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Trend Estimation

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Trend estimation is a statistical technique used to analyze and predict the direction and magnitude of changes in data over time. It involves identifying patterns within historical data to forecast future