine the �finite-sample performance of our test

Testing for Noncausal Vector Autoregressive Representation

We propose a test for noncausal vector autoregressive representation generated by non-Gaussian shocks. We prove that in these models the Wold innovations are martingale difference if and only if the model is correctly specified. We propose a test based on a generalized spectral density to check for martingale difference property of the Wold innovations. Our approach does not require to identify and estimate the noncausal models. No specific estimation method is required, and the test has the appealing nuisance parameter free property. The test statistic uses all lags in the sample and it has a convenient asymptotic standard normal distribution under the null hypothesis. A Monte Carlo study is conducted to examine the �finite-sample performance of our test

Laboratory for Engineering Man/Machine Systems (LEMS): System identification, model reduction and deconvolution filtering using Fourier based modulating signals and high order statistics

Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP–R and MCBv–MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20 breaths minute^-1 as well as from 13 subjects at supine rest and during 60 head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling

Testing for simplification in spatial models

Data collected on a rectangular lattice occur frequently in many areas such as field trials, geostatistics, remotely sensed data, and image analysis. Models for the spatial process often make simplifying assumptions, including axial symmetry and separability. We consider methods for testing these assumptions and compare tests based on sample covariances, tests based on the sample spectrum, and model-based tests

Two-dimensional spectrum estimation using the radon transform

An alternative approach to two-dimensional power spectrum estimation incorporating the Radon transform in conjunction with each of the one-dimensional periodogram, Blackman-Tukey, and Autoregressive parameter estimation algorithms is examined. The Radon transform is used to express a two-dimensional data set in terms of its projections onto a set of one-dimensional radial lines, effectively reducing the two-dimensional estimation problem to a series of one-dimensional problems. The resulting two-dimensional power spectrum estimates are compared to the known power spectra for a variety of data types. The Radon transform approach combined with autoregressive parameter estimation can provide a high-resolution power spectrum estimate, effectively surpassing the resolution limitations of the Fourier methods without the cumbersome implementations of the more direct high resolution estimation methods in two dimensions

Dynamic modeling of commodity futures prices

Theory suggests that physical commodity prices may exhibit nonlinear features such as bubbles and various types of asymmetries. This paper investigates these claims empirically by introducing a new time series model apt to capture such features. The data set is composed of 25 individual, continuous contract, commodity futures price series, representative of a number of industry sectors including softs, precious metals, energy, and livestock. It is shown that the linear causal ARMA model with Gaussian innovations is unable to adequately account for the features of the data. In the purely descriptive time series literature, often a threshold autoregression (TAR) is employed to model cycles or asymmetries. Rather than take this approach, we suggest a novel process which is able to accommodate both bubbles and asymmetries in a flexible way. This process is composed of both causal and noncausal components and is formalized as the mixed causal/noncausal autoregressive model of order (r, s). Estimating the mixed causal/noncausal model with leptokurtic errors, by an approximated maximum likelihood method, results in dramatically improved model fit according to the Akaike information criterion. Comparisons of the estimated unconditional distributions of both the purely causal and mixed models also suggest that the mixed causal/noncausal model is more representative of the data according to the Kullback-Leibler measure. Moreover, these estimation results demonstrate that allowing for such leptokurtic errors permits identification of various types of asymmetries. Finally, a strategy for computing the multiple steps ahead forecast of the conditional distribution is discussed

Generalized Hidden Filter Markov Models Applied to Speaker Recognition

Classification of time series has wide Air Force, DoD and commercial interest, from automatic target recognition systems on munitions to recognition of speakers in diverse environments. The ability to effectively model the temporal information contained in a sequence is of paramount importance. Toward this goal, this research develops theoretical extensions to a class of stochastic models and demonstrates their effectiveness on the problem of text-independent (language constrained) speaker recognition. Specifically within the hidden Markov model architecture, additional constraints are implemented which better incorporate observation correlations and context, where standard approaches fail. Two methods of modeling correlations are developed, and their mathematical properties of convergence and reestimation are analyzed. These differ in modeling correlation present in the time samples and those present in the processed features, such as Mel frequency cepstral coefficients. The system models speaker dependent phonemes, making use of word dictionary grammars, and recognition is based on normalized log-likelihood Viterbi decoding. Both closed set identification and speaker verification using cohorts are performed on the YOHO database. YOHO is the only large scale, multiple-session, high-quality speech database for speaker authentication and contains over one hundred speakers stating combination locks. Equal error rates of 0.21% for males and 0.31% for females are demonstrated. A critical error analysis using a hypothesis test formulation provides the maximum number of errors observable while still meeting the goal error rates of 1% False Reject and 0.1% False Accept. Our system achieves this goal

Studies in Multidimensional Stochastic Processes: Multivariate Long-Range Dependence and Synthesis of Gaussian Random Fields

This thesis is concerned with the study of multidimensional stochastic processes with special dependence structures. It is comprised of 3 parts. The first two parts concern multivariate long-range dependent time series. These are stationary multivariate time series exhibiting long-range dependence in the sense that the impact of past values of the series to the future ones dies out slowly with the increasing lag. In contrast to the univariate case, where long-range dependent time series are well understood and applied across a number of research areas such as Economics, Finance, Computer Networks, Physics, Climate Sciences and many others, the study of multivariate long-range dependent time series has not matured yet. This thesis sets proper theoretical foundations of such series and examines their statistical inference under novel models. The third part of the thesis is concerned with two-dimensional stationary Gaussian random fields. In particular, a fast algorithm is proposed for exact synthesis of such fields based on convex optimization and is shown to outperform existing approaches.Doctor of Philosoph