A bayesian analysis of some threshold switching models

A Bayesian estimation procedure is developed for estimating multiple regime (multiple threshold) vector autoregressive models appropriate for deviations from financial arbitrage relationships. This approach has clear advantages over classical stepwise threshold autoregressive analysis. Whereas classical procedures first have to identify thresholds and then perform piecewise autoregressions, we simultaneously estimate threshold and autoregression parameters. To illustrate the Bayesian procedure, we estimate a no-arbitrage band within which index futures arbitrage is not profitable despite (persistent) deviations from parity.

show abstract

“…' Pole and Smith (1985) present a Bayesian analysis of the related threshold regime switching models.…”

mentioning

confidence: 99%

Bayesian Arbitrage Threshold Analysis

Forbes¹,

Kalb²,

Kofman³

1999

Journal of Business & Economic Statistics

View full text Add to dashboard Cite

show abstract

“…The proposed approach may be related to the Bayesian approach to nonlinear time series and Bayesian econometrics. See, for example, Pole and Smith ( 1985 ) for Bayesian analysis of SETAR models and Koop ( 2003 ) for an excellent account on Bayesian econometrics. However, the key difference between them is that the proposed approach is a two-stage approach, where the reference model is specified and estimated in the first stage, and the second stage is concerned with prediction in the presence of model uncertainty or misspecification using the Bayesian nonlinear expectations over a set of alternative models.…”

Section: Introductionmentioning

confidence: 99%

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

Siu

2022

Empir Econ

View full text Add to dashboard Cite

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.

show abstract

“…Usually there is a threshold variable indicating at each point in time which regime prevails. This variable can be a function of the observable history, or an unobservable latent variable, e.g., a saturating consumption utility level; see Pole and Smith (1985). Markov Chain regime switching models typically allow for unobservables to identify the regime.…”

Section: Introductionmentioning

confidence: 99%