Results 11  20
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40
Denoising Deterministic Time Series
, 2002
"... This paper addresses a problem of statistical inference from dependent processes, namely how to recover a deterministic time series from observations that are corrupted by additive, independent noise. We will refer to this as the denoising problem. A distinctive feature of the denoising problem i ..."
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This paper addresses a problem of statistical inference from dependent processes, namely how to recover a deterministic time series from observations that are corrupted by additive, independent noise. We will refer to this as the denoising problem. A distinctive feature of the denoising problem is that the available observations exhibit dependence across long time scales and, as a consequence, existing statistical theory and methods are not readily applicable. This paper describes one analysis of the denoising problem, beginning from rst principles. We establish both positive and negative results.
Adaptive Estimation in Partially Linear Autoregressive Models
, 2000
"... The authors consider a partially linear autoregressive model and construct kernelbased estimates for both the parametric and nonparametric components. They propose an estimation procedure for the model and illustrate it through simulated and real data. Their work shows that the proposed estimation ..."
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The authors consider a partially linear autoregressive model and construct kernelbased estimates for both the parametric and nonparametric components. They propose an estimation procedure for the model and illustrate it through simulated and real data. Their work shows that the proposed estimation procedure has not only good asymptotic properties but also works well numerically. It also suggests that a partially linear autoregression is more appropriate than a completely nonparametric autoregression for some sets of data. R ESUM E Les auteurs montrent comment estimer par la methode du noyau les composantes parametriques et non parametriques d'un modele autoregressif partiellement lineaire. Ils proposent une methode d'estimation du modele et l'illustrent a l'aide de donnees reelles et simulees. En plus de faire ressortir le bon comportement asymptotique et numerique de la methode, leur travail suggere que dans certains cas, un modele autoregressif partiellement lineaire peut etre plus ...
A Test of the GARCH(1,1) Specification for Daily Stock Returns
, 2009
"... Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1,1) processes. Here we test this specification using new model evaluation technology developed in Ashley and Patterson (2006), which examines the ability of the estimated model to reproduce features of pa ..."
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Daily financial returns (and daily stock returns, in particular) are commonly modeled as GARCH(1,1) processes. Here we test this specification using new model evaluation technology developed in Ashley and Patterson (2006), which examines the ability of the estimated model to reproduce features of particular interest: various aspects of nonlinear serial dependence, in the present instance. Using daily returns to the CRSP equally weighted stock index, we find that the GARCH(1,1) specification cannot be rejected; thus, this model appears to be reasonably adequate in terms of reproducing the kinds of nonlinear serial dependence addressed by the battery of nonlinearity tests used here.
Random Walk or Chaos: A Formal Test on the Lyapunov Exponent
, 1999
"... A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system. The test is based on the NadarayaWatson kernel estimate of the Lyapunov exponent. We show that the estimator is consistent: The estimated Lyapunov exponent converges to zero under the rando ..."
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A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system. The test is based on the NadarayaWatson kernel estimate of the Lyapunov exponent. We show that the estimator is consistent: The estimated Lyapunov exponent converges to zero under the random walk hypothesis, while it converges to a positive constant for the chaotic system. The test is thus expected to have discriminatory powers. We derive the asymptotic distribution of the estimator, and make it possible to formally test for the null hypothesis of random walk against chaos. The proposed test statistic is a simple normalization of the estimated Lyapunov exponent. It is shown that the null distribution of the test statistic is given by the range of standard Brownian motion on the unit interval. We con...rm through simulation that our test performs reasonably well in ... nite samples. We also apply our test to some of the standard macro and ... nancial time series. For various st...
The Identification of Multiple Outliers in Online Monitoring Data
, 1999
"... We present a robust graphical procedure for routine detection of isolated and patchy outliers in univariate time series. This procedure is suitable for retrospective as well as for online identification of outliers. It is based on a phase space reconstruction of the time series which allows to regar ..."
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We present a robust graphical procedure for routine detection of isolated and patchy outliers in univariate time series. This procedure is suitable for retrospective as well as for online identification of outliers. It is based on a phase space reconstruction of the time series which allows to regard the time series as a multivariate sample with identically distributed but non independent observations. Thus, multivariate outlier identifiers can be transfered into the context of time series which is done here. Some applications to online monitoring data from intensive care are given. Key words: Multivariate sample, online monitoring, outlier identification, phase space reconstruction, process control, time series. 2 1 Introduction Increasing technical possibilities for online recording process data produce manifold challenges for statistical methods. In many fields like intensive care medicine, industrial process control, supply chain management, or electrical energy systems more and...
Finitary Reconstruction of a Measure Preserving Tranformation
 Israel Journal of Mathematics
, 2000
"... This paper considers the finitary reconstruction of an ergodic measure preserving transformation T of a complete separable metric space X from a single trajectory x; T x; : : :, or more generally, from a suitable reconstruction sequence x = x 1 ; x 2 ; : : : with x i 2 X . An nsample reconstruction ..."
