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Title: A free-knot spline-GARCH model Authors:  Oliver Old - FernUniversität in Hagen (Germany) [presenting]
Abstract: Global estimation of parameters in GARCH models could easily lead to the premature conclusion of a nearly integrated volatility process due to a very strong volatility persistence. This could be caused by the erroneous assumption of a constant unconditional variance over the entire sample, in particular for long financial time-series. The assumption of constant unconditional variance is taken into account by volatility models with a multiplicative decomposition of the conditional variance into a short-term and a long-term component. The short-term component is represented by an asymmetric GJR-GARCH model, and the time-varying long-term volatility is modelled by a B-spline function. The location of the knots affects the shape of the spline-function. The main contribution is a free-knot spline smoothing approach. Therefore, knot locations are not given in advance but rather estimated within the optimisation routine with all other parameters. Besides, enhanced mitigation of the volatility persistence, the aim is to test whether forecast accuracy is improved compared to the spline-GARCH model. That would imply a good approximation of the spline-function to the data and a great improvement for modelling time-varying unconditional variance. Therefore, the free-knot spline GARCH model is investigated by a comprehensive simulation study and by the S\&P500 composite index.