Finite-Sample Properties of GARCH Models in the Presence of Time-Varying Unconditional Variance : A Simulation Study

Old, Oliver GND

In this paper, the finite-sample properties of symmetric GARCH and asymmetric GJR-GARCH models in the presence of time-varying long term variance are considered. In particular, the deterministic spline-GARCH model is investigated by Monte-Carlo simulation, where the true parameter values are taken from estimated real equity index data. As a proxy for the behaviour of equity indices of developed countries, the S&P500 Index is estimated with the Quasi-Maximum-Likelihood (QML) method for dierent conditional heteroscedastic models (GARCH, GJR-GARCH, spline-GARCH and spline-GJR-GARCH). The estimated S&P500 parameter values are used to simulate a broad range of 6 dierent time-series lengths {100, 500, 1000, 5000, 10000, 25000} and 4 different numbers of spline knots {1,4,9,14}, combining to a total amount of 60 different model setups. To the best of my knowledge, there exist only a few limited simulation studies that focus on the spline-GARCH model. The main contribution of this paper is therefore to highlight the behaviour of the QML estimates when the long-term variance is implemented by the spline-GARCH model. Beside this, the paper provides a least-square approach to get useful starting values for the numerical estimation routine.

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Old, Oliver: Finite-Sample Properties of GARCH Models in the Presence of Time-Varying Unconditional Variance. A Simulation Study. Hagen 2020. FernUniversität in Hagen.

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