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A Hybrid Metaheuristic for the Efficient Solution of GARCH with Trend Models

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  • Lourdes Uribe
  • Benjamin Perea
  • Gerardo Hernández-del-Valle

    (Banco de México)

  • Oliver Schütze

Abstract

GARCH with trend models represent an efficient tool for the analysis of different commodities via testing for a linear trend in the volatilities. However, to obtain the volatility of a given time series an instance from a particular class of scalar optimization problems (SOPs) has to be solved which still represents a challenge for existing solvers. We propose here a novel algorithm for the efficient numerical solution of such global optimization problems. The algorithm, DE–N, is a hybrid of Differential Evolution and the Newton method. The latter is widely used for the treatment of GARCH related models, but cannot be used as standalone algorithm in this case as the SOPs contain many local minima. The algorithm is tested and compared to some state-of-the-art methods on a benchmark suite consisting of 42 monthtly agricultural commodities series of the Mexican Consumer Price Index basket as well as on two series related to international prices. The results indicate that DE–N is highly competitive and that it is able to reliably solve SOPs derived from GARCH with trend models.

Suggested Citation

  • Lourdes Uribe & Benjamin Perea & Gerardo Hernández-del-Valle & Oliver Schütze, 2018. "A Hybrid Metaheuristic for the Efficient Solution of GARCH with Trend Models," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 145-166, June.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9666-8
    DOI: 10.1007/s10614-017-9666-8
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