Fundamentals of Time Series Analysis

A time series is a data set whose individual entries are ordered chronologically, that is, let the time series Y be defined as follows  

For a time series, it is possible to compute such statistical properties as mean and standard deviation. However, these values can easily depend on time, that is, different subsets will have completely different means, for example, a growing crystal will initially have a small mean value, which will increase as the crystal grows. Since dealing with changing values can be difficult in many statistical applications, some assumptions are made about the properties of the time series. 

A time series is said to be strictly stationary if the probabilistic behaviour of 

The mean of the time series is constant and independent of time, that is, = 

Unless otherwise specified, references to a stationary signal will imply that we are dealing with the weakly stationary definition. 

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Until recently mathematical methods of time series analysis in the environmental sciences have only been used quite rarely the methods have mostly been applied in economic science. Consequently, the mathematical fundamentals of time series analysis are mainly described in textbooks and papers dealing with statistics and econometrics [FORSTER and RONZ, 1979 COX, 1981 SCHLITTGEN and STREITBERG, 1989 CHATFIELD, 1989 BROCKWELL and DAVIS, 1987 BOX and JENKINS, 1976 FOMBYet al., 1984 METZLER and NICKEL, 1986 PANDIT and WU, 1990], This section explains the basic methods of time series analysis and their applicability in environmental analysis. 

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