Volatility GARCH models with the ordered weighted average (OWA) operators

doi:10.1016/j.ins.2021.02.051

Information Sciences

Volume 565, July 2021, Pages 46-61

https://doi.org/10.1016/j.ins.2021.02.051 Get rights and content

Abstract

Volatility is an important issue for companies, policy-makers, and researches. Autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) models are frequently used to study volatility. However, forecasting efficiency tends to fail when complex data is used. This paper proposes the use of ordered weighted average (OWA) operators in combination with ordinary least squares (OLS) to create an estimator that can treat high degrees of uncertainty. In the application of the ARCH-GARCH models, we develop approaches with the OWA and the induced OWA operator. Some further generalizations are also developed by using generalized means. The main advantage of this new methodology is to add additional information to the process of estimating the models according to the attitudinal character of the decision-maker. Finally, the work presents an application in the volatility of the MX/US exchange rate, where the efficiency of the OWA operators in forecasting is proved.

Introduction

One of the most studied volatility models is the autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) models [18], [7], [31], [22]. The ARCH-GARCH models and their extensions have been used in the stock market [48], oil price [56], derivates markets [4], the exchange rate [16], [10] and others.

GARCH models reflect the non-linear dependence of the conditional variance in time series, estimating a conditional variance. However, these models can present structural problems when the data is imprecise and with uncertainty. Hung [27], [28] shows fuzzy adaptation in GARCH modeling to obtain favorable results in the estimation and forecast. Thavaneswaran, Appadoo, & Paseka [45] use fuzzy numbers to moderate the complex data in GARCH modeling. D'Urso, Giovanni, & Massari [13] proposed different fuzzy clustering models for classifying heteroskedastic time series usefulness in volatility.

The ordered weighted averaging (OWA) operator [50] provides an aggregation mean, which lies between the maximum and minimum. The OWA operator has been used for better results in complex and uncertain scenarios [55], [30]. Additionally, this methodology has been combined with other proposals to deal with data and risks such as linear regression [53], [29], variance [6], [34] and covariance [41], [39].

An interesting extension of the OWA operator is the induced ordered weighted averaging (IOWA) operator [54], which works with variables influenced by other variables. Yager [52] proposes the generalized ordered weighted aggregation operator (GOWA), which provides a generalization of the OWA operator by combining it with the generalized mean operator. These two operators are combined in one formulation called induced generalized (IGOWA) operator developed by Merigó and Gil-Lafuente [40].

This work proposes the use of OWA operators with multiple linear regressions to estimate a GARCH volatility model. The main advantage of this new methodology is to add to the GARCH models a component (OWA operator) for periods of great uncertainty. This component has the characteristic of adding additional information from the studied scenarios to underestimate or overestimate the parameters and obtain a forecast that is close to reality.

The remainder of this paper is organized as follows. Section 2 gives some background about the OWA operator, the regression and ARCH-GACH models. Section 3 develops OWA operators in linear regression, where LR-IOWA, MLR-IOWA, LR-IGOWA and MLR-IGOWA are proposed. Section 4 proves OWA operators in ARCH-GARCH models, we call them OWA-ARCH, IOWA-ARCH, GOWA-ARCH, IGOWA-ARCH, OWA-GARCH, IOWA-GARCH, GOWA-GARCH, IGOWA-GARCH. Section 5 presents an application in volatility exchange rate MX/US. Section 6 summarizes the main results and gives some future works.

Section snippets

Preliminaries

In this section, a review of the OWA operators, linear regression and ARCH-GARCH models is presented to analyze the main properties.

OWA operators in linear regression

The main limitation in linear regression and ordinary least squares is to consider absolute linearity when the data tend to be non-linear [47], [42]. IOWA operator in linear regression uses a non-linear method where IOWA means, variance and covariance IOWA are employed to estimate the parameters in a simple linear regression (LR-IOWA) and multiple linear regression (MLR-IOWA). In the case of simple linear regression, it is defined as follows:

Definition 9

Is an LR-IOWA of dimension n if we have a mapping IOWA

An ARCH model with OWA operators

Estimating and forecasting volatility with ARCH-GARCH models implies that we consider a given behavior in the financial series. However, many of the data tend to present non-normality and atypical behaviors caused by impression on the variables [1], [49], [2]. The use of OWA operators in the estimation of ARCH-GARCH parameters allows us to analyze a series of scenarios from maximum to minimum where the above characteristics can appear. We present an ARCH Model estimated with simple linear

Conclusions

The volatility forecast is a controversial issue due to the statistical behavior in the financial time series. Features such as data accuracy and high uncertainty make volatility difficult to predict. In this sense, two of the most used models are the autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH).

