Time series analysis is a part of mathematical statistics representing a useful tool for data elaboration in several areas. It has a lot of interesting applications. A time series is an ordered sequence of observations. We can record daily closing stock prices, weekly interest rates or monthly price indices in business and economics, annual birth or mortality rates in demography, accident rates or unemployment rates in social sciences, EKG and EEG tracings in medicine, annual crop production in agriculture, daily temperature or annual rainfall in meteorology, electric signals in engineering and many other characteristics in different fields of human activity. This book summarizes some results obtained in this field by its author and other scientists. Some models for estimating non-negative time series have been applied to real data sets from hydrology, meteorology and finances. The results received using new methods have been compared with the ones given by standard procedures implemented in various types of statistical and mathematical software.