Multiple Bilinear Time Series Models

Stensholt, Boonchai K.; Tjøstheim, Dag

doi:10.1111/j.1467-9892.1987.tb00434.x

Cited by 46 publications

(18 citation statements)

References 2 publications

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“…we can express Vn, D, and F , in the following equivalent form: Liu and Brockwell (1988) (see also Stensholt and Tjostheim (1987) or Bhaskara et al (1983)), 1 D,, 1 s const.Anj2…”

Section: Proof In This Casementioning

confidence: 98%

“…To compare this approach with that of Stensholt and Tjostheim (1987) then Equation (3.10) has a unique strictly stationary solution given by the L2 or almost sure limit of S,,(t) defined by the recursion (3.11).…”

Section: The Subdiagonal Bilinear Modelmentioning

confidence: 99%

“…Subba Rao and Gabr 1984), this model may give a reasonably good approximation to seismological data. More recently, Stensholt and Tjostheim (1987) are zero reduces to the well-known multivariate autoregressive moving-average (ARMA) model. To obtain the state space representation of model ( l .…”

Section: Introductionmentioning

confidence: 99%

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On the Existence of a General Multiple Bilinear Time Series

Liu

1989

Journal Time Series Analysis

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A sufficient condition is derived for the existence of a strictly stationary solution of the general multiple bilinear time series equations (without assuming subdiagonality). The condition is shown to reduce to the condition of Stensholt and Tjostheim in the special case which they consider. Under this condition a solution is constructed which is shown to be casual in the sense we define, strictly stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non-linear terms, i.e. the multiple autoregressive moving-average (ARMA) model, the condition given here reduces to the well-known sufficient condition for the existence of a casual stationary solution.

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“…we can express Vn, D, and F , in the following equivalent form: Liu and Brockwell (1988) (see also Stensholt and Tjostheim (1987) or Bhaskara et al (1983)), 1 D,, 1 s const.Anj2…”

Section: Proof In This Casementioning

confidence: 98%

Section: The Subdiagonal Bilinear Modelmentioning

confidence: 99%

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On the Existence of a General Multiple Bilinear Time Series

Liu

1989

Journal Time Series Analysis

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“…The problem of testing the processes for linearity (nonlinearity) is considered in many studies [10][11][12][13][14][15][16]. Usually combination of several tests helps to detect existing nonlinearity and to select appropriate model structure.…”

Section: Testing For Linearity and Some Models For Nonlinear Nonstatimentioning

confidence: 99%

Methodology of Modeling and Forecasting Nonlinear Processes in Finances

et al. 2018

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Background.Most of the models of financial and economic processes are characterized by considerable computational complexity, and construction of predictions of acceptable quality for the required time horizon -by considerable efforts. Therefore, the development and implementation of effective tools for forecasting the modeling of financial and economic processes are one of the actual and practically meaningful tasks. The paper deals with the modeling and forecasting of nonlinear nonstationary processes in macroeconomics and finance using a methodology based on the principles of system analysis such as hierarchical modeling, consideration of the influence of uncertainties, optimization of the characteristics of models using complex criteria, structural and parametric adaptation. The application of the proposed methodology will improve the quality of forecasting by studying the features of the analyzed process and adapting models to new data, etc. Objective. The purpose of this article is to develop a methodology for predictive modeling of nonstationary processes in finance and macroeconomics using statistical data, as well as its implementation in the corresponding computer system. Methods. The methodology is based on the technologies of preliminary processing of statistical data intended to eliminate possible uncertainties, the use of correlation analysis to evaluate structure of the model and choice of methods for estimating its parameters, calculating forecast estimates and generating alternative solutions. This allows us to objectively evaluate the results obtained at each stage of solving the problem of modeling nonlinear nonstationary processes in macroeconomics and finance. The paper proposes an original methodology for determining the structure of the model and its implementation in the information system for decision support. Results. Appropriate models were built for the selected financial and macroeconomic processes. High quality of the final result of data analysis and forecasting is achieved due to implementation of evaluation of the results obtained using statistical quality criteria at each stage of data processing, modeling and forecasting, and also due to the possibility of adapting models to new data through analysis of statistical characteristics of the processes under study and application of combined criteria for the adequacy of models and quality of estimates of forecasts, and the convenient presentation of intermediate and final results. Conclusions. The proposed methodology is used for forecasting modeling of some macroeconomic and financial processes in Ukraine. The obtained results show that it can be successfully used to solve practical problems of constructing models and prediction of nonlinear nonstationary processes under conditions of uncertainties of various types, which, as a rule, have to be considered during modeling and forecasting on the basis of statistical data.

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“…In the nonlinear case, probabilistic properties, such as stationarity and ergodicity, do not seem to be available except in a few special cases, see Stensholt and Tjøstheim (1987), for example.…”

Section: Standard Linear Granger Noncausality Testmentioning

confidence: 99%

Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form

Péguin-Feissolle¹,

Strikholm²,

Teräsvirta³

2013

Communications in Statistics - Simulation and Computation

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may January 2012Abstract In this paper we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests by a Monte Carlo experiment and compare these to the most widely used linear test. Our tests appear to be well-sized and have reasonably good power properties.

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Multiple Bilinear Time Series Models

Abstract: A definition of multiple bilinear time series models is given. Sufficient conditions are obtained for the existence of strictly stationary solutions conforming to the model, and a brief discussion of the first and second order structure is included.

Cited by 46 publications

References 2 publications

On the Existence of a General Multiple Bilinear Time Series

On the Existence of a General Multiple Bilinear Time Series

Methodology of Modeling and Forecasting Nonlinear Processes in Finances

Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form

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