Siu Tak Kuen
Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW 2109 Australia.
Empir Econ. 2023;64(1):505-537. doi: 10.1007/s00181-022-02255-z. Epub 2022 May 25.
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.
The online version contains supplementary material available at 10.1007/s00181-022-02255-z.
本文提出了一种用于离散时间参数非线性时间序列建模的两阶段方法，目的是在条件均值和波动率中纳入不确定性或模型误设。在第一阶段，指定并估计一个参考或近似时间序列模型。在第二阶段，引入贝叶斯非线性期望，通过指定一族替代模型在预测中纳入模型不确定性或模型误设。预测的贝叶斯非线性期望由使用共轭先验和估计的近似模型的残差评估的闭式贝叶斯可信区间构建。使用包括一些新冠疫情时期的真实比特币数据，通过三个主要的参数非线性时间序列模型，即自激励阈值自回归模型、广义自回归条件异方差模型和随机波动率模型，讨论了所提出方法在比特币预测和风险评估中的应用。
在线版本包含可在10.1007/s00181-022-02255-z获取的补充材料。
