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.

Jatkuvatoimisen sellukeittimen säätöjen suorituskyvyn analysointi

Työssä tarkastellaan yleisiä menetelmiä säätöpiirien suorituskyvyn analysointiin ja sovelletaan niitä jatkuvatoimisen sellukeittimen säätöihin. Esitellyt menetelmät tarjoavat keinoja myös huonon säätötuloksen syyn selvittämiseen ja vinkkejä paremman suorituskyvyn saavuttamiseksi. Analyysissä edettiin top-down periaatteen mukaisesti lähtien liikkeelle keittimen tärkeimmästä säädöstä eli kappaluvun säädöstä. Sitten etsittiin tähän vaikuttavia tekijöitä mitatuista suureista. Seuraavaksi arvioitiin tärkeimmäksi katsotun tekijän (hakepinnankorkeus) säädön suorituskyky, jossa havaittiin parannettavaa. Lopuksi hakepinnankorkeuden säädön viritystämuutettiin ja tehtiin identifiointikoe säätörakenteen uudelleen järjestelyä varten.

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.

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.

Future of Newspaper Business Models in Finland

The purpose of this Master’s thesis was to study the business model development in Finnish newspaper industry during the next then years through scenario planning. The objective was to see how will the business models develop amidst the many changes in the industry, what factors are affecting the change, what are the implications of these changes for the players in the industry and how should the Finnish newspaper companies evolve in order to succeed in the future. In this thesis the business model change is studied based on all the elements of business models, as it was discovered that the industry is too often focusing on changes in only few of those elements and a more broader view can provide valuable information for the companies. The results revealed that the industry is affected by many changes during the next ten years. Scenario planning provides a good tool for analyzing this change and for developing valuable options for businesses. After conducting series of interviews and discovering forces affecting the change, four different scenarios were developed centered on the role that newspaper will take and the level at which they are providing the content in the future. These scenarios indicated that there are varieties of options in the way the business models may develop and that companies should start making decisions proactively in order to succeed. As the business model elements are interdepended, changes made in the other elements will affect the whole model, making these decisions about the role and level of content important for the companies. In the future, it is likely that the Finnish newspaper industry will include many different kinds of business models, some of which can be drastically different from the current ones and some of which can still be similar, but take better into account the new kind of media environment.