Bayesian Estimation of GARCH(1,1) Model Using Tierney-Kadane’s Approximation

Yakup Ari

Chapter Chapter 24 in Advances in Time Series Data Methods in Applied Economic Research, 2018, pp 355-364 from Springer

Abstract: Abstract The Generalized Autoregressive Conditionally Heteroscedastic (GARCH) process models the dependency of conditional second moments of financial time series. The maximum likelihood estimation (MLE) procedure is most commonly used for estimating the unknown parameters of a GARCH model. In this study, the parameters of the GARCH models with normal innovations are discussed for estimations using the Bayesian approach in which the parameters of the GARCH model are assumed as random variables having known prior probability density functions. The prior probability density functions of the parameters satisfy the conditions on GARCH parameters such as positivity and stationarity. The Bayesian estimators are not in a closed form. Thus Tierney-Kadane’s approximation that is a numerical integration method to calculate the ratio of two integrals is used to estimate. The Bayesian estimators are derived under squared error loss function. Finally, simulations are performed in order to compare the ML estimates to the Bayesian ones and furthermore, an example is given in order to illustrate the findings.

Keywords: Bayes; Tierney-Kadane; GARCH; MLE (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:prbchp:978-3-030-02194-8_24

Ordering information: This item can be ordered from
http://www.springer.com/9783030021948

DOI: 10.1007/978-3-030-02194-8_24

Access Statistics for this chapter

More chapters in Springer Proceedings in Business and Economics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().