Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models

Paul Beaumont and Aaron Smallwood

MPRA Paper from University Library of Munich, Germany

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.

Keywords: k-factor Gegenbauer processes; Asymptotic distributions; ARFIMA; Conditional sum of squares (search for similar items in EconPapers)
JEL-codes: C22 C40 C5 C58 G1 G12 (search for similar items in EconPapers)
Date: 2019-09-29
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:96314

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