Autocopulas: Investigating the Interdependence Structure of Stationary Time Series

Rakonczai, P.; Márkus, László; Zempléni, András

doi:10.1007/s11009-011-9230-2

Cited by 5 publications

(8 citation statements)

References 17 publications

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Section: Autocorrelationmentioning

confidence: 99%

“…In some studies, copulas have been applied to autocorrelated data using so-called serial copulas (Genest and Rémillard, 2004;Ghoudi and Rémillard, 2004) or autocopulas (Rakonczai et al, 2012). But the mathematical procedure to drive these copulas is quite demanding and further uncertainties may emerge (Rakonczai et al, 2012). In contrast, other papers argued that copulas are still applicable in case of only low-degree (removable) auto-correlation in the time series (Laux et al, 2011;Vogl et al, 2012).…”

Section: Autocorrelationmentioning

confidence: 99%

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Copulas for hydroclimatic applications – A practical note on common misconceptions and pitfalls

Tootoonchi

Haerter

Räty

et al. 2020

Preprint

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Abstract. For most hydroclimatic applications, precipitation and temperature are of particular interest as they strongly affect the water cycle, can easily be measured and are often readily available from many meteorological stations worldwide. To account for precipitation and temperature variability, their co-dependence and their correlation, several multivariate analysis methods have been adopted in the hydroclimatic literature in recent years. In line with the steadily rising number of publications on this topic, the notion of copula-based probability distribution has also attracted tremendous interest to deal with the complexity of compound events in the multidimensional context. A copula is a function that connects a multivariate distribution to its one-dimensional margins, which allows for a joint distribution of random variables with great flexibility for the marginal distribution. However, there seems to be a lack of comprehensive understanding of the fundamental requirements of the copula concept such as the strength and significance of correlation between variables, autocorrelation effects and the choice of representative copula families, which potentially compromises the robustness of projections of future environmental processes and natural hazards. Therefore, by combining a systematic literature review with a specific hydroclimatic case study in Sweden, we illustrate a practical approach to copula-based modeling, which (1) provides end-users with an overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) highlights possible pitfalls and misconceptions, and (3) offers a decision support framework for the application of copulas to support researchers and decision makers in addressing climatological hazards and sustainable development, thereby demystifying what is currently an area of great confusion.

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Section: Autocorrelationmentioning

confidence: 99%

Section: Autocorrelationmentioning

confidence: 99%

Copulas for hydroclimatic applications – A practical note on common misconceptions and pitfalls

Tootoonchi

Haerter

Räty

et al. 2020

Preprint

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“…In a time series setting, we use a copula (or autocopula) to capture the dependence structure between successive observations. More generally, we have the following definition (Rakonczai et al [2012]).…”

Section: Copulas and Autocopulasmentioning

confidence: 99%

“…The term 'autocopula' was first used to describe the unit lag self dependence structure of a univariate time series in Rakonczai et al [2012], and we adopt the terminology here. We make use of the framework presented in Darsow et al [1992] to produce Markov processes such that the marginal distribution changes over time.…”

Section: Introductionmentioning

confidence: 99%

Semi-parametric Time Series Modelling with Autocopulas

Ware

Asadzadeh

2016

Mathematical and Computational Approaches in Advancing Modern Science and Engineering

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In this paper we present an application of the use of autocopulas for modelling financial time series showing serial dependencies that are not necessarily linear. The approach presented here is semi-parametric in that it is characterized by a non-parametric autocopula and parametric marginals. One advantage of using autocopulas is that they provide a general representation of the auto-dependency of the time series, in particular making it possible to study the interdependence of values of the series at different extremes separately. The specific time series that is studied here comes from daily cash flows involving the product of daily natural gas price and daily temperature deviations from normal levels. Seasonality is captured by using a time dependent normal inverse Gaussian (NIG) distribution fitted to the raw values.arXiv:1507.04767v1 [q-fin.RM]

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“…Relying on the concept of conditional copulas (Patton, 2006), these copulas allow for a conditional distribution of variables and their dependence to be applied on lagged version of the marginal variables (Größer & Okhrin, 2021). However, the mathematical procedure to obtain these copulas are generally more complex, and further uncertainties may emerge (Rakonczai et al, 2012). For more information and an advanced review of copulas for autocorrelated time series, the reader is referred to Größer and Okhrin (2021), Oh and Patton (2018), and Patton (2006, 2012).…”

Section: Introductionmentioning

confidence: 99%

Copulas for hydroclimatic analysis: A practice‐oriented overview

et al. 2022

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A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula‐based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re‐emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula‐based modeling. Here, we (1) provide end‐users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user‐friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion. This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods

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Autocopulas: Investigating the Interdependence Structure of Stationary Time Series

Cited by 5 publications

References 17 publications

Copulas for hydroclimatic applications – A practical note on common misconceptions and pitfalls

Copulas for hydroclimatic applications – A practical note on common misconceptions and pitfalls

Semi-parametric Time Series Modelling with Autocopulas

Copulas for hydroclimatic analysis: A practice‐oriented overview

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