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Book part
Publication date: 21 October 2019

Miriam Sosa, Edgar Ortiz and Alejandra Cabello

One important characteristic of cryptocurrencies has been their high and erratic volatility. To represent this complicated behavior, recent studies have emphasized the use…

Abstract

One important characteristic of cryptocurrencies has been their high and erratic volatility. To represent this complicated behavior, recent studies have emphasized the use of autoregressive models frequently concluding that generalized autoregressive conditional heteroskedasticity (GARCH) models are the most adequate to overcome the limitations of conventional standard deviation estimates. Some studies have expanded this approach including jumps into the modeling. Following this line of research, and extending previous research, our study analyzes the volatility of Bitcoin employing and comparing some symmetric and asymmetric GARCH model extensions (threshold ARCH (TARCH), exponential GARCH (EGARCH), asymmetric power ARCH (APARCH), component GARCH (CGARCH), and asymmetric component GARCH (ACGARCH)), under two distributions (normal and generalized error). Additionally, because linear GARCH models can produce biased results if the series exhibit structural changes, once the conditional volatility has been modeled, we identify the best fitting GARCH model applying a Markov switching model to test whether Bitcoin volatility evolves according to two different regimes: high volatility and low volatility. The period of study includes daily series from July 16, 2010 (the earliest date available) to January 24, 2019. Findings reveal that EGARCH model under generalized error distribution provides the best fit to model Bitcoin conditional volatility. According to the Markov switching autoregressive (MS-AR) Bitcoin’s conditional volatility displays two regimes: high volatility and low volatility.

Details

Disruptive Innovation in Business and Finance in the Digital World
Type: Book
ISBN: 978-1-78973-381-5

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Book part
Publication date: 29 March 2006

Peter A. Zadrozny

A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m…

Abstract

A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m, eigenvalue restrictions have been proposed as necessary and sufficient restrictions for existence of a unique mth moment of the output of a univariate GARCH process or, equivalently, the 2mth moment of the underlying variable. However, proofs in the literature that an eigenvalue restriction is necessary and sufficient for existence of unique 4th or higher even moments of the underlying variable, are either incorrect, incomplete, or unnecessarily long. Thus, the paper contains a short and general proof that an eigenvalue restriction is necessary and sufficient for existence of a unique 4th moment of the underlying variable of a univariate GARCH process. The paper also derives an expression for computing the 4th moment in terms of the GARCH parameters, which immediately implies a necessary and sufficient inequality restriction for existence of the 4th moment. Because the inequality restriction is easily computed in a finite number of basic arithmetic operations on the GARCH parameters and does not require computing eigenvalues, it provides an easy means for computing “by hand” the 4th moment and for checking its existence for low-dimensional GARCH processes. Finally, the paper illustrates the computations with some GARCH(1,1) processes reported in the literature.

Details

Econometric Analysis of Financial and Economic Time Series
Type: Book
ISBN: 978-0-76231-274-0

Book part
Publication date: 29 February 2008

Eric Hillebrand and Marcelo C. Medeiros

In this chapter, we outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies…

Abstract

In this chapter, we outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies to approach the problem. The first strategy is to identify regimes of constant unconditional volatility using a change point detector and estimate a separate GARCH model on the resulting segments. The second approach is to use a multiple-regime GARCH model, such as the Flexible Coefficient GARCH (FCGARCH) specification, where the regime-switches are governed by an observable variable. We apply both alternatives to an array of financial time series and compare their forecast performance.

Details

Forecasting in the Presence of Structural Breaks and Model Uncertainty
Type: Book
ISBN: 978-1-84950-540-6

Book part
Publication date: 29 February 2008

David E. Rapach, Jack K. Strauss and Mark E. Wohar

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns…

Abstract

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns for the S&P 500 market index and ten sectoral stock indices for 9/12/1989–1/19/2006 using an iterative cumulative sum of squares procedure. We find evidence of multiple variance breaks in almost all of the return series, indicating that structural breaks are an empirically relevant feature of return volatility. We then undertake an out-of-sample forecasting exercise to analyze how instabilities in unconditional variance affect the forecasting performance of asymmetric volatility models, focusing on procedures that employ a variety of estimation window sizes designed to accommodate potential structural breaks. The exercise demonstrates that structural breaks present important challenges to forecasting stock return volatility. We find that averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well in many cases and appears to offer a useful approach to forecasting stock return volatility in the presence of structural breaks.

Details

Forecasting in the Presence of Structural Breaks and Model Uncertainty
Type: Book
ISBN: 978-1-84950-540-6

Book part
Publication date: 30 November 2011

Massimo Guidolin

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of…

Abstract

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

Details

Missing Data Methods: Time-Series Methods and Applications
Type: Book
ISBN: 978-1-78052-526-6

Keywords

Abstract

Details

Modelling the Riskiness in Country Risk Ratings
Type: Book
ISBN: 978-0-44451-837-8

Article
Publication date: 15 August 2018

Samit Paul and Prateek Sharma

This study aims to implement a novel approach of using the Realized generalized autoregressive conditional heteroskedasticity (GARCH) model within the conditional extreme…

Abstract

Purpose

This study aims to implement a novel approach of using the Realized generalized autoregressive conditional heteroskedasticity (GARCH) model within the conditional extreme value theory (EVT) framework to generate quantile forecasts. The Realized GARCH-EVT models are estimated with different realized volatility measures. The forecasting ability of the Realized GARCH-EVT models is compared with that of the standard GARCH-EVT models.