This paper proposes OWA aggregation operators' use in conjunction with the ordinary least squares estimator for the volatility forecast with ARCH-GARCH models. We

CRediT authorship contribution statement

Martha Flores-Sosa: Conceptualization, Validation, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Supervision. Ezequiel Avilés-Ochoa: Validation, Formal analysis, Resources, Data curation, Writing - original draft. José M. Merigó: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Supervision. Ronald R. Yager: Methodology, Validation, Writing - original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (57)

R.J. Almeida et al.
Estimation of flexible fuzzy GARCH models for conditional density estimation
Inf. Sci.
(2014)
S.A. Basher et al.
The impact of oil shocks on exchange rates: a Markov-switching approach
Energy Econ.
(2016)
T. Bollerslev
Generalized autoregressive conditional heteroskedasticity
J. Econ.
(1986)
P. D'Urso et al.
GARCH-based robust clustering of time series
Fuzzy Sets Syst.
(2016)
K. Daly
Financial volatility: issues and measuring techniques
Phys. A Statist. Mech. Appl.
(2008)
H. Dyckhoff et al.
Generalized means as model of compensative connectives
Fuzzy Sets Syst.
(1984)
R. Engle et al.
Combining competing forecasts of inflation using a bivariate arch model
J. Econ. Dyn. Control
(1984)
J. Figueroa-López et al.
Optimum thresholding using mean and conditional mean squared error
J. Econ.
(2019)
J.-C. Hung
A fuzzy asymmetric GARCH model applied to stock markets
Inf. Sci.
(2009)
J.-C. Hung
Adaptive Fuzzy-GARCH model applied to forecasting the volatility of stock markets using particle swarm optimization
Inf. Sci.
(2011)

P. Katsiampa

Volatility estimation for Bitcoin: a comparison of GARCH models

Econ. Lett.

(2017)

T. Korol

A fuzzy logic model for forecasting exchange rates

Knowl.-Based Syst.

(2014)

S. Lahmiri

Modeling and predicting historical volatility in exchange rate markets

Phys. A

(2017)

H. Leung et al.

Volatility spillovers and determinants of contagion: exchange rate and equity markets during crises

Econ. Model.

(2017)

J.M. Merigó

A unified model between the weighted average and the induced OWA operator

Expert Syst. Appl.

(2011)

J. Merigo et al.

The induced generalized OWA operator

Inf. Sci.

(2009)

B. Mu et al.

A globally consistent non-linear least squares estimator for identification of non-linear rational systems

Automatica

(2017)

A. Thavaneswaran et al.

Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing

Math. Comput. Modell.

(2009)

Y. Wei et al.

Hot money and China’s stock market volatility: further evidence using the GARCH–MIDAS model

Physica A

(2018)

F.Z. Xing et al.

Sentiment-aware volatility forecasting

Knowl.-Based Syst.

(2019)

R.R. Yager

Induced aggregation operators

Fuzzy Sets Syst.

(2003)

M. Zarghami et al.

Revising the OWA operator for multi criteria decision making problems under uncertainty

Eur. J. Operational

(2009)

Y.-J. Zhang et al.

Volatility forecasting of crude oil market: Can the regime switching GARCH model beat the single-regime GARCH models?

Int. Rev. Econ. Finance

(2019)

Z. Zhou et al.

Can economic policy uncertainty predict exchange rate volatility? New evidence from the GARCH-MIDAS model

Finance Res. Lett.

(2020)

H. Anjum et al.

Forecasting risk in the US Dollar exchange rate under volatility shifts

North Am. J. Econ. Finance

(2020)

M. Augustyniak et al.

Maximum likelihood estimation of the Markov-Switching GARCH model based on a general collapsing procedure

Methodol. Comput. Appl. Probability

(2018)

A. Badescu et al.

Closed-form variance swap prices under general affine GARCH models and their continuous-time limits

Ann. Oper. Res.

(2019)

F. Blanco‐Mesa et al.

Variances with Bonferroni means and ordered weighted averages

Int. J. Intell. Syst.

(2019)

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Volatility GARCH models with the ordered weighted average (OWA) operators

Abstract

Introduction

Section snippets

Preliminaries

OWA operators in linear regression

An ARCH model with OWA operators

Conclusions

CRediT authorship contribution statement

Declaration of Competing Interest

Inf. Sci.

Energy Econ.

J. Econ.

Fuzzy Sets Syst.

Phys. A Statist. Mech. Appl.

Fuzzy Sets Syst.

J. Econ. Dyn. Control

J. Econ.

Inf. Sci.

Inf. Sci.

Econ. Lett.

Knowl.-Based Syst.

Phys. A

Econ. Model.

Expert Syst. Appl.

Inf. Sci.

Automatica

Math. Comput. Modell.

Physica A

Knowl.-Based Syst.

Fuzzy Sets Syst.

Eur. J. Operational

Int. Rev. Econ. Finance

Finance Res. Lett.

Forecasting risk in the US Dollar exchange rate under volatility shifts

North Am. J. Econ. Finance

Maximum likelihood estimation of the Markov-Switching GARCH model based on a general collapsing procedure

Methodol. Comput. Appl. Probability

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