Improving probabilistic forecasts by using intra-day data: an application to financial and temperature data

The thesis consists of three studies. The first two contribute to financial market risk modelling and the third contributes to the modelling of temperature extremes.
Value at risk (VaR) is a popular measure of market risk. The first study proposes new approximate long-memory VaR models that incorporate intra-day price ranges. These models use lagged intra-day range with the feature of considering different range components calculated over different time horizons. We also investigate the impact of the market overnight return on the VaR forecasts, which has not yet been considered with the range in VaR estimation. Model estimation is performed using linear quantile regression. An empirical analysis is conducted on 18 market indices. In spite of the simplicity of the proposed methods, the empirical results show that they successfully capture the main features of the financial returns and are competitive with established benchmark methods. The empirical results also show that several of the proposed range-based VaR models, utilising both the intra-day range and the overnight returns, are able to outperform generalised autoregressive conditional heteroskedasticity (GARCH) based methods and conditional autoregressive value at risk (CAViaR) models.
The second study contributes to the literature of VaR and expected shortfall (ES) forecasting. To convey information regarding potential exceedances beyond the VaR, ES has been advocated for future regulatory frameworks. However, the estimation of VaR and ES is challenging, as it requires the estimation of the tail behaviour of daily returns. Furthermore, ES is not elicitable, which means it is difficult to estimate and evaluate. In this paper, we take advantage of recent research that shows that VaR and ES are jointly elicitable, and that provides scoring functions for the joint estimation and evaluation of these two risk measures. We consider the use of intra-day data in this context. We focus on the intra-day range, which is the absolute difference between the highest and lowest intra-day log prices. In contrast to intra-day observations, the intra-day low and high are widely available for many financial assets. To alleviate the challenge of modelling extreme risk measures, we propose the use of the intra-day low series. We draw on a theoretical result for Brownian motion to show that a quantile of the daily returns can be estimated as the product of a constant term and a less extreme quantile of the intra-day low returns, which we define as the difference between the lowest log price of the day and the log closing price of the previous day. In view of this, we use estimates of the VaR and ES of the intra-day low returns to estimate the VaR and ES of the daily returns. We provide empirical support for the new proposals using daily stock index data.
The third study contributes to extreme temperature forecasting, which is related to environmental risk. Understanding changes in the frequency, severity and seasonality of daily temperature extremes is important for public policy decisions regarding heat waves and cold snaps. Temperature forecasts are needed to trigger warnings, and to enable adequate preparation of public services. The uncertainty in the weather implies that forecasting daily temperature is inherently a probabilistic forecasting problem. Autoregressive moving average and GARCH (ARMA-GARCH) models have been applied to daily temperature time series to produce density forecasts. However, a heat wave is sometimes defined in terms of both the daily minimum and maximum temperature, which necessitates the generation of forecasts of the joint distribution of these two variables. We consider the modelling of the daily minimum and maximum temperature using a bivariate vector ARMA and multivariate GARCH (VARMA-MGARCH) model, with conditional dependency modelled using a dynamic copula. A useful by-product is the implicit modelling of the daily average and the diurnal temperature range, which has been used as an index of climate change. Using Spanish data recorded over a 65-year period, we find that a bivariate VARMA-MGARCH model is able to outperform univariate models in terms of the forecast accuracy of both the marginal and joint distributions.

Advisor: Taylor, J