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This paper considers the finitary reconstruction of an ergodic measure preserving transformation T of a complete separable metric space X from a single trajectory x; T x; : : :, or more generally, from a suitable reconstruction sequence x = x 1 ; x 2 ; : : : with x i 2 X . An nsample reconstruction is a function Tn : X n+1 ! X ; the map ^ Tn ( ; x 1 ; : : : ; xn ) is treated as an estimate of T ( ) based on the n initial elements of x. Given a reference probability measure 0 and constant M > 1, functions T 1 , T 2 , . . . are defined, and it is shown that for every with 1=M d =d 0 M , every  preserving transformation T , and every reconstruction sequence x for T , the estimates ^ Tn ( ; x 1 ; : : : ; xn ) converge to T in the weak topology. For the family of interval exchange transformations of [0; 1) a simple family of estimates is described and shown to be consistent both pointwise and in the strong topology. However, it is also shown that no finitary estimati...
On NonLinear, Stochastic Dynamics in Economic and Financial Time Series
 Studies in Nonlinear Dynamics and Econometrics
, 2001
"... The search for deterministic chaos in economic and financial time series has attracted much interest over the past decade. However, clear evidence of chaotic structures is usually prevented by large random components in the time series. In the first part of this paper we show that even if a sophi ..."
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The search for deterministic chaos in economic and financial time series has attracted much interest over the past decade. However, clear evidence of chaotic structures is usually prevented by large random components in the time series. In the first part of this paper we show that even if a sophisticated algorithm estimating and testing the positivity of the largest Lyapunov exponent is applied to time series generated by a stochastic dynamical system or a return series of a stock index, the results are difficult to interpret. We conclude that the notion of sensitive dependence on initial conditions as it has been developed for deterministic dynamics, can hardly be transfered into a stochastic context. Therefore, in the second part of the paper our starting point for measuring dependencies for stochastic dynamics is a distributional characterization of the dynamics, e.g. by heteroskedastic models for economic and financial time series. We adopt a sensitivity measure proposed...
Neural models for estimating Lyapunov exponents and embedding dimension from time series of nonlinear dynamical systems
, 1995
"... this paper have been extended to time varying systems and was applied to time series of a saxophone and a piano signal. From the Lyapunov spectrum we found that the saxophone attractor has 1 = 0, while the piano attractor has 1 ? 0 and hence exhibits chaotic behavior. The music instrument models h ..."
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this paper have been extended to time varying systems and was applied to time series of a saxophone and a piano signal. From the Lyapunov spectrum we found that the saxophone attractor has 1 = 0, while the piano attractor has 1 ? 0 and hence exhibits chaotic behavior. The music instrument models have been used to resynthesize the training signals showing the stability of the neural models. Further results will soon be published elsewhere.
Quantifying the effects of dynamical noise on the predictability of
"... a simple ecosystem model ..."
The Maximum Likelihood Neural Network As A Statistical Classification Model
"... this paper we utilize the inputoutput relationship associated with a simple feedforward neural network as the basis for a nonlinear multivariate classifier. A statistical model for the data is defined based on a logistic likelihood function. Neural network parameters are estimated using the metho ..."
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this paper we utilize the inputoutput relationship associated with a simple feedforward neural network as the basis for a nonlinear multivariate classifier. A statistical model for the data is defined based on a logistic likelihood function. Neural network parameters are estimated using the method of maximum likelihood instead of the backpropagation technique often used in the neural network literature. An extension for the multinomial case is presented. These maximum likelihood based models can be compared using readily available techniques such as the likelihood ratio test and the Akaike criterion (1973). We provide empirical comparisons of this network approach with standard logistic regression for both the binomial and multinomial cases. keywords: classification, feedforward neural networks, logistic likelihood, maximum likelihood. 3 1. INTRODUCTION The problem of classifying observations into two or more groups based on covariates has received much attention in the statistical literature. Many methods of classification have been developed including linear and nonlinear discriminant analysis (Cacoullos, 1973), nearest neighbor analysis (Johnson, 1967), cluster analysis (Cormack, 1971; Hartigan, 1975) and classification trees (Breiman, Friedman, Olshen and Stone, 1984). Another approach is to model the probability of belonging to a specific group as a function of the covariates. Logistic models are most commonly used (Cox and Snell, 1989). Recently neural networks (Rumelhart, Hinton and Williams, 1986) have received considerable attention by nonstatisticians for problems of classification and prediction. Applications include areas such as speech recognition (Sejnowski and Rosenberg, 1987), diagnostic image analysis (DaPonte and Sherman, 1991), clinical diagn...