408 research outputs found
Optimal phase space projection for noise reduction
In this communication we will re-examine the widely studied technique of
phase space projection. By imposing a time domain constraint (TDC) on the
residual noise, we deduce a more general version of the optimal projector,
which includes those appearing in previous literature as subcases but does not
assume the independence between the clean signal and the noise. As an
application, we will apply this technique for noise reduction. Numerical
results show that our algorithm has succeeded in augmenting the signal-to-noise
ratio (SNR) for simulated data from the R\"ossler system and experimental
speech record.Comment: Accepted version for PR
Identification of Economic Shocks by Inequality Constraints in Bayesian Structural Vector Autoregression
Theories often make predictions about the signs of the effects of economic shocks on observable variables, thus implying inequality constraints on the parameters of a structural vector autoregression (SVAR). We introduce a new Bayesian procedure to evaluate the probabilities of such constraints, and, hence, to validate the theoretically implied economic shocks. We first estimate a SVAR, where the shocks are identified by statistical properties of the data, and subsequently label these statistically identified shocks by the Bayes factors calculated from their probabilities of satisfying given inequality constraints. In contrast to the related sign restriction approach that also makes use of theoretically implied inequality constraints, no restrictions are imposed. Hence, it is possible that only a subset or none of the theoretically implied shocks can be labelled. In the latter case, we conclude that the data do not lend support to the theory implying the signs of the effects in question. We illustrate the method by empirical applications to the crude oil market, and U.S. monetary policy.Peer reviewe
Problems Related to Bootstrapping Impulse Responses of Autoregressive Processes
Bootstrap confidence intervals for impulse responses computed from autoregressive processes are considered. A detailed analysis of the methods in current use shows that they are not very reliable in some cases. In particular, there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance. For a simple case alternative bootstrap methods are proposed which provide correct results asymptotically
Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
Continuing on recent computational and experimental work on jammed packings
of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider
jamming in packings of smooth strictly convex nonspherical hard particles. We
explain why the isocounting conjecture, which states that for large disordered
jammed packings the average contact number per particle is twice the number of
degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to
nonspherical particles. We develop first- and second-order conditions for
jamming, and demonstrate that packings of nonspherical particles can be jammed
even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm
using these conditions to computer-generated hypoconstrained ellipsoid and
ellipse packings and demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also consider packings that are
nearly jammed and draw connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions for nearly spherical
particles and explain quantitatively the behavior we observe in the vicinity of
the sphere point.Comment: 33 pages, third revisio
Testing for periodic integration
A periodic autoregressive time-series model assumes that the autoregressive parameters vary with the season. This model can also be represented by a multivariate model for the annual vector containing the seasonal observations. When this multivariate model contains one unit root, a time-series is said to be periodically integrated of order 1. In this paper we propose tests for such a single unit root. These tests for periodic integration are applied to a periodic model for the quarterly German consumption series
A Random Matrix Approach to VARMA Processes
We apply random matrix theory to derive spectral density of large sample
covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2)
processes. In particular, we consider a limit where the number of random
variables N and the number of consecutive time measurements T are large but the
ratio N/T is fixed. In this regime the underlying random matrices are
asymptotically equivalent to Free Random Variables (FRV). We apply the FRV
calculus to calculate the eigenvalue density of the sample covariance for
several VARMA-type processes. We explicitly solve the VARMA(1,1) case and
demonstrate a perfect agreement between the analytical result and the spectra
obtained by Monte Carlo simulations. The proposed method is purely algebraic
and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic
Security Evaluation of Support Vector Machines in Adversarial Environments
Support Vector Machines (SVMs) are among the most popular classification
techniques adopted in security applications like malware detection, intrusion
detection, and spam filtering. However, if SVMs are to be incorporated in
real-world security systems, they must be able to cope with attack patterns
that can either mislead the learning algorithm (poisoning), evade detection
(evasion), or gain information about their internal parameters (privacy
breaches). The main contributions of this chapter are twofold. First, we
introduce a formal general framework for the empirical evaluation of the
security of machine-learning systems. Second, according to our framework, we
demonstrate the feasibility of evasion, poisoning and privacy attacks against
SVMs in real-world security problems. For each attack technique, we evaluate
its impact and discuss whether (and how) it can be countered through an
adversary-aware design of SVMs. Our experiments are easily reproducible thanks
to open-source code that we have made available, together with all the employed
datasets, on a public repository.Comment: 47 pages, 9 figures; chapter accepted into book 'Support Vector
Machine Applications
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
Nonlinear Factor-Augmented Predictive Regression Models with Functional Coefficients
This paper introduces a new class of functional-coefficient predictive regression models, where the regressors consist of auto-regressors and latent factor regressors, and the coefficients vary with certain index variable. The unobservable factor regressors are estimated through imposing an approximate factor model on high dimensional exogenous variables and subsequently implementing the classical principal component analysis. With the estimated factor regressors, a local linear smoothing method is used to estimate the coefficient functions (with appropriate rotation) and obtain a one-step ahead nonlinear forecast of the response variable, and then a wild bootstrap procedure is introduced to construct the prediction interval. Under regularity conditions, the asymptotic properties of the proposed methods are derived, showing that the local linear estimator and the nonlinear forecast using the estimated factor regressors are asymptotically equivalent to those using the true latent factor regressors. The developed model and methodology are further generalised to the factor-augmented vector predictive regression with functional coefficients. Finally, some extensive simulation studies and an empirical application to forecast the UK inflation are given to examine the finite-sample performance of the proposed model and methodology
Seasonality and stochastic trends in German consumption and income, 1960.1- 1987.4
The quarterly time series of German consumption and income are analyzed with respect to seasonality and stochastic trends. It emerges that both variables can be appropriately described by a periodically integrated autoregression. An implication is that the stochastic trend and the seasonal fluctuations are not independent for each of the univariate series. In order to test for cointegration across the two series, we propose several methods which take account of the relationship between seasons and trends in the univariate series. Some of these methods boil down to extracting the stochastic trend from the univariate series in a first step and to relating these trends using cointegration techniques in a second step. Another method is an extension of the Johansen cointegration testing approach to periodic vector autoregressions. Monte Carlo simulations are used to evaluate the empirical performance of the various methods. The main empirical result is that only in the first quarter there seems to be cointegration between German consumption and income
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