Random Models in Space and Time
Statistical Methods for Economic, Engineering, and Environmental Data
The spatio-temporal stochastic modelling group works with development and application of models for spatio-temporal data. The main themes are computational and theoretical aspects of the models, along with applications to data. The group's theoretical work includes random fields based on stochastic partial differential equations, non-Gaussian random fields.
- Asymmetric and heavy tailed second order models - general theory and statistics methods
- Statistical distributions at level crossing contours for random fields
- Dynamically evolving spatial random fields for modeling environmental data
- Non-Gaussian models in mechanical engineering
- Non-linear stochastic modelling in economics and finance - non-linear model building and statistical inference
- Bayesian Statistics
- Big Data Analytics
- Data Mining and Visualization Techniques
Examples of applications
A model of significant wave height for reliability assessment of a ship
Significant wave heights are modeled by means of a spatial–temporal random Gaussian field. Its dependent structure can be localized by introduction of time and space dependent parameters in the spectrum. The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed significant wave height records. The fitted spatial–temporal significant wave field allows for prediction of fatigue accumulation in ship details and of extreme responses encountered. The method is exemplified by analyzing a container ship data relevant for North Atlantic trade and the results show a high agreement with actual on-board measurements.
Leverage effect for volatility with generalized Laplace errors
We propose a new model that accounts for the asymmetric response of volatility to positive ('good news') and negative ('bad news') shocks in economic time series – the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape parameter, that is used instead of power to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including an explicit form for the conditional distribution of 'bad' and 'good' news processes given the past – the property that can be utilized in statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.