On the Empirical Importance of Periodicity In the Volatility of Financial Time Series

Mazur, Błażej; Pipień, Mateusz

doi:10.2139/ssrn.2163509

Cited by 14 publications

(15 citation statements)

References 31 publications

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“…A common approach to non-stationary volatility is to decompose σ 2 t multiplicatively, see (amongst other) Van Bellegem and Von Sachs (2004), Engle and Rangel (2008), Mazur and Pipien (2012), and Terasvirta (2014a, 2014b). This means…”

Section: Non-stationary Modelsmentioning

confidence: 99%

The log-GARCH model via ARMA representations

Sucarrat¹

2019

Financial Mathematics, Volatility and Covariance Modelling

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The log-GARCH model provides a flexible framework for the modelling of economic uncertainty, financial volatility and other positively valued variables. Its exponential specification ensures fitted volatilities are positive, allows for flexible dynamics, simplifies inference when parameters are equal to zero under the null, and the logtransform makes the model robust to jumps or outliers. An additional advantage is that the model admits ARMA-like representations. This means log-GARCH models can readily be estimated by means of widely available software, and enables a vast range of well-known time-series results and methods. This chapter provides an overview of the log-GARCH model and its ARMA representation(s), and of how estimation can be implemented in practice. After the introduction, we delineate the univariate log-GARCH model with volatility asymmetry ("leverage"), and show how its (nonlinear) ARMA representation is obtained. Next, stationary covariates ("X") are added, before a first-order specification with asymmetry is illustrated empirically. Then we turn our attention to multivariate log-GARCH-X models. We start by presenting the multivariate specification in its general form, but quickly turn our focus to specifications that can be estimated equation-by-equation-even in the presence of Dynamic Conditional Correlations (DCCs) of unknown form. Next, a multivariate non-stationary log-GARCH-X model is formulated, in which the X-covariates can be both stationary and/or nonstationary. A common critique directed towards the log-GARCH model is that its ARCH terms may not exist in the presence of inliers. An own Section is devoted to how this can be handled in practice. Next, the generalisation of log-GARCH models to logarithmic Multiplicative Error Models (MEMs) is made explicit. Finally, the chapter concludes.

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Section: Non-stationary Modelsmentioning

confidence: 99%

The log-GARCH model via ARMA representations

Sucarrat¹

2019

Financial Mathematics, Volatility and Covariance Modelling

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“…More precisely, the model is capable of accommodating systematic changes in the amplitude of the volatility clusters that cannot be explained by a constantparameter GARCH model. Recently, Mazur and Pipien (2012) show that financial market data often exhibit volatility clustering and cyclical behavior, where time series show periods of high volatility and periods of low volatility.…”

Section: Linearmentioning

confidence: 99%

Exchange volatility and export performance in Egypt: New insights from wavelet decomposition and optimal GARCH model

Bouoiyour

Selmi

2014

The Journal of International Trade & Economic Development

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This paper assesses the link between exchange volatility and exports in Egypt by combining wavelet analysis with an optimal GARCH model chosen among various extensions. The observed outcomes reveal that this relationship is complex and depends then widely to frequency-to-frequency variation and slightly to leverage effect and to switching regime. Indeed, it is well shown that at the low frequency, the coefficient associated to exchange rate volatility's effect on trade performance is more intense than that at the high frequency and conversely when subtracting energy share from the total of exports. We attribute the apparently conflicting results to the financial speculation, the composition of trade partners and the choice of a reference basket's currencies.

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“…The nonstationary component is typically a deterministic function of time, whereas the stationary component follows a GARCH process; see van Bellegem and von Sachs (2004), Feng (2004), Engle and Rangel (2008) and Teräsvirta (2008, 2013). For a similar approach see also Brownlees and Gallo (2010), Mazur and Pipień (2012), and Osiewalski and Pajor (2009). Mishra, Su and Ullah (2010) suggested yet another, completely stochastic, decomposition in which the second component is a slow-moving one.…”

Section: Introductionmentioning

confidence: 97%