Methods for Time Series Analysis

Abstract

Natural time series, including hydrologic, climatic and environmental time series, which satisfy the assumptions of homogeneity, randomness, non- periodic, non-persistence and stationarity, seem to be the exception rather than the rule (Rao et al., 2003). In fact, for all water resources studies involving the use of hydrologic time series data, preliminary statistical analyses must always be carried out to confirm whether the hydrologic time series possess all the required assumptions/characteristics (Adeloye and Montaseri, 2002). Nevertheless, most time series analysis is performed using standard methods after relaxing the required conditions one way or another in the hope that the departure from these assumptions is not large enough to affect the analysis results (Rao et al., 2003). A comprehensive survey of the past studies on the hydrologic time series analysis (Machiwal and Jha, 2006) revealed that no studies considered all the aspects of time series analysis. Major work is reported dealing with only linear trend analysis, and the homogeneity, stationarity, periodicity, and persistence, which are equally important characteristics of the hydrologic time series, have been ignored. In most past studies on time series analysis, only regression and/or Kendall's rank correlation tests are applied for trend detection. Esterby (1996) and Hess et al. (2001) presented an overview of selected trend tests. Thus, very limited studies are reported to date concerning a detailed analysis of homogeneity, stationarity, periodicity and persistence in the hydrologic time series.