System identification, time series analysis and forecasting:The Captain Toolbox handbook.

CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control

Bayesian spatio-temporal modelling for forecasting ground level ozone concentration levels

Accurate, instantaneous and high resolution spatial air-quality information can better inform the public and regulatory agencies of the air pollution levels that could cause adverse health effects. The most direct way to obtain accurate air quality information is from measurements made at surface monitoring stations across a study region of interest. Typically, however, air monitoring sites are sparsely and irregularly spaced over large areas. That is why, it is now very important to develop space-time models for air pollution which can produce accurate spatial predictions and temporal forecasts.This thesis focuses on developing spatio-temporal models for interpolating and forecasting ground level ozone concentration levels over a vast study region in the eastern United States. These models incorporate output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model that can forecast up to 24 hours in advance. However, these forecasts are known to be biased. The models proposed hereare shown to improve upon these forecasts for a two-week study period during August 2005.The forecasting problems in both hourly and daily time units are investigated in detail. A fast method, based on Gaussian models is constructed for instantaneous interpolation and forecasts of hourly data. A more complexdynamic model, requiring the use of Markov chain Monte Carlo (MCMC) techniques, is developed for forecasting daily ozone concentration levels. A set of model validation analyses shows that the prediction maps that are generated by the aforementioned models are more accurate than the maps based solely on the Eta-CMAQ forecast data. A non-Gaussian measurement error model is also considered when forecasting the extreme levels of ozone concentration. All of the methods presented are based on Bayesian methods and MCMC sampling techniques are used in exploring posterior and predictive distributions

Methods in machine learning for probabilistic modelling of environment, with applications in meteorology and geology

Earth scientists increasingly deal with ‘big data’. Where once we may have struggled to obtain a handful of relevant measurements, we now often have data being collected from multiple sources, on the ground, in the air, and from space. These observations are accumulating at a rate that far outpaces our ability to make sense of them using traditional methods with limited scalability (e.g., mental modelling, or trial-and-error improvement of process based models). The revolution in machine learning offers a new paradigm for modelling the environment: rather than focusing on tweaking every aspect of models developed from the top down based largely on prior knowledge, we now have the capability to instead set up more abstract machine learning systems that can ‘do the tweaking for us’ in order to learn models from the bottom up that can be considered optimal in terms of how well they agree with our (rapidly increasing number of) observations of reality, while still being guided by our prior beliefs. In this thesis, with the help of spatial, temporal, and spatio-temporal examples in meteorology and geology, I present methods for probabilistic modelling of environmental variables using machine learning, and explore the considerations involved in developing and adopting these technologies, as well as the potential benefits they stand to bring, which include improved knowledge-acquisition and decision-making. In each application, the common theme is that we would like to learn predictive distributions for the variables of interest that are well-calibrated and as sharp as possible (i.e., to provide answers that are as precise as possible while remaining honest about their uncertainty). Achieving this requires the adoption of statistical approaches, but the volume and complexity of data available mean that scalability is an important factor — we can only realise the value of available data if it can be successfully incorporated into our models.Engineering and Physical Sciences Research Council (EPSRC

A General Framework for Observation Driven Time-Varying Parameter Models

We propose a new class of observation driven time series models that we refer to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled likelihood score. This provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity and single source of error models. In addition, the GAS specification gives rise to a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.dynamic models, time-varying parameters, non-linearity, exponential family, marked point processes, copulas

Forecasting of commercial sales with large scale Gaussian Processes

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.Comment: 1o pages, 5 figure

Modelling cross-dependencies between Spain’s regional tourism markets with an extension of the Gaussian process regression model

This study presents an extension of the Gaussian process regression model for multiple-input multiple-output forecasting. This approach allows modelling the cross-dependencies between a given set of input variables and generating a vectorial prediction. Making use of the existing correlations in international tourism demand to all seventeen regions of Spain, the performance of the proposed model is assessed in a multiple-step-ahead forecasting comparison. The results of the experiment in a multivariate setting show that the Gaussian process regression model significantly improves the forecasting accuracy of a multi-layer perceptron neural network used as a benchmark. The results reveal that incorporating the connections between different markets in the modelling process may prove very useful to refine predictions at a regional level.Peer ReviewedPostprint (author's final draft