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Bayesian nonlinear expectation for time series modelling and its application to Bitcoin.

ABSTRACT: This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model.

Supplementary information

The online version contains supplementary material available at 10.1007/s00181-022-02255-z.

SUBMITTER: Siu TK

PROVIDER: S-EPMC9130704 | biostudies-literature | 2022 May

REPOSITORIES: biostudies-literature

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Bayesian nonlinear expectation for time series modelling and its application to Bitcoin.

Siu Tak Kuen TK

Empirical economics 20220525 1

This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesia ...[more]

PMID: 35645455

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Dataset Information

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin.

Supplementary information

Publications

Bayesian nonlinear expectation for time series modelling and its application to Bitcoin.

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