Time series analysis : Gap filling and feature recognition

Time series are very common in many fields of science as well as in, for example, economics. Nowadays time series are a more common way of expressing data because of the wide range of sensors and equipments collecting ordered data, such as stock prices and wind speed. Desire for a time series analysis usually rises from a wish to both understand a time-related data and interpolate missing values. In this research we had two different time series and two different aims for the analyze. The first goal was to analyze one-dimensional time series of temperature measurements and try to fill in a self-created gap in the time series. Missing values are commonly present in a real life measurement data, often caused by a failure of a measurement device or a simple human error. The missing values are problematic when analyzing time series: some of the common analyzing methods are not applicable to a data containing gaps and even a small, unfilled gap reduces the reliability of the observation analysis such as future value predictions. The second aim was to work with a selection of satellite image data. These satellite images were all taken from the same location and together they formed a two-dimensional time series. The goal was to analyze the time series of images, aiming to find some common features between different land types and by using these features divide the image pixels into five different clusters, depending on the land types the pixels were representing. The motivation behind such analysis was to test feature recognition possibilities for the recently collected satellite image data, which was measured using the synthetic aperture radar imaging. The data was provided by the Electric Brain project. For analyzing the time series we used techniques based on Fourier analysis, wavelet analysis, cross-correlation and k-means clustering algorithm. As the results presented in the chapter 3 present, the gap filling for the one-dimensional temperature data was performed successfully with two different approaches based on Fourier and wavelet analysis. Especially the wavelet analysis approach performed a very good reconstruction for a missing year of temperatures using data from two to five surrounding years. The results of the feature recognition of the two-dimensional satellite image data were not as successful and results did not offer a good land type based separation of the pixels.