Regime Switching Models for Electricity Time Series that Capture Fat Tailed Distributions

In the power market, electricity prices play an important role at the economic level. The behavior of a price trend usually known as a structural break may change over time in terms of its mean value, its volatility, or it may change for a period of time before reverting back to its original behavior or switching to another style of behavior, and the latter is typically termed a regime shift or regime switch. Our task in this thesis is to develop an electricity price time series model that captures fat tailed distributions which can explain this behavior and analyze it for better understanding. For NordPool data used, the obtained Markov Regime-Switching model operates on two regimes: regular and non-regular. Three criteria have been considered price difference criterion, capacity/flow difference criterion and spikes in Finland criterion. The suitability of GARCH modeling to simulate multi-regime modeling is also studied.

A comparison of electricity spot prices simulation using ARMA-GARCH and mean-reverting models

The aim of this work is to compare two families of mathematical models for their respective capability to capture the statistical properties of real electricity spot market time series. The first model family is ARMA-GARCH models and the second model family is mean-reverting Ornstein-Uhlenbeck models. These two models have been applied to two price series of Nordic Nord Pool spot market for electricity namely to the System prices and to the DenmarkW prices. The parameters of both models were calibrated from the real time series. After carrying out simulation with optimal models from both families we conclude that neither ARMA-GARCH models, nor conventional mean-reverting Ornstein-Uhlenbeck models, even when calibrated optimally with real electricity spot market price or return series, capture the statistical characteristics of the real series. But in the case of less spiky behavior (System prices), the mean-reverting Ornstein-Uhlenbeck model could be seen to partially succeeded in this task.

The effect of the birth hospital and the time of birth on the outcome of Finnish very preterm infants

The purpose of this study was to evaluate the effect of the birth hospital and the time of birth on mortality and the long-term outcome of Finnish very low birth weight (VLBW) or very low gestational age (VLGA) infants. This study included all Finnish VLBW/VLGA infants born at <32 gestational weeks or with a birth weight of ≤1500g, and controls born full-term and healthy. In the first part of the study, the mortality of VLBW/VLGA infants born in 2000–2003 was studied. The second part of the study consisted of a five-year follow-up of VLBW/VLGA infants born in 2001–2002. The study was performed using data from parental questionnaires and several registers. The one-year mortality rate was 11% for live-born VLBW/VLGA infants, 22% for live-born and stillborn VLBW/VLGA infants, and 0% for the controls. In live-born and in all (including stillbirths) VLBW/VLGA infants, the adjusted mortality was lower among those born in level III hospitals compared with level II hospitals. Mortality rates of live-born VLBW/VLGA infants differed according to the university hospital district where the birth hospital was located, but there were no differences in mortality between the districts when stillborn infants were included. There was a trend towards lower mortality rates in VLBW/VLGA infants born during office hours compared with those born outside office hours (night time, weekends, and public holidays). When stillborn infants were included, this difference according to the time of birth was significant. Among five-year-old VLBW/VLGA children, morbidity, use of health care resources, and problems in behaviour and development were more common in comparison with the controls. The health-related quality of life of the surviving VLBW/VLGA children was good but, statistically, it was significantly lower than among the controls. The median and the mean number of quality-adjusted life-years were 4.6 and 3.6 out of a maximum five years for all VLBW/VLGA children. For the controls, the median was 4.8 and the mean was 4.9. Morbidity rates, the use of health care resources, and the mean quality-adjusted life-years differed for VLBW/VLGA children according to the university hospital district of birth. However, the time of birth, the birth hospital level or university hospital district were not associated with the health-related quality of life, nor with behavioural and developmental scores of the survivors at the age of five years. In conclusion, the decreased mortality in level III hospitals was not gained at the expense of long-term problems. The results indicate that VLBW/VLGA deliveries should be centralized to level III hospitals and the regional differences in the treatment practices should further be clarified. A long-term follow-up on the outcome of VLBW/VLGA infants is important in order to recognize the critical periods of care and to optimise the care. In the future, quality-adjusted life-years can be used as a uniform measure for comparing the effectiveness of care between VLBW/VLGA infants and different patient groups

A Soft Contact Collision Method For Real-Time Simulation of Triangularized Geometries in Multibody Dynamics

When modeling machines in their natural working environment collisions become a very important feature in terms of simulation accuracy. By expanding the simulation to include the operation environment, the need for a general collision model that is able to handle a wide variety of cases has become central in the development of simulation environments. With the addition of the operating environment the challenges for the collision modeling method also change. More simultaneous contacts with more objects occur in more complicated situations. This means that the real-time requirement becomes more difficult to meet. Common problems in current collision modeling methods include for example dependency on the geometry shape or mesh density, calculation need increasing exponentially in respect to the number of contacts, the lack of a proper friction model and failures due to certain configurations like closed kinematic loops. All these problems mean that the current modeling methods will fail in certain situations. A method that would not fail in any situation is not very realistic but improvements can be made over the current methods.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.