Essays on the modelling and prediction of financial volatility and trading volumes
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Aim of this thesis is to propose and discuss novel model specifications for predicting financial volatility and trading volumes using intra-daily information. Chapter 1 provides a literature overview on modelling financial volatility and volumes and introduces thè most important contributions and findings of thè thesis. Chapter 2 presents an extension of thè Realized GARCH model by Hansen et al. (2012) along three different directions. First, we allow for heteroskedasticity of thè noise term in thè measurement equation, since it is assumed to be time-varying as a function of an estimator of thè integrated quarticity of intra-daily returns. Second, in order to account for attenuation bias effects, we let thè volatility dynamics to depend on thè accuracy of thè realized measure. This is achieved by leaving thè response coefficient of thè lagged realized measure, to depend on thè time-varying variance of thè volatility measurement error, giving more weight to lagged volatilities when they are more accurately measured. Finally, we account for jumps by introducing in thè measurement equation an additional explanatory variable aimed at quantify thè bias due to thè effect of jumps. Chapter 3 develops a further extension of thè Realized GARCH model of Hansen et al. (2012) for forecasting daily volatility incorporating information from multiple realized volatility measures computed at different sampling frequencies in order to achieve thè optimal trade-off between bias and efficiency. Namely, future volatility forecasts are determined by a weighted average of thè considered realized measures, where thè weights are time-varying and adaptively determined according to thè estimated amount of noise and jumps. This specification aims to reduce, in an adaptive fashion, bias effects related to thè different sampling frequency at which thè realized measure are computed. Chapter 4 proposes a novel approach for modelling and forecasting high-frequency trading volumes, extending thè logie of thè Component Multiplicative Error Model of Brownlees et al. (2011), by a more flexible specification of thè long-run component, since it is based on a MIDAS polynomial structure through an additive cascade of linear filters adopting heterogeneous components which can take on multiple frequencies, in order to reproduce thè strong persistent autocorrelation structure featuring intra-daily trading volumes. Finally, Appendix A presents an empirical application on tick-by-tick data filtering and highlights thè main features and issues surrounding ultra high-frequency datasets.