Demographic Modelling of Human Population Growth

This work presents models and methods that have been used in producing forecasts of population growth. The work is intended to emphasize the reliability bounds of the model forecasts. Leslie model and various versions of logistic population models are presented. References to literature and several studies are given. A lot of relevant methodology has been developed in biological sciences. The Leslie modelling approach involves the use of current trends in mortality,fertility, migration and emigration. The model treats population divided in age groups and the model is given as a recursive system. Other group of models is based on straightforward extrapolation of census data. Trajectories of simple exponential growth function and logistic models are used to produce the forecast. The work presents the basics of Leslie type modelling and the logistic models, including multi- parameter logistic functions. The latter model is also analysed from model reliability point of view. Bayesian approach and MCMC method are used to create error bounds of the model predictions.

Factors Affecting the Forecasting Accuracy of Diffusion Models

Tutkielman tavoitteena oli tarkastella innovaatioiden leviämismallien ennustetarkkuuteen vaikuttavia tekijöitä. Tutkielmassa ennustettiin logistisella mallilla matkapuhelinliittymien leviämistä kolmessa Euroopan maassa: Suomessa, Ranskassa ja Kreikassa. Teoriaosa keskittyi innovaatioiden leviämisen ennustamiseen leviämismallien avulla. Erityisesti painotettiin mallien ennustuskykyä ja niiden käytettävyyttä eri tilanteissa. Empiirisessä osassa keskityttiin ennustamiseen logistisella leviämismallilla, joka kalibroitiin eri tavoin koostetuilla aikasarjoilla. Näin tehtyjä ennusteita tarkasteltiin tiedon kokoamistasojen vaikutusten selvittämiseksi. Tutkimusasetelma oli empiirinen, mikä sisälsi logistisen leviämismallin ennustetarkkuuden tutkimista otosdatan kokoamistasoa muunnellen. Leviämismalliin syötettävä data voidaan kerätä kuukausittain ja operaattorikohtaisesti vaikuttamatta ennustetarkkuuteen. Dataan on sisällytettävä leviämiskäyrän käännöskohta, eli pitkän aikavälin huippukysyntäpiste.

Determinants of credit risk in secured loans – Evidence from the auto loan industry

The purpose of this study is to examine attributes which have explanation power to the probability of default or serious overdue in secured auto loans. Another goal is to find out differences between defaulted loans and loans which have had payment difficulties but survived without defaulting. 19 independent variables used in this study reflect information available at the time of credit decision. These variables were tested with logistic regression and backward elimination procedure. The data includes 8931 auto loans from a Finnish finance company. 1118 of the contracts were taken by company customers and 7813 by private customers. 130 of the loans defaulted and 584 had serious payment problems but did not default. The maturities of those loans were from one month to 60 months and they have ended during year 2011. The LTV (loan-to-value) variable was ranked as the most significant explainer because of its strong positive relationship with probability of payment difficulties. Another important explainer in this study was the credit rating variable which got a negative relationship with payment problems. Also maturity and car age performed well having both a positive relationship with the probability of payment problems. When compared default and serious overdue situations, the most significant differences were found in the roles of LTV, Maturity and Gender variables.

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.