Three essays in semi-parametric modelling of time-varying distribution

During the last century we have been frustrated by the number of economic crises which trigger extreme uncertainty in the global economic system. Economic agents are sensitive to the uncertainty of inflations, as well as to asset values, for survival in such circumstances. Hence, modern finance and monetary economics emphasise that risk modelling of asset values and inflations are key inputs to financial theory and monetary policy. The risk is completely described by the distribution which is verified to be time-varying and non-normal. Although various parametric and non-parametric approaches have been developed to model the time-varying nature and the non-normality, they still suffer from intrinsic limitations. This study proposes the dynamic modelling of the non-parametric distribution (Functional Autoregressive Model (FAR) and Spatial Distribution Analysis) in order to overcome the limitations. Firstly, we apply FAR to the Value-at-Risk analysis. It forecasts an intraday return density function by the functional autoregressive process and calculates a daily Value-at-Risk by the Normal Inverse Gaussian distribution. It reduces economic cost and improves coverage ability in the Value-at-Risk analysis. Secondly, we apply FAR to forecasting the cross-sectional distribution of sectoral inflation rates, which holds the information of the heterogeneous variation across sectors. As a result, it improves the aggregate inflation rate forecasting. Further, the heterogeneous variation is utilised for constructing the uncertainty band of the aggregate inflation forecast, like the fan-chart of the Bank of England. Thirdly, we apply the spatial distribution analysis to rank investment strategies by comparing their time aggregated utilities over the investment horizon. To this end, we use a spatial dominance test. Since a classical stochastic dominance approach considers only the return distribution at the terminal time point of the investment horizon, it cannot properly evaluate the risk, broken out exogenously or endogenously, in the middle of the investment horizon. However, the proposed spatial dominance approach considers completely the interim risk in evaluating alternative investment strategies.