Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time, by proposing a deterministic time variation of its loadings. In this respect we generalise existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a "double-asymptotic" framework of both cross-section and time dimension tending to infinity. A simulation study illustrates the performance of our estimators.econometrics;

Modelling discrepancy in Bayesian calibration of reservoir models

Simulation models of physical systems such as oil field reservoirs are subject to numerous uncertainties such as observation errors and inaccurate initial and boundary conditions. However, after accounting for these uncertainties, it is usually observed that the mismatch between the simulator output and the observations remains and the model is still inadequate. This incapability of computer models to reproduce the real-life processes is referred to as model inadequacy. This thesis presents a comprehensive framework for modelling discrepancy in the Bayesian calibration and probabilistic forecasting of reservoir models. The framework efficiently implements data-driven approaches to handle uncertainty caused by ignoring the modelling discrepancy in reservoir predictions using two major hierarchical strategies, parametric and non-parametric hierarchical models. The central focus of this thesis is on an appropriate way of modelling discrepancy and the importance of the model selection in controlling overfitting rather than different solutions to different noise models. The thesis employs a model selection code to obtain the best candidate solutions to the form of non-parametric error models. This enables us to, first, interpolate the error in history period and, second, propagate it towards unseen data (i.e. error generalisation). The error models constructed by inferring parameters of selected models can predict the response variable (e.g. oil rate) at any point in input space (e.g. time) with corresponding generalisation uncertainty. In the real field applications, the error models reliably track down the uncertainty regardless of the type of the sampling method and achieve a better model prediction score compared to the models that ignore discrepancy. All the case studies confirm the enhancement of field variables prediction when the discrepancy is modelled. As for the model parameters, hierarchical error models render less global bias concerning the reference case. However, in the considered case studies, the evidence for better prediction of each of the model parameters by error modelling is inconclusive

Event-Triggered Time-Varying Bayesian Optimization

We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). Here, the key challenge is the exploration-exploitation trade-off under time variations. Current approaches to TVBO require prior knowledge of a constant rate of change. However, in practice, the rate of change is usually unknown. We propose an event-triggered algorithm, ET-GP-UCB, that treats the optimization problem as static until it detects changes in the objective function online and then resets the dataset. This allows the algorithm to adapt to realized temporal changes without the need for prior knowledge. The event-trigger is based on probabilistic uniform error bounds used in Gaussian process regression. We provide regret bounds for ET-GP-UCB and show in numerical experiments that it outperforms state-of-the-art algorithms on synthetic and real-world data. Furthermore, these results demonstrate that ET-GP-UCB is readily applicable to various settings without tuning hyperparameters

The role of tropical and extra-tropical waves in the Hadley circulation

The tropical overturning circulation is examined in a moist aquaplanet general circulation model forced using a non-interactive sea surface temperature (SST) distribution that varies between a present-day Earth-like profile and one that is globally uniform. A traditional Hadley Cell (HC)-like flow is observed in all experiments along with the poleward transport of heat and angular momentum. In simulations with non-zero SST gradients, latent heat released from organized convection near the equator sets up a deep tropical cell; midlatitude baroclinic Rossby waves flux heat and angular momentum poleward, reinforcing the thermally direct circulation. As the imposed SST gradient is weakened, the HC transitions from a thermally and eddy-driven regime to one that's completely eddy-driven. When the SST is globally uniform, equatorial waves concentrate precipitation in the tropics and facilitate the lower-level convergence necessary for the ascending branch of the HC. Conventional midlatitude Rossby waves become very weak, but upper-level baroclinicity generates waves that cause equatorward transport of heat and poleward transport of momentum. Moreover, these upper-level waves induce a circulation that opposes the time-mean HC, thus highlighting the role of tropical waves in driving a traditional overturning flow for uniform SSTs. In all cases, anomalies associated with the tropical waves closely resemble those that sum to give the upper-level zonal mean divergent outflow. Through their ability to modulate tropical rainfall and the related latent heating, equatorial waves cause considerable hemispheric asymmetry in the HC and impart synoptic and intraseasonal variability to the tropical overturning circulation.Comment: 30 pages, 12 figures, submitted to QJRM

Learning in a changing environment

Multiple cue probability learning studies have typically focused on stationary environments. We present three experiments investigating learning in changing environments. A fine-grained analysis of the learning dynamics shows that participants were responsive to both abrupt and gradual changes in cue-outcome relations. We found no evidence that participants adapted to these types of change in qualitatively different ways. Also, in contrast to earlier claims that these tasks are learned implicitly, participants showed good insight into what they learned. By fitting formal learning models, we investigated whether participants learned global functional relationships or made localized predictions from similar experienced exemplars. Both a local (the Associative Learning Model) and a global learning model (the novel Bayesian Linear Filter) fitted the data of the first two experiments. However, the results of Experiment 3, which was specifically designed to discriminate between local and global learning models, provided more support for global learning models. Finally, we present a novel model to account for the cue competition effects found in previous research and displayed by some of our participants