In this paper we present an econometric framework aimed at obtaining projections of income growth in Europe at the regional level. We account for model uncertainty in terms of the choice of explanatory variables, as well as the nature of the spatial spillovers of output growth and human capital investment. Building on recent advances in Bayesian model averaging, we construct projected trajectories of income and human capital simultaneously, while integrating out the effects of other covariates. This approach allows us to assess the potential contribution of future educational attainment to economic growth and income convergence among European regions over the next decades. Our findings suggest that income convergence dynamics and human capital act as important drivers of income growth for the decades to come. In addition we find that the relative return of improving educational attainment levels in terms of economic growth appears to be higher in peripheral European regions. (authors' abstract) / Series: Department of Economics Working Paper Series

This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging techniques both in terms of in-sample predictive performance and computational efficiency. (authors' abstract) / Series: Department of Economics Working Paper Series

Electricity price forecasting is an important task for electricity market participants since the very beginning of the deregulation. Accurate forecasting is essential for designing bidding strategy, risk management, and market operation. However, due to the compli-cated factors affecting electricity prices, there are more uncertainties in electricity price forecasting and hence more complex than demand forecasting. This makes accurate price forecasting very difficult. In the last decade, several methods have been developed in order to fully capture the peculiarities of electricity price dynamics, from classic econometric time series models, e.g., autoregressive moving average (ARMA) model, generalized autoregressive conditional heteroscedasticity (GARCH) model to modern machine learning based techniques such as artificial neural networks (ANN) and sup-port vector machine (SVM). In spite of all models proposed in the literature, there is still no clear consensus about which model is substantively outperforming others. Therefore, when a single method is used, decision-makers are facing the risk of not choosing the best one. On the other hand, the prediction of electricity market prices still involves large errors. If decision-makers take the prediction result on faith, prediction errors could exposure them to serious financial risks. Based on these findings, it can conclude that (1) systematic methodologies and implementations which can efficiently address model selection uncertainty in price forecasting require an investigation; (2) more powerful and robust price forecasting models are still needed to reduce the fore-cast errors; and (3) In addition, the emphasis of price forecasting should shift away from point forecast to uncertainty around the forecast. Unfortunately, most researches in this area have been devoted to finding the single “best” estimates rather than dealing with the uncertainty in model selection and quantifying the predictive uncertainty. In this thesis the research focus is on: (1) finding methodologies and efficient imple-mentations to deal with the uncertainty in model selection; (2) developing more power-ful machine learning based approaches to model electricity spot prices and further im-proving the accuracy of electricity market price forecast; and (3) incorporating uncer-tainty estimation into the application of price forecasting. The thesis makes three main contributions to the study of this topic. Firstly, it proposes linear, nonlinear forecast combination frameworks to deal with model selection prob-lem; secondly, it introduces two novel models: support vector machine based nonlinear generalized autoregressive conditional heteroscedasticity model (SVM-GARCH) and extreme learning machine (ELM) to the price forecasting and furthermore gives a series of bootstrap-based interval construction procedures to quantify the prediction uncer-tainty. Finally, it proposes a more robust interval forecasting approach which is based on quantile regression to electricity price forecasting literature. The effectiveness and efficiency of the proposed approaches have been tested based on real market data of Australian National Electricity Market (NEM).

Electricity price forecasting is an important task for electricity market participants since the very beginning of the deregulation. Accurate forecasting is essential for designing bidding strategy, risk management, and market operation. However, due to the compli-cated factors affecting electricity prices, there are more uncertainties in electricity price forecasting and hence more complex than demand forecasting. This makes accurate price forecasting very difficult. In the last decade, several methods have been developed in order to fully capture the peculiarities of electricity price dynamics, from classic econometric time series models, e.g., autoregressive moving average (ARMA) model, generalized autoregressive conditional heteroscedasticity (GARCH) model to modern machine learning based techniques such as artificial neural networks (ANN) and sup-port vector machine (SVM). In spite of all models proposed in the literature, there is still no clear consensus about which model is substantively outperforming others. Therefore, when a single method is used, decision-makers are facing the risk of not choosing the best one. On the other hand, the prediction of electricity market prices still involves large errors. If decision-makers take the prediction result on faith, prediction errors could exposure them to serious financial risks. Based on these findings, it can conclude that (1) systematic methodologies and implementations which can efficiently address model selection uncertainty in price forecasting require an investigation; (2) more powerful and robust price forecasting models are still needed to reduce the fore-cast errors; and (3) In addition, the emphasis of price forecasting should shift away from point forecast to uncertainty around the forecast. Unfortunately, most researches in this area have been devoted to finding the single “best” estimates rather than dealing with the uncertainty in model selection and quantifying the predictive uncertainty. In this thesis the research focus is on: (1) finding methodologies and efficient imple-mentations to deal with the uncertainty in model selection; (2) developing more power-ful machine learning based approaches to model electricity spot prices and further im-proving the accuracy of electricity market price forecast; and (3) incorporating uncer-tainty estimation into the application of price forecasting. The thesis makes three main contributions to the study of this topic. Firstly, it proposes linear, nonlinear forecast combination frameworks to deal with model selection prob-lem; secondly, it introduces two novel models: support vector machine based nonlinear generalized autoregressive conditional heteroscedasticity model (SVM-GARCH) and extreme learning machine (ELM) to the price forecasting and furthermore gives a series of bootstrap-based interval construction procedures to quantify the prediction uncer-tainty. Finally, it proposes a more robust interval forecasting approach which is based on quantile regression to electricity price forecasting literature. The effectiveness and efficiency of the proposed approaches have been tested based on real market data of Australian National Electricity Market (NEM).