Design/methodology/approach

One-step-ahead forecasts of Value-at-Risk (VaR) and expected shortfall (ES) for five European stock indices, using different two-stage GARCH-EVT models, are generated. The forecasting ability of the standard GARCH-EVT model and the asymmetric exponential GARCH (EGARCH)-EVT model is compared with that of the Realized GARCH-EVT model. Additionally, five realized volatility measures are used to test whether the choice of realized volatility measure affects the forecasting performance of the Realized GARCH-EVT model.

Findings

In terms of the out-of-sample comparisons, the Realized GARCH-EVT models generally outperform the standard GARCH-EVT and EGARCH-EVT models. However, the choice of the realized estimator does not affect the forecasting ability of the Realized GARCH-EVT model.

Originality/value

It is one of the earliest implementations of the two-stage Realized GARCH-EVT model for generating quantile forecasts. To the best of the authors’ knowledge, this is the first study that compares the performance of different realized estimators within Realized GARCH-EVT framework. In the context of high-frequency data-based forecasting studies, a sample period of around 11 years is reasonably large. More importantly, the data set has a cross-sectional dimension with multiple European stock indices, whereas most of the earlier studies are based on the US market.

Details

Studies in Economics and Finance, vol. 35 no. 4
Type: Research Article
ISSN: 1086-7376

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Article
Publication date: 1 October 2006

M. Ghahramani and A. Thavaneswaran

Financial returns are often modeled as stationary time series with innovations having heteroscedastic conditional variances. This paper seeks to derive the kurtosis of…

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Abstract

Purpose

Financial returns are often modeled as stationary time series with innovations having heteroscedastic conditional variances. This paper seeks to derive the kurtosis of stationary processes with GARCH errors. The problem of hypothesis testing for stationary ARMA(p, q) processes with GARCH errors is studied. Forecasting of ARMA(p, q) processes with GARCH errors is also discussed in some detail.

Design/methodology/approach

Estimating‐function methodology was the principal method used for the research. The results were also illustrated using examples and simulation studies. Volatility modeling is the subject of the paper.

Findings

The kurtosis of stationary processes with GARCH errors is derived in terms of the model parameters (ψ), Ψ‐weights, and the kurtosis of the innovation process. Hypothesis testing for stationary ARMA(p, q) processes with GARCH errors based on the estimating‐function approach is shown to be superior to the least‐squares approach. The fourth moment of the l‐steps‐ahead forecast error is related to the model parameters and the kurtosis of the innovation process.

Originality/value

This paper will be of value to econometricians and to anyone with an interest in the statistical properties of volatility modeling.

Details

The Journal of Risk Finance, vol. 7 no. 5
Type: Research Article
ISSN: 1526-5943

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Article
Publication date: 31 December 2013

Laila Arjuman Ara and Mohammad Masudur Rahman

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t…

Abstract

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

Details

Journal of International Logistics and Trade, vol. 11 no. 3
Type: Research Article
ISSN: 1738-2122

Keywords

Article
Publication date: 13 November 2018

Rangga Handika and Dony Abdul Chalid

This paper aims to investigate whether the best statistical model also corresponds to the best empirical performance in the volatility modeling of financialized commodity markets.

Abstract

Purpose

This paper aims to investigate whether the best statistical model also corresponds to the best empirical performance in the volatility modeling of financialized commodity markets.

Design/methodology/approach

The authors use various p and q values in Value-at-Risk (VaR) GARCH(p, q) estimation and perform backtesting at different confidence levels, different out-of-sample periods and different data frequencies for eight financialized commodities.

Findings

They find that the best fitted GARCH(p,q) model tends to generate the best empirical performance for most financialized commodities. Their findings are consistent at different confidence levels and different out-of-sample periods. However, the strong results occur for both daily and weekly returns series. They obtain weak results for the monthly series.

Research limitations/implications

Their research method is limited to the GARCH(p,q) model and the eight discussed financialized commodities.

Practical implications

They conclude that they should continue to rely on the log-likelihood statistical criteria for choosing a GARCH(p,q) model in financialized commodity markets for daily and weekly forecasting horizons.

Social implications

The log-likelihood statistical criterion has strong predictive power in GARCH high-frequency data series (daily and weekly). This finding justifies the importance of using statistical criterion in financial market modeling.

Originality/value

First, this paper investigates whether the best statistical model corresponds to the best empirical performance. Second, this paper provides an indirect test for evaluating the accuracy of volatility modeling by using the VaR approach.

Details

Review of Accounting and Finance, vol. 17 no. 4
Type: Research Article
ISSN: 1475-7702

Keywords

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