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

¹Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW 2109 Australia.

Empirical Economics

|June 1, 2022

Summary

This study introduces a two-stage method for nonlinear time series modeling, enhancing predictions by accounting for model uncertainty. The approach uses Bayesian nonlinear expectations for improved forecasting and risk assessment, demonstrated with Bitcoin data.

Keywords:

Bayesian statistics Bitcoin Drift and volatility uncertainties Girsanov’s transform Nonlinear expectations Parametric time series modelling

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Area of Science:

Econometrics
Computational Statistics
Time Series Analysis

Background:

Parametric nonlinear time series models are crucial for analyzing complex financial data.
Existing models often struggle to fully capture uncertainty or misspecification in conditional mean and volatility.
Accurate forecasting and risk evaluation require methods that explicitly address these limitations.

Purpose of the Study:

To propose a novel two-stage approach for parametric nonlinear time series modeling in discrete time.
To incorporate uncertainty or misspecification in conditional mean and volatility into predictions.
To apply the method for forecasting and risk evaluation of Bitcoin data.

Main Methods:

A two-stage modeling process: first, estimating an approximating time series model.
Second, employing Bayesian nonlinear expectations using closed-form credible intervals and residuals from the approximating model.
Utilizing conjugate priors for efficient computation.

Main Results:

The proposed method effectively incorporates model uncertainty and misspecification in predictions.
Demonstrated successful application to Bitcoin data, including the Covid-19 period.
Forecasting and risk evaluation were performed using three established parametric nonlinear time series models.

Conclusions:

The developed two-stage approach offers a robust framework for handling uncertainty in nonlinear time series.
Bayesian nonlinear expectations provide a powerful tool for enhancing predictive accuracy and risk assessment.
The method's efficacy is validated through its application to real-world Bitcoin financial data.