Results 1  10
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21
Large Sample Sieve Estimation of SemiNonparametric Models
 Handbook of Econometrics
, 2007
"... Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method o ..."
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Cited by 92 (17 self)
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Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in seminonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. This chapter describes estimation of seminonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve Mestimates, pointwise normality of series estimates of regression functions, rootn asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.
Finding Chaos in Noisy Systems
, 1991
"... In the past twenty years there has been much interest in the physical and biological sciences in nonlinear dynamical systems that appear to have random, unpredictable behavior. One important parameter of a dynamic system is the dominant Lyapunov exponent (LE). When the behavior of the system is comp ..."
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Cited by 50 (1 self)
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In the past twenty years there has been much interest in the physical and biological sciences in nonlinear dynamical systems that appear to have random, unpredictable behavior. One important parameter of a dynamic system is the dominant Lyapunov exponent (LE). When the behavior of the system is compared for two similar initial conditions, this exponent is related to the rate at which the subsequent trajectories diverge. A bounded system with a positive LE is one operational definition of chaotic behavior. Most methods for determining the LE have assumed thousands of observations generated from carefully controlled physical experiments. Less attention has been given to estimating the LE for biological and economic systems that are subjected to random perturbations and observed over a limited amount of time. Using nonparametric regression techniques (Neural Networks and Thin Plate Splines) it is possible to consistently estimate the LE. The properties of these methods have been studied using simulated data and are applied to a biological time series: marten fur returns for the Hudson Bay Company (18201900). Based on a nonparametric analysis there is little evidence for lowdimensional chaos in these data. Although these methods appear to work well for systems perturbed by small amounts of noise, finding chaos in a system with a significant stochastic component may be difficult.
A SingleBlind Controlled Competition Among Tests for Nonlinearity and Chaos
 Journal of Econometrics
, 1997
"... Abstract: Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a singleblind controlled competition among five highly regard ..."
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Cited by 39 (5 self)
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Abstract: Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a singleblind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by email, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.
Implementing Projection Pursuit Learning
, 1996
"... This paper examines the implementation of projection pursuit regression (PPR) in the context of machine learning and neural networks. We propose a parametric PPR with direct training which achieves improved training speed and accuracy when compared with nonparametric PPR. Analysis and simulations ..."
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Cited by 11 (0 self)
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This paper examines the implementation of projection pursuit regression (PPR) in the context of machine learning and neural networks. We propose a parametric PPR with direct training which achieves improved training speed and accuracy when compared with nonparametric PPR. Analysis and simulations are done for heuristics to choose good initial projection directions. A comparison of a projection pursuit learning network with a one hidden layer sigmoidal neural network shows why grouping hidden units in a projection pursuit learning network is useful. Learning robot arm inverse dynamics is used as an example problem.
Chaotic time series Part I: Estimation of some invariant properties in state space
 Modeling, Identification and Control, 15(4):205  224
, 1995
"... Certain deterministic nonlinear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows constructing more realistic and better models and thus impro ..."
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Cited by 8 (5 self)
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Certain deterministic nonlinear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows constructing more realistic and better models and thus improved predictive capabilities. This paper provides a review of two main key features of chaotic systems, the dimensions of their strange attractors and the Lyapunov exponents. The emphasis is on state space reconstruction techniques that are used to estimate these properties, given scalar observations. Data generated from equations known to display chaotic behaviour are used for illustration. A compilation of applications to real data from widely different fields is given. If chaos is found to be present, one may proceed to build nonlinear models, which is the topic of the second paper in this series.
Chaos with Confidence: Asymptotics and Applications of Local Lyapunov Exponents
, 1997
"... . In this paper we define a version of Local Lyapunov Exponents (LLEs) for discretetime dynamical systems perturbed by noise, which are related to shortterm predictability and noise amplification and thus can be used to detect regions of state space where the dynamics may be more predictable. We p ..."
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Cited by 8 (1 self)
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. In this paper we define a version of Local Lyapunov Exponents (LLEs) for discretetime dynamical systems perturbed by noise, which are related to shortterm predictability and noise amplification and thus can be used to detect regions of state space where the dynamics may be more predictable. We present a Central Limit Theorem for fluctuations of LLEs about the global LE, as the number of forward time steps used in computing LLEs is increased. We also present some largesample statistical properties when LLEs are estimated by fitting a statistical model to a time series, that justify the construction of confidence intervals for maximum likelihood estimates. As an application of these results we analyze time series of measles monthly case reports, using a neural network time series model. The results show large changes in dynamic structure and predictability over the course of an epidemic. Because LLEs provide a detailed description of a systems' nonlinearity, they are well suited to ...
Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
, 2000
"... This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the est ..."
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Cited by 8 (2 self)
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This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1 % level with an exception in some higher power transformed absolute returns.
Is there chaos in the world economy? A nonparametric test using consistent standard errors.” International Economic Review, forthcoming
, 2001
"... A positive Lyapunov exponent is one practical deÞnition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the ..."
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Cited by 5 (3 self)
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A positive Lyapunov exponent is one practical deÞnition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the positive Lyapunov exponent is signiÞcantly rejected in many cases. One possible interpretation of this result is that the traditional exogenous models are better able to explain business cycle ßuctuations than is the chaotic endogenous approach. However, our results are subject to a number of caveats, in particular our results could have been inßuenced by small sample bias, high noise level, incorrect Þltering, and long memory of the data.
Penalized Sieve Estimation and Inference of Seminonparametric Dynamic Models: A Selective Review
, 2011
"... In this selective review, we …rst provide some empirical examples that motivate the usefulness of seminonparametric techniques in modelling economic and …nancial time series. We describe popular classes of seminonparametric dynamic models and some temporal dependence properties. We then present pe ..."
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Cited by 3 (1 self)
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In this selective review, we …rst provide some empirical examples that motivate the usefulness of seminonparametric techniques in modelling economic and …nancial time series. We describe popular classes of seminonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for seminonparametric models with crosssectional, panel, time series, or spatial data. The method is especially powerful in estimating di ¢ cult illposed inverse problems such as seminonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plugin PSE estimators of functionals that are either smooth (i.e., rootn estimable) or nonsmooth (i.e., slower than rootn estimable); (3) simple criterionbased inference for plugin PSE estimation of smooth or nonsmooth functionals; and (4) rootn asymptotic normality of semiparametric twostep estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH,
Characterizing the Degree of Stability of NonLinear Dynamic Models
, 2001
"... The purpose of this paper is to show how the stability properties of nonlinear dynamic models may be characterized, where the degree of stability is defined by the effects of exogenous shocks on the evolution of the observed stochastic system. Smoothed Lyapunov exponents are a generalization of Lya ..."
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Cited by 3 (0 self)
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The purpose of this paper is to show how the stability properties of nonlinear dynamic models may be characterized, where the degree of stability is defined by the effects of exogenous shocks on the evolution of the observed stochastic system. Smoothed Lyapunov exponents are a generalization of Lyapunov exponents for deterministic systems. We argue that smoothed Lyapunov exponents can be used to measure the degree of stability of a stochastic dynamic model. When such a model is fitted to observed data, an estimator of the largest smooth Lyapunov exponent is presented which is consistent and asymptotically normal. This is further examined in a Monte Carlo study. Finally, we illustrate how the presented framework can be used to study the degree of stability of exchange rates.