Complex sentence: The initial stages in the analysis of a time series may involve plotting values against time to examine homogeneity of the series in various ways: stability across time as opposed to a trend; stability of local fluctuations over time.
Split into simpler sentences: The initial stages in the analysis of a time series may involve plotting values against time to examine homogeneity of the series in various ways. For example, whether or not there is stability across time as opposed to a trend, or if there is stability of local fluctuations over time.