No abstract

Undocumented changepoints (inhomogeneities) are ubiquitous features of climatic time series. Level shifts in time series caused by changepoints confound many inference problems and are very important data features. Tests for undocumented changepoints from models that have independent and identically distributed errors are by now well understood. However, most climate series exhibit serial autocorrelation. Monthly, daily, or hourly series may also have periodic mean structures. This article develops a test for undocumented changepoints for periodic and autocorrelated time series. Classical changepoint tests based on sums of squared errors are modified to take into account series autocorrelations and periodicities. The methods are applied in the analyses of two climate series.

We developed and evaluated a stratified index redd area method to estimate Chinook salmon Oncorhynchus tshawytscha, coho salmon O. kisutch, and steelhead O. mykiss escapement in several coastal streams in northern California based on the assumption that redd size is related to the number of redds a female builds. Sources of error in redd counts were identified, including the use of logistic regression to classify redd species (necessary due to temporal overlap in the spawning of these species in coastal northern California). Redd area escapement estimates were compared with estimates from more conventional methods and releases above a counting structure. Observer efficiency in redd detection ranged from 0.64 (SE = 0.10) to 0.75 (SE = 0.14) and was significantly associated with streamflow and water visibility (analysis of variance (ANOVA): F = 41.8; P < 0.001). Logistic regression reduced uncertainty in redd identification. Redd area and date observed were significant in predicting coho salmon and steelhead redd species (Wald's z = 11.9 and 18.09, respectively; P < 0.001). Pot substrate and redd area were significant in classifying Chinook and coho salmon redds (Wald's z = 5.88 and 4.03; P = 0.015 and 0.04, respectively). Stratified index redd area escapement estimates and estimates based on capture–recapture experiments, area‐under‐the‐curve estimates, and known releases above the counting structure (coho salmon only) were not significantly different (ANOVA: F < 13.6; P > 0.06). Escapement estimates assuming one redd per female were only significantly different from other methods for steelhead (ANOVA: F = 13.11; P = 0.006). Redd counts were significantly correlated with escapement estimates (r > 0.82; P < 0.04). Reduction of counting errors and uncertainty in redd identification, biweekly surveys throughout the spawning period, and the use of redd areas in a stratified index sampling design produced precise, reliable, and cost‐effective escapement estimates for Chinook salmon, coho salmon, and steelhead.

Several tests for detecting mean shifts at an unknown time in stationary time series have been proposed, including cumulative sum (CUSUM), Gaussian likelihood ratio (LR), maximum of F(F max ) and extreme value statistics. This article reviews these tests, connects them with theoretical results, and compares their finite sample performance via simulation. We propose an adjusted CUSUM statistic which is closely related to the LR test and which links all tests. We find that tests based on CUSUMing estimated one-step-ahead prediction residuals from a fitted autoregressive moving average perform well in general and that the LR and F max tests (which induce substantial computational complexities) offer only a slight increase in power over the adjusted CUSUM test. We also conclude that CUSUM procedures work slightly better when the changepoint time is located near the centre of the data, but the adjusted CUSUM methods are preferable when the changepoint lies closer to the beginning or end of the data record. Finally, an application is presented to demonstrate the importance of the choice of method.

Climate time series often have artificial shifts induced by instrumentation changes, station relocations, observer changes, etc. Climate time series also often exhibit long-term trends. Much of the recent literature has focused on identifying the structural breakpoint time(s) of climate time series-the so-called changepoint problem. Unfortunately, application of rudimentary mean-shift changepoint tests to scenarios with trends often leads to the erroneous conclusion that a mean shift occurred near the series' center. This paper examines this problem in detail, constructing some simple homogeneity tests for series with trends. The asymptotic distribution of the proposed statistic is derived; en route, an attempt is made to unify the asymptotic properties of the changepoint methods used in today's climate literature. The tests presented here are linked to the ubiquitous t test. Application is made to two temperature records: 1) the continental United States record and 2) a local record from Jacksonville, Illinois.