Trajectory prediction uncertainty modelling for Air Traffic Management

The anticipated growth of air traffic worldwide requires enhanced Air Traffic Management (ATM) technologies and procedures to increase the system capacity, efficiency, and resilience, while reducing environmental impact and maintaining operational safety. To deal with these challenges, new automation and information exchange capabilities are being developed through different modernisation initiatives toward a new global operational concept called Trajectory Based Operations (TBO), in which aircraft trajectory information becomes the cornerstone of advanced ATM applications. This transformation will lead to higher levels of system complexity requiring enhanced Decision Support Tools (DST) to aid humans in the decision making processes. These will rely on accurate predicted aircraft trajectories, provided by advanced Trajectory Predictors (TP). The trajectory prediction process is subject to stochastic effects that introduce uncertainty into the predictions. Regardless of the assumptions that define the aircraft motion model underpinning the TP, deviations between predicted and actual trajectories are unavoidable. This thesis proposes an innovative method to characterise the uncertainty associated with a trajectory prediction based on the mathematical theory of Polynomial Chaos Expansions (PCE). Assuming univariate PCEs of the trajectory prediction inputs, the method describes how to generate multivariate PCEs of the prediction outputs that quantify their associated uncertainty. Arbitrary PCE (aPCE) was chosen because it allows a higher degree of flexibility to model input uncertainty. The obtained polynomial description can be used in subsequent prediction sensitivity analyses thanks to the relationship between polynomial coefficients and Sobol indices. The Sobol indices enable ranking the input parameters according to their influence on trajectory prediction uncertainty. The applicability of the aPCE-based uncertainty quantification detailed herein is analysed through a study case. This study case represents a typical aircraft trajectory prediction problem in ATM, in which uncertain parameters regarding aircraft performance, aircraft intent description, weather forecast, and initial conditions are considered simultaneously. Numerical results are compared to those obtained from a Monte Carlo simulation, demonstrating the advantages of the proposed method. The thesis includes two examples of DSTs (Demand and Capacity Balancing tool, and Arrival Manager) to illustrate the potential benefits of exploiting the proposed uncertainty quantification method.

Forecasting exchange rates in the presence of instabilities

Many exchange rate papers articulate the view that instabilities constitute a major impediment to exchange rate predictability. In this thesis we implement Bayesian and other techniques to account for such instabilities, and examine some of the main obstacles to exchange rate models' predictive ability. We first consider in Chapter 2 a time-varying parameter model in which fluctuations in exchange rates are related to short-term nominal interest rates ensuing from monetary policy rules, such as Taylor rules. Unlike the existing exchange rate studies, the parameters of our Taylor rules are allowed to change over time, in light of the widespread evidence of shifts in fundamentals - for example in the aftermath of the Global Financial Crisis. Focusing on quarterly data frequency from the crisis, we detect forecast improvements upon a random walk (RW) benchmark for at least half, and for as many as seven out of 10, of the currencies considered. Results are stronger when we allow the time-varying parameters of the Taylor rules to differ between countries. In Chapter 3 we look closely at the role of time-variation in parameters and other sources of uncertainty in hindering exchange rate models' predictive power. We apply a Bayesian setup that incorporates the notion that the relevant set of exchange rate determinants and their corresponding coefficients, change over time. Using statistical and economic measures of performance, we first find that predictive models which allow for sudden, rather than smooth, changes in the coefficients yield significant forecast improvements and economic gains at horizons beyond 1-month. At shorter horizons, however, our methods fail to forecast better than the RW. And we identify uncertainty in coefficients' estimation and uncertainty about the precise degree of coefficients variability to incorporate in the models, as the main factors obstructing predictive ability. Chapter 4 focus on the problem of the time-varying predictive ability of economic fundamentals for exchange rates. It uses bootstrap-based methods to uncover the time-specific conditioning information for predicting fluctuations in exchange rates. Employing several metrics for statistical and economic evaluation of forecasting performance, we find that our approach based on pre-selecting and validating fundamentals across bootstrap replications generates more accurate forecasts than the RW. The approach, known as bumping, robustly reveals parsimonious models with out-of-sample predictive power at 1-month horizon; and outperforms alternative methods, including Bayesian, bagging, and standard forecast combinations. Chapter 5 exploits the predictive content of daily commodity prices for monthly commodity-currency exchange rates. It builds on the idea that the effect of daily commodity price fluctuations on commodity currencies is short-lived, and therefore harder to pin down at low frequencies. Using MIxed DAta Sampling (MIDAS) models, and Bayesian estimation methods to account for time-variation in predictive ability, the chapter demonstrates the usefulness of suitably exploiting such short-lived effects in improving exchange rate forecasts. It further shows that the usual low-frequency predictors, such as money supplies and interest rates differentials, typically receive little support from the data at monthly frequency, whereas MIDAS models featuring daily commodity prices are highly likely. The chapter also introduces the random walk Metropolis-Hastings technique as a new tool to estimate MIDAS regressions.