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Estimation and selection of time-varying volatility models

Skregelid, Øystein
Master thesis
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URI
http://hdl.handle.net/11250/168411
Date
2009
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  • Master Thesis [4657]
Abstract
This paper describes methods that can be applied to select the best conditional volatility

model for an individual asset. Three exchange traded funds (ETFs) for the financials, energy

and utilities sectors of the Dow Jones Total Market Index are evaluated to illustrate the

complexity of model selection. For the univariate series, the symmetric GARCH model and

three asymmetric models (EGARCH, GJR-GARCH and TGARCH) with a variety of lag structures

are parameterized under the assumption of both normal and t-distributed errors. The

ranking of these models are based on how well the parameters of each model fit to the

underlying data set (the likelihood), on selection criterions (AIC and BIC) and on their

forecasting ability (through statistic and economic loss functions). The results show that

different volatility models with different lag structures are selected for each of the three

sectors. For the financial sector a t-distributed EGARCH(1,2,1) model gives the most

satisfying results. The energy sector is best described by a t-distributed GJR-GARCH(1,1,2)

model, while a normal distributed GJR-GARCH(1,1,1) model is recommended for the utilities

sector.

In addition to the selection of univariate models, multivariate models are described and

tested. The main focus in this part is on the Dynamic Conditional Correlation model that

builds on univariate parameterizations of the volatility. A DCC model based on three

univariate normal distributed GJR-GARCH(1,1,1) models is compared to the BEKK model and

to a multivariate EWMA model. This comparison shows that while the DCC model performs

best when it comes to minimizing the risk of a portfolio, the BEKK model is superior when

evaluated on the reward-to-variability ratio (Sharpe). This is mainly due to the fact that the

DCC model is unable to catch the time-varying correlation between the three chosen assets.

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