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Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance

Todd Prono ()

No 2016-083, Finance and Economics Discussion Series from Board of Governors of the Federal Reserve System (US)

Abstract: Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation to sizably outperform quasi maximum likelihood estimation in (relatively) small samples. This outperformance is most pronounced when returns are heavily skewed.

Keywords: ARCH; Closed form; Heavy tails; Instrumental variables; Regular variation; Two stage least squares (search for similar items in EconPapers)
JEL-codes: C13 C22 C58 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2016-10, Revised 2017-07
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fedgfe:2016-83

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DOI: 10.17016/FEDS.2016.083r1

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