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Deterministic Part (deterministic + part)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Dynamic two state stochastic models for ecological regime shifts

ENVIRONMETRICS, Issue 8 2009
Jan Kloppenborg Møller
Abstract A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the non-linear functions. The dynamical behavior of the deterministic part of the model illustrates that hysteresis effect and regime shifts can be obtained for a limited range of parameter values only. The effect of multiplicative noise components entering at different levels of the model is presented and discussed. Including noise leads to very different results on the stability of regimes, depending on how the noise propagates through the system. The dynamical properties of a system should therefore be described through propagation of the state distributions rather than the state means and consequently, stochastic models should be compared in a probabilistic framework. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Spatial-temporal model for ambient air pollutants in the state of Kuwait

ENVIRONMETRICS, Issue 7 2006
Fahimah A. Al-Awadhi
Abstract In this paper we consider dynamic Bayesian models for four different pollutants: nitric oxide(NO), carbon monoxide(CO), sulphur dioxide(SO2) and non-methane hydrocarbon (NCH4) recorded daily in six different stations in Kuwait from 1999 to 2002. The structure of the models depends on time, space and pollutants dependencies. The approach strives to incorporate the uncertainty of the covariance structure into simulated models and final inference; therefore, hierarchical Bayesian model is applied. Association between level of pollutants and different meteorological variables, such as wind speed, wind directions, temperature and humidity are considered. The models will decompose into two main components: a deterministic part to represent the observed components term and a stochastic term to represent the unobservable components. Our analysis will start with basic model and gradually increase its complexity. At each stage the efficiency of the model will be measured. The resulting models subsequently are tested by comparing the output terms and by comparing and the predictions with the real observations. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Granger's representation theorem: A closed-form expression for I(1) processes

THE ECONOMETRICS JOURNAL, Issue 1 2005
Peter Reinhard Hansen
Summary, The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This proof enables us to derive closed-form expressions of all terms of the representation and allows a unified treatment of models with different deterministic specifications. The applicability of our results is illustrated by examples. For example, the closed-form expressions are useful for impulse response analyses and facilitate the analysis of cointegration models with structural changes. [source]

Comparison of unit root tests for time series with level shifts

JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2002
MARKKU LANNE
Unit root tests are considered for time series which have a level shift at a known point in time. The shift can have a very general nonlinear form, and additional deterministic mean and trend terms are allowed for. Prior to the tests, the deterministic parts and other nuisance parameters of the data generation process are estimated in a first step. Then, the series are adjusted for these terms and unit root tests of the Dickey,Fuller type are applied to the adjusted series. The properties of previously suggested tests of this sort are analysed and modifications are proposed which take into account estimation errors in the nuisance parameters. An important result is that estimation under the null hypothesis is preferable to estimation under local alternatives. This contrasts with results obtained by other authors for time series without level shifts. [source]