An experiment on Autoregressive and Threshold Autoregressive models with non-Gaussian error with application to realized volatility

Ziyi ZHANG, Wai Keung LI

Research output: Contribution to journalArticle

Abstract

This article explores the fitting of Autoregressive (AR) and Threshold AR (TAR) models with a non-Gaussian error structure. This is motivated by the problem of finding a possible probabilistic model for the realized volatility. A Gamma random error is proposed to cater for the non-negativity of the realized volatility. With many good properties, such as consistency even for non-Gaussian errors, the maximum likelihood estimate is applied. Furthermore, a non-gradient numerical Nelder–Mead method for optimization and a penalty method, introduced for the non-negative constraint imposed by the Gamma distribution, are used. In the simulation experiments, the proposed fitting method found the true model with a rather insignificant bias and mean square error (MSE), given the true AR or TAR model. The AR and TAR models with Gamma random error are then tested on empirical realized volatility data of 30 stocks, where one third of the cases are fitted quite well, suggesting that the model may have potential as a supplement for current Gaussian random error models with proper adaptation. Copyright © 2019 by the authors.
Original languageEnglish
Article number58
JournalEconomies
Volume7
Issue number2
DOIs
Publication statusPublished - Jun 2019

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Realized Volatility
Threshold Autoregressive Model
Random Error
AR Model
Threshold Model
Experiment
Error Model
Penalty Method
Nonnegativity
Gamma distribution
Maximum Likelihood Estimate
Mean square error
Probabilistic Model
Simulation Experiment
Non-negative
Numerical Methods
Optimization
Model

Bibliographical note

Zhang, Z., & Li, W. K. (2019). An experiment on Autoregressive and Threshold Autoregressive models with non-Gaussian error with application to realized volatility. Economies, 7(2). Retrieved from https://doi.org/10.3390/economies7020058

Keywords

  • Autoregressive Model
  • Non-Gaussian error
  • Realized volatility
  • Threshold Autoregressive Model