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

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  • PREMINGER Arie
  • STORTI Giuseppe

    (Universita degli Studi di Salerno)

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

Suggested Citation

  • PREMINGER Arie & STORTI Giuseppe, 2017. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," LIDAM Discussion Papers CORE 2017015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2017015
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    More about this item

    Keywords

    GARCH (1; 1); least squares estimation; heavy tails; consistency; asymptotic normality; two-step esti-mator;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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