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.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Analysis of Patterns in Electricity Spot Market Time Series

Due to its non-storability, electricity must be produced at the same time that it is consumed, as a result prices are determined on an hourly basis and thus analysis becomes more challenging. Moreover, the seasonal fluctuations in demand and supply lead to a seasonal behavior of electricity spot prices. The purpose of this thesis is to seek and remove all causal effects from electricity spot prices and remain with pure prices for modeling purposes. To achieve this we use Qlucore Omics Explorer (QOE) for the visualization and the exploration of the data set and Time Series Decomposition method to estimate and extract the deterministic components from the series. To obtain the target series we use regression based on the background variables (water reservoir and temperature). The result obtained is three price series (for Sweden, Norway and System prices) with no apparent pattern.

Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Geometrically accurate time series of archived aerial images and airborne lidar data in a forest environment

Abstract

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

The time series convergence of dispersion in financial analysts' forecasts

Finansanalytiker har en stor betydelse för finansmarknaderna, speciellt igenom att förmedla information genom resultatprognoser. Typiskt är att analytiker i viss grad är oeniga i sina resultatprognoser, och det är just denna oenighet analytiker emellan som denna avhandling studerar. Då ett företag rapporterar förluster tenderar oenigheten gällande ett företags framtid att öka. På ett intuitivt plan är det lätt att tolka detta som ökad osäkerhet. Det är även detta man finner då man studerar analytikerrapporter - analytiker ser ut att bli mer osäkra då företag börjar gå med förlust, och det är precis då som även oenigheten mellan analytikerna ökar. De matematisk-teoretiska modeller som beskriver analytikers beslutsprocesser har däremot en motsatt konsekvens - en ökad oenighet analytiker emellan kan endast uppkomma ifall analytikerna blir säkrare på ett individuellt plan, där den drivande kraften är asymmetrisk information. Denna avhandling löser motsägelsen mellan ökad säkerhet/osäkerhet som drivkraft bakom spridningen i analytikerprognoser. Genom att beakta mängden publik information som blir tillgänglig via resultatrapporter är det inte möjligt för modellerna för analytikers beslutsprocesser att ge upphov till de nivåer av prognosspridning som kan observeras i data. Slutsatsen blir därmed att de underliggande teoretiska modellerna för prognosspridning är delvis bristande och att spridning i prognoser istället mer troligt följer av en ökad osäkerhet bland analytikerna, i enlighet med vad analytiker de facto nämner i sina rapporter. Resultaten är viktiga eftersom en förståelse av osäkerhet runt t.ex. resultatrapportering bidrar till en allmän förståelse för resultatrapporteringsmiljön som i sin tur är av ytterst stor betydelse för prisbildning på finansmarknader. Vidare används typiskt ökad prognosspridning som en indikation på ökad informationsasymmetri i redovisningsforskning, ett fenomen som denna avhandling därmed ifrågasätter.

Hydrologisen tilanteen ja tuulivoimatuotannon muutosten vaikutus vesiarvoihin pohjoismaisilla sähkön spot-markkinoilla

Vesivoimalla on merkittävä rooli pohjoismaisessa sähköntuotantojärjestelmässä. Spot-markkinoille tarjottavan vesivoiman hinta riippuu vaihtoehtoisen tuotannon hinnasta ja odotetusta vesivoimantuottajien käytettävissä olevasta veteen sitoutuneen potentiaalienergian määrästä. Hydrologisella tilanteella tarkoitetaan tässä tämän potentiaalienergian poikkeamaa normaalitasostaan. Viime vuosina tuulivoimatuotanto pohjoismaisella sähkömarkkina-alueella on kasvanut voimakkaasti, ja on tullut aiheelliseksi tarkastella, millaisia vaikutuksia tällä on vesivoimantuottajien toimintaan. Työssä määritellään vesivoimalle vaihtoehtoisen sähköntuotannon tuotantokustannus, joka pitkällä aikavälillä toimii vertailutasona, jonka perusteella vesivoimantuottajat määrittävät markkinoilla tarjontahinnan tuotannolleen. Tarkastellaan, kuinka hydrologisen tilanteen ja vaihtoehtoisen tuotannon tuotantokustannusten muutokset vaikuttavat vesiarvoon, joka on hinta, jolla hintariippuvaista eli säätyvää vesivoimaa tarjotaan spot-markkinoille. Todetaan, että hydrologisen tilanteen vahvistuminen ja vaihtoehtoisen tuotantokustannuksen aleneminen alentavat vesiarvoja. Todetaan lisäksi, että tuulivoima vaikuttaa sähkön hinnanmuodostukseen markkinoilla samankaltaisesti kuin hintariippumaton vesivoimatuotanto. Esitetään aikasarjamalli vesivoimatuotannon hintariippuvuuden mallintamiseksi. Vertaillaan vesivoimatuottajien toimintaa kahdella vesivoimatuotantoa sisältävällä hinta-alueella, joista toisella tuulivoimatuotanto on kasvanut voimakkaammin kuin toisella. Havaitaan, että molemmilla hinta-alueilla hydrologisen tilanteen vahvistuminen on alentanut ja heikkeneminen nostanut vesiarvoja. Lisäksi havaitaan, että alueella, jonka tuulivoimatuotanto on kasvanut enemmän, vesiarvot ovat laskeneet suhteessa alueen, jolla tuulivoimatuotanto on kasvanut vähemmän, vesiarvoihin. Tuulivoiman voidaan todeta syrjäyttäneen markkinoilta tuotantokustannuksiltaan kalliimpaa tuotantoa.