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Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

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  • Sbrana, Giacomo
  • Silvestrini, Andrea

Abstract

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of a widely employed class of integrated moving average (IMA) models. We obtain a closed-form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. These results are useful due to the close analogy between the integrated GARCH (1,1) model for conditional volatility and the IMA (1,1) model for squared returns, which share the same autocorrelation function. In this framework, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the aggregate parameter in the portfolio volatility equation from the estimated vector IMA (1,1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying standard univariate methodologies, such as RiskMetrics.

Suggested Citation

  • Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1437-1450.
  • Handle: RePEc:eee:jbfina:v:37:y:2013:i:5:p:1437-1450
    DOI: 10.1016/j.jbankfin.2012.06.015
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    1. repec:oup:jfinec:v:15:y:2017:i:4:p:649-677. is not listed on IDEAS
    2. Ana María Iregui B. & Luis Fernando Melo V. & María Teresa Ramírez G. & Carmen Cecilia Delgado R., 2013. "El efecto de la volatilidad y del desalineamiento de la tasa de cambio real sobre la actividad de las empresas en Colombia," BORRADORES DE ECONOMIA 011106, BANCO DE LA REPÚBLICA.
    3. Sbrana, Giacomo & Silvestrini, Andrea, 2014. "Random switching exponential smoothing and inventory forecasting," International Journal of Production Economics, Elsevier, vol. 156(C), pages 283-294.
    4. Erik Kole & Thijs Markwat & Anne Opschoor & Dick van Dijk, 2017. "Forecasting Value-at-Risk under Temporal and Portfolio Aggregation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(4), pages 649-677.

    More about this item

    Keywords

    Contemporaneous and temporal aggregation; ARIMA; Volatility; Value-at-Risk;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - 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
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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