Current Status of Time Series Analysis in Hydrological Sciences - Hydrologic Time Series Analysis: Theory and Practice - page 98

Tsakalias and Koutsoyiannis (1999) developed a new approach for the
computer-aided exploration and analysis of hydrologic time series with a
focus on identification of multiple stage-discharge relationships in a river
section, analyses for homogeneity and temporal consistency, detection of
outliers, shifts and trends. To demonstrate the developed methodology, initially
a mathematical representation was proposed based on the set theory. It was
demonstrated that an exhaustive search of all candidate solutions is intractable.
Therefore, a heuristic algorithm is proposed, which emulates the exploratory
data analysis of the human expert. This algorithm encodes a number of search
strategies in a pattern directed computer program, and results in an automatic
determination of a satisfactory solution.
Anderson et al. (1999) used periodic ARMA, or PARMA time series to
model periodically stationary time series. The innovations algorithm was
developed for periodically stationary processes. Thereafter, the algorithm was
used to obtain parameter estimates for the PARMA model. These estimates
were proved to be weakly consistent for PARMA processes whose underlying
noise sequence has either finite or infinite fourth moment. Since many time
series from the fields of economics and hydrology exhibit heavy tails, the
results regarding the infinite fourth moment case are of particular interest.
Haywood and Wilson (2000) proposed a method for investigating the
evolution of trend and seasonality in observed time series. A general model
was fitted to a residual spectrum, using components to represent the seasonality.
The method was applied to model two time series and the resulting forecasts
and seasonal adjustment for one series are presented.
Darken et al. (2000) developed a methodology for testing the equivalence
of two modified Kendall's tau nonparametric correlation coefficients. Several
estimators of the variance tau mod (i.e., bootstrap estimate, the standard null-
case variance estimate, and a delta method variance estimate) were evaluated
using simulation. The variance estimators and their corresponding Wald-type
tests were studied under different conditions, including the presence of varying
degrees of serial correlation, different distributions, and different percentages
of tied data. The power study revealed that in the presence of serial correlation,
a new method for estimating variance, called the effective sample size bootstrap ,
allowed the hypothesis test to consistently hold its level while no other methods
of variance estimation did so. Finally, it was demonstrated how this test can
be used to detect changes in trend of water-quality variables over time.
Perreault et al. (2000) proposed a Bayesian method for the analysis of two
types of sudden change at an unknown time-point in a sequence of energy
inflows modelled by independent normal random variables. To our knowledge,
this study is the first of its kind in hydrology from a Bayesian perspective.
Even if this model is quite simple, no analytic solutions for parameter inference
are available. It is shown that the Gibbs sampler is particularly suitable for
change-point analysis, and Markovian updating scheme is used. Finally, a
case study involving annual energy inflows of two large hydropower systems
of Canada is presented.