The amount of carbon dioxide in the Earth’s atmosphere has significantly increased in the last few decades as compared to the last 80,000 years approximately. The increase in carbon dioxide levels are affecting the temperature and therefore need to be understood better. In order to study the effects of global events on the carbon dioxide levels, one need to properly estimate the trends in carbon dioxide in the previous years. In this project, we will perform the task of estimating the trend in carbon dioxide measurements taken in Mauna Loa for the last 46 years, also known as the Keeling Curve, using estimation techniques based on a Taylor and Fourier series model equation. To perform the estimation, we will employ Maximum Likelihood Estimation (MLE) and the Cramér-Rao Lower Bound (CRLB) and review our results by comparing it to other estimation techniques. The estimation of the trend in Keeling Curve is well-posed however, the estimation for the first derivative of the trend is an ill-posed problem. We will further calculate if the estimation error is under a suitable limit and conduct statistical analyses for our estimated results.

The building sector is responsible for around 39% of the energy consumption in Sweden, and one way to work towards sustainable societies could be to make the buildings more energy efficient. One approach to make a building more energy efficient is to use knowledge gained from digitalization of the building and to make the building smart. This thesis aims to study the area of smart buildings, and the ongoing work with smart solutions within the real estate sector.  Two parallel investigations are used to study the area. One is an interview study in order to map the ongoing work with smart buildings. The situation on the market, the matureness of technical solutions as well as ongoing trends and challenges are amongst other things studied. The second investigation consists of a pilot project which aims to exemplify how time series data analysis could be used in order to make a building smarter. Time-series prediction provides a way to discover and quantify regularities in such data, and methods of time series prediction point to how to make building management more efficient.  The result of the study shows that the smart building market is not yet stabilized, but that the interest in working with smart buildings is big. There are many smaller solutions which are being tested and implemented, but there is no consensus of what the definition of a smart building really is. The results of the data analysis indicate two results, firstly, it provides insight in the data, and reports how one should prepare the data for subsequent analysis, and secondly we report results for different autoregressive (AR)-based time series models. For the second result, we indicate how methods of K-means improve over linear AR-based modelling, pointing to the possible use of nonlinear modelling. We however question whether performance improvements are sufficiently large for this application to justify the additional computational demands.