Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model

Haggan, V.; Ozaki, Tohru

doi:10.1093/biomet/68.1.189

Cited by 344 publications

(51 citation statements)

References 8 publications

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“…By Karamata's Theorem (28) where R is a measurable function. The framework 11 is quite general, and it includes many popular nonlinear time series models, such as threshold autoregressive models (33), exponential autoregressive models (34), bilinear autoregressive models, autoregressive models with conditional heteroscedasticity (35), among others. If there exists ␣ Ͼ 0 and x 0 such that…”

Section: Dependence Measuresmentioning

confidence: 99%

Nonlinear system theory: Another look at dependence

2005

Proc. Natl. Acad. Sci. U.S.A.

490

475

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Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.nonlinear time series ͉ limit theory ͉ kernel estimation ͉ weak convergence

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Section: Dependence Measuresmentioning

confidence: 99%

Nonlinear system theory: Another look at dependence

2005

Proc. Natl. Acad. Sci. U.S.A.

490

475

View full text Add to dashboard Cite

show abstract

“…This model implies that the dynamics of the middle ground differ from those of the larger returns. The ESTAR model is a generalisation of the regular exponential autoregressive (EAR) model of Haggan and Ozaki (1981), where q 0 = c = 0, this generalisation making the EAR model location invariant. The ESTARX model, which identifies differing behaviour resulting from larger and small trades, may therefore capture the effects of transactions costs on trader behaviour or market depth.…”

Section: Starx Modelmentioning

confidence: 99%

Nonlinear predictability of stock market returns: Evidence from nonparametric and threshold models

McMillan

2001

International Review of Economics & Finance

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Recent empirical evidence suggests that stock market returns are predictable from a variety of financial and macroeconomic variables. However, with two exceptions this predictability is based upon a linear functional form. This paper extends this research by considering whether a nonlinear relationship exists between stock market returns and these conditioning variables, and whether this nonlinearity can be exploited for forecast improvements. General nonlinearities are examined using a nonparametric regression technique, which suggest possible threshold behaviour. This leads to estimation of a smooth-transition threshold type model, with the results indicating an improved insample performance and marginally superior out-of-sample forecast results. D 2001 Elsevier Science Inc. All rights reserved.JEL classification: G12; G13

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“…However, the decisionmaking problem associated with this type of change is static. The exponential smooth transition autoregressive (ESTAR) [27] model provides a compromise between the two aforementioned types of variation. Two interpretations of the ESTAR model are possible.…”

Section: Artificial Dynamic Environmentmentioning

confidence: 99%

Prospects for Bandit Solutions in Sensor Management

Pavlidis

Adams

Nicholson

et al. 2010

The Computer Journal

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Sensor management in information-rich and dynamic environments can be posed as a sequential action selection problem with side information. To study such problems we employ the dynamic multi-armed bandit with covariates framework. In this generalization of the multi-armed bandit, the expected rewards are time-varying linear functions of the covariate vector. The learning goal is to associate the covariate with the optimal action at each instance, essentially learning to partition the covariate space adaptively. Applications of sensor management are frequently in environments in which the precise nature of the dynamics is unknown. In such settings, the sensor manager tracks the evolving environment by observing only the covariates and the consequences of the selected actions. This creates difficulties not encountered in static problems, and changes the exploitationexploration dilemma. We study the relationship between the different factors of the problem and provide interesting insights. The impact of the environment dynamics on the action selection problem is influenced by the covariate dimensionality. We present the surprising result that strategies that perform very little or no exploration perform surprisingly well in dynamic environments.

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Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model

Cited by 344 publications

References 8 publications

Nonlinear system theory: Another look at dependence

Nonlinear system theory: Another look at dependence

Nonlinear predictability of stock market returns: Evidence from nonparametric and threshold models

Prospects for Bandit Solutions in Sensor Management

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