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High‐protein wheats (Triticum aestivum L.) are not preferred for Oriental diets. Because the protein content of soft white winter wheat grown extensively in the U.S. Pacific Northwest is often higher than the optimum (100 g kg−1) for export, there has been a decline of wheat exports to Japan and other Pacific Rim countries. The present study was undertaken to examine the trends in protein levels during 1979 to 1988 and to evaluate the influence of wheat cultivars and climatic parameters on protein content of SWW wheat in the Pacific Northwest. The maximum and minimum temperatures, precipitation, and evaporation during each of 9 wk prior to crop harvest were tested for their effect on protein content. Data on protein content used in the analysis were obtained from the annual reports of USDA Western Wheat Quality Laboratory for wheat grown at 10 different locations in Washington, Idaho, and Oregon. Five‐year moving averages indicated a rising trend in the protein content at Lind, WA, and Moro, OR, the two driest locations. Commercially grown cultivars had no significant influence on protein content in the presence of climatic parameters. Climatic parameters were found to have a significant influence on wheat protein content with coefficients of multiple determination ranging from 0.36 to 0.82 for the 10 locations. Maximum temperature during the grain‐filling stage influenced the protein content at 9 out of 10 locations, and, generally, a rise in temperature resulted in higher protein contents. With climatic factors significantly influencing protein levels in SWW wheat, suitable agronomic and fertility management practices are needed to ameliorate the climatic effects.

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The article reviews methods of inference for single and multiple change‐points in time series, when data are of retrospective (off‐line) type. The inferential methods reviewed for a single change‐point in time series include likelihood, Bayes, Bayes‐type and some relevant non‐parametric methods. Inference for multiple change‐points requires methods that can handle large data sets and can be implemented efficiently for estimating the number of change‐points as well as their locations. Our review in this important area focuses on some of the recent advances in this direction. Greater emphasis is placed on multivariate data while reviewing inferential methods for a single change‐point in time series. Throughout the article, more attention is paid to estimation of unknown change‐point(s) in time series, and this is especially true in the case of multiple change‐points. Some specific data sets for which change‐point modelling has been carried out in the literature are provided as illustrative examples under both single and multiple change‐point scenarios.

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We derive exact computable expressions for the asymptotic distribution of the change-point mle when a change in the mean occurred at an unknown point of a sequence of time-ordered independent Gaussian random variables. The derivation, which assumes that nuisance parameters such as the amount of change and variance are known, is based on ladder heights of Gaussian random walks hitting the half-line. We then show that the exact distribution easily extends to the distribution of the change-point mle when a change occurs in the mean vector of a multivariate Gaussian process. We perform simulations to examine the accuracy of the derived distribution when nuisance parameters have to be estimated as well as robustness of the derived distribution to deviations from Gaussianity. Through simulations, we also compare it with the well-known conditional distribution of the mle, which may be interpreted as a Bayesian solution to the change-point problem. Finally, we apply the derived methodology to monthly averages of water discharges of the Nacetinsky creek, Germany. The change-point problem allows modelers to detect the presence of any such unknown change-points and further capture them through either point or interval estimates. Such modeling has found applications from all areas of scientific endeavor, including environmental monitoring, global climatic changes, quality control, reliability, financial and econometric time series, and medicine, to name a few. For examples of real life applications, see Braun and Müller (1998) for application of change-point methods in DNA segmentation and bioinformatics; for applications in statistical process control. Even though there are recent advances in addressing multiple changes in scientific phenomena [see Fearnhead (2006), Fearnhead and Liu (2007), Girón, Moreno and Casella (2007) and Seidou and Ouarda (2007)], the classical change-point literature is most well developed in the case of a single unknown change-point in time-ordered processes.Classical change-point methods involve two fundamental inferential problems, detection and estimation. Under the likelihood-based approach, the detection part is addressed through likelihood ratio statistics and their asymptotic sampling distributions. Maximum likelihood estimation of an unknown change-point first begins with obtaining the mle as a point estimate. Interval estimates of any desired level, which are preferred over point estimates, can be constructed around the mle, provided distribution theory for the mle is available. However, distribution theory for a change-point mle can be analytically intractable, particularly when no smoothness conditions are assumed regarding the amount of change. In contrast, advances in the Bayesian approach to change-point methodology have been occurring at a faster pace. Ever since Markov chain Monte Carlo (MCMC) methods were seen as a tool for overcoming the computational complexities in Bayesian analysis, there has been rapid progress in the overall development of this important methodological tool, ...

The annual discharges of the Nile River at Aswan are examined for change-points in both mean level and in serial correlation structure. The methodology used identifies 1899 as a change-point for the mean level; this has been observed by others. Second and third change-points for the mean level are identified at 1954 and 1965. In addition, a change is observed in the serial correlation structure of the detrended series. For the segment prior to 1907 this structure is compatible with white noise; after 1907 it is characterized by strong serial correlation and is closely modelled by an ARMA(2,2) model. This serial correlation is taken into account when identifying the 1954 and 1965 changes in mean level.The history of the Nile basin is examined for significant hydrological and political events that might be connected with these change-points. It is speculated that the changes in mean level at 1899 and 1954 and in serial correlation structure are changes in the data due to measurement and hydropolitical issues. A competing hypothesis for the cause of changes in mean level involves long-term climatic shifts that could be modelled by longmemory or doubly stochastic models.