In this paper we put forward a Bayesian Model Averaging method aimed at performing inference under model uncertainty in the presence of potential spatial autocorrelation. The method uses spatial filtering in order to account for uncertainty in spatial linkages. Our procedure is applied to a dataset of income per capita growth and 50 potential determinants for 255 NUTS-2 European regions. We show that ignoring uncertainty in the type of spatial weight matrix can have an important effect on the estimates of the parameters attached to the model covariates. After integrating out the uncertainty implied by the choice of regressors and spatial links, human capital investments and transitional dynamics related to income convergence appear as the most robust determinants of growth at the regional level in Europe. Our results imply that a quantitatively important part of the income convergence process in Europe is influenced by spatially correlated growth spillovers.

Representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and stochastic parametrisation schemes have been proposed for this purpose. Such schemes have been shown to improve the skill of ensemble forecasts, resulting in a growing use of stochastic parametrisation schemes in numerical weather prediction. However, little research has explicitly tested the ability of stochastic parametrisations to represent model uncertainty, since the presence of other sources of forecast uncertainty has complicated the results. This study seeks to provide firm foundations for the use of stochastic parametrisation schemes as a representation of model uncertainty in numerical weather prediction models. Idealised experiments are carried out in the Lorenz `96 (L96) simplified model of the atmosphere, in which all sources of uncertainty apart from model uncertainty can be removed. Stochastic parametrisations are found to be a skilful way of representing model uncertainty in weather forecasts in this system. Stochastic schemes which have a realistic representation of model error produce reliable forecasts, improving on the deterministic and the more "traditional" perturbed parameter schemes tested. The potential of using stochastic parametrisations for simulating the climate is considered, an area in which there has been little research. A significant improvement is observed when stochastic parametrisation schemes are used to represent model uncertainty in climate simulations in the L96 system. This improvement is particularly pronounced when considering the regime behaviour of the L96 system - the stochastic forecast models are significantly more skilful than using a deterministic perturbed parameter ensemble to represent model uncertainty. The reliability of a model at forecasting the weather is found to be linked to that model's ability to simulate the climate, providing some support for the seamless prediction paradigm. The lessons learned in the L96 system are then used to test and develop stochastic and perturbed parameter representations of model uncertainty for use in an operational numerical weather prediction model, the Integrated Forecasting System (IFS). A particular focus is on improving the representation of model uncertainty in the convection parametrisation scheme. Perturbed parameter schemes are tested, which improve on the operational stochastic scheme in some regards, but are not as skilful as a new generalised version of the stochastic scheme. The proposed stochastic scheme has a potentially more realistic representation of model error than the operational scheme, and improves the reliability of the forecasts. While studying the L96 system, it was found that there is a need for a proper score which is particularly sensitive to forecast reliability. A suitable score is proposed and tested, before being used for verification of the forecasts made in the IFS. This study demonstrates the power of using stochastic over perturbed parameter representations of model uncertainty in weather and climate simulations. It is hoped that these results motivate further research into physically-based stochastic parametrisation schemes, as well as triggering the development of stochastic Earth-system models for probabilistic climate prediction.

This thesis introduces a novel theoretical option pricing ensemble framework to improve the bias and variance of option pricing models, especially those based on Levy Processes. In particular, we present a completely new, yet very general theoretical framework to calibrate and combine several option pricing models using ensemble methods. This framework has four main steps: general option pricing tasks, ensemble generation, ensemble pruning and ensemble integration. The modularity allows for a exible implementation in terms of asset classes, base models, pricing techniques and ensemble architecture.

Combining forecasts have been proven as one of the most successful methods to improve predictive performance. However, while there often is a focus on theoretically optimal methods, this is an ill-posed issue in practice where the problem of robustness is of more empirical relevance. This thesis focuses on the latter issue, where the risk associated with different combination methods is examined. The problem is addressed using Monte Carlo experiments and an application to automated forecasting with data from the M4 competition. Overall, our results indicate that the choice of combining methodology could constitute an important source of risk. While equal weighting of forecasts generally works well in the application, there are also cases where estimating weights improve upon this benchmark. In these cases, many robust and simple alternatives perform the best. While estimating weights can be beneficial, it is important to acknowledge the role of estimation uncertainty as it could outweigh the benefits of combining. For this reason, it could be advantageous to consider methods that effectively acknowledge this source of risk. By doing so, a forecaster can effectively utilize the benefits of combining forecasts while avoiding the risk associated with uncertainty in weights.

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