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Tail Behavior and Dependence Structure in the APARCH Model

Author

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  • Javed Farrukh

    (Örebro School of Business, Örebro University, Örebro, Sweden)

  • Podgórski Krzysztof

    (Örebro School of Business, Örebro University, Örebro, Sweden)

Abstract

The APARCH model attempts to capture asymmetric responses of volatility to positive and negative ‘news shocks’ – the phenomenon known as the leverage effect. Despite its potential, the model’s properties have not yet been fully investigated. While the capacity to account for the leverage is clear from the defining structure, little is known how the effect is quantified in terms of the model’s parameters. The same applies to the quantification of heavy-tailedness and dependence. To fill this void, we study the model in further detail. We study conditions of its existence in different metrics and obtain explicit characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose an extension of the model. Through theoretical results we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data and country indices for dominant European economies.

Suggested Citation

  • Javed Farrukh & Podgórski Krzysztof, 2017. "Tail Behavior and Dependence Structure in the APARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 9(2), pages 1-48, July.
    • Handle: RePEc:bpj:jtsmet:v:9:y:2017:i:2:p:48:n:2
    DOI: 10.1515/jtse-2016-0002
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    References listed on IDEAS

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    More about this item

    Keywords

    time series models; heavy tails; leverage effect; estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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