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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 of…

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.

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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.

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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 to…

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.

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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 for the…

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.

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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 Markov…

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.

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

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Abstract

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

Book part
Publication date: 21 November 2014

Igor Vaynman and Brendan K. Beare

The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and…

Abstract

The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.

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Essays in Honor of Peter C. B. Phillips
Type: Book
ISBN: 978-1-78441-183-1

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Book part
Publication date: 29 February 2008

Namwon Hyung, Ser-Huang Poon and Clive W.J. Granger

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three…

Abstract

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three short-memory models (i.e., GARCH, GJR and volatility component). Using S&P 500 returns, we find that structural break models produced the best out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR models produced the best short-horizon forecasts and FI models dominated for volatility forecasts of 10 days and beyond. The results suggest that S&P 500 volatility is non-stationary at least in some time periods. Controlling for extreme events (e.g., the 1987 crash) significantly improved forecasting performance.

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

Book part
Publication date: 24 March 2006

Eric Hillebrand

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find…

Abstract

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from generalized auto-regressive conditional heteroskedasticity (GARCH) models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long-memory models for absolute returns appear to be promising.

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Econometric Analysis of Financial and Economic Time Series
Type: Book
ISBN: 978-1-84950-388-4

Book part
Publication date: 19 November 2012

Sabrina Khanniche

Purpose – This chapter aimed to investigate hedge funds market risk. One aims to go further the traditional measures of risk that underestimates it by introducing a more…

Abstract

Purpose – This chapter aimed to investigate hedge funds market risk. One aims to go further the traditional measures of risk that underestimates it by introducing a more appropriate method to hedge funds. One demonstrates that daily hedge fund return distributions are asymmetric and leptokurtic. Furthermore, volatility clustering phenomenon and the existence of ARCH effects demonstrate that hedge funds volatility varies through time. These features suggest the modelisation of their volatility using symmetric (GARCH) and asymmetric (EGARCH and TGARCH) models used to evaluate a 1-day-ahead value at risk (VaR).

Methodology/Approach – The conditional variances were estimated under the assumption that residuals t follow the normal and the student law. The knowledge of the conditional variance was used to forecast 1-day-ahead VaR. The estimations are compared with the Gaussian, the student and the modified VaR. To sum up, 12 VaRs are computed; those based on standard deviation and computed with normal, student and cornish fisher quantile and those based on conditional volatility models (GARCH, TGARCH and EGARCH) computed with the same quantiles.

Findings – The results demonstrate that VaR models based on normal quantile underestimate risk while those based on student and cornish fisher quantiles seem to be more relevant measurements. GARCH-type VaRs are very sensitive to changes in the return process. Back-testing results show that the choice of the model used to forecast volatility has an importance. Indeed, the VaR based on standard deviation is not relevant to measure hedge funds risks as it fails the appropriate tests. On the opposite side, GARCH-, TGARCH- and EGARCH-type VaRs are accurate as they pass most of the time successfully the back-testing tests. But, the quantile used has a more significant impact on the relevance of the VaR models considered. GARCH-type VaR computed with the student and especially cornish fisher quantiles lead to better results, which is consistent with Monteiro (2004) and Pochon and Teïletche (2006).

Originality/Value of chapter – A large set of GARCH-type models are considered to estimate hedge funds volatility leading to numerous evaluation of VaRs. These estimations are very helpful. Indeed, public savings under institutional investors management then delegate to hedge funds are concerned. Therefore, an adequate risk management is required. Another contribution of this chapter is the use of daily data to measure all hedge fund strategies risks.

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Recent Developments in Alternative Finance: Empirical Assessments and Economic Implications
Type: Book
ISBN: 978-1-78190-399-5

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