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Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models

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  • Beaumont, Paul
  • Smallwood, Aaron

Abstract

We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model parameters. The parameters that determine the cycle lengths are asymptotically independent, converging at rate T for finite cycles. This result does not hold generally, most notably for the differencing parameters associated with the cycle lengths. Remaining parameters are typically not independent and converge at the standard rate of T1/2. We present simulation results to explore small sample properties of the estimator, which strongly support most distributional results while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume.

Suggested Citation

  • Beaumont, Paul & Smallwood, Aaron, 2019. "Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models," MPRA Paper 96314, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:96314
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    References listed on IDEAS

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    1. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.

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    More about this item

    Keywords

    k-factor Gegenbauer processes; Asymptotic distributions; ARFIMA; Conditional sum of squares;
    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
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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