Least squares estimation for GARCH (1,1) model with heavy tailed errors

Arie Preminger () and Giuseppe Storti

No 2017015, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: GARCH (1,1) models are widely used for modelling processes with time varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least squares approach to the estimation of GARCH(1,1) models. Within this approach the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this di culty, we propose two alternative two-stage least squares estimators (LSE) and derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of √n for our estimators. Their finite sample properties are assessed by means of an extensive simulation study

Keywords: GARCH (1; 1); least squares estimation; heavy tails; consistency; asymptotic normality; two-step esti-mator (search for similar items in EconPapers)
JEL-codes: C12 C13 C15 C22 C53 C58 (search for similar items in EconPapers)
Date: 2017-04-21
New Economics Papers: this item is included in nep-ets and nep-ore
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Working Paper: Least squares estimation for GARCH (1,1) model with heavy tailed errors (2014)
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