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To infinity and beyond: Efficient computation of ARCH(1) models

Author

Listed:
  • Morten Ørregaard Nielsen

    (Queens University and CREATES)

  • Antoine L. Noël

    (Queens University)

Abstract

This paper provides an exact algorithm for efficient computation of the time series of conditional variances, and hence the likelihood function, of models that have an ARCH(\infty) representation. This class of models includes, e.g., the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen and Nielsen (2014). It takes advantage of the fast Fourier transform (FFT) to achieve an order of magnitude improvement in computational speed. The efficiency of the algorithm allows estimation (and simulation/bootstrapping) of ARCH(\infty) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. In Monte Carlo simulations, we show that the elimination of the truncation of the filter reduces the bias of the quasi-maximum-likelihood estimators and improves out-of-sample forecasting. Our results are illustrated in two empirical examples.

Suggested Citation

  • Morten Ørregaard Nielsen & Antoine L. Noël, 2020. "To infinity and beyond: Efficient computation of ARCH(1) models," CREATES Research Papers 2020-13, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2020-13
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Circular convolution theorem; conditional heteroskedasticity; fast Fourier transform; FIGARCH; truncation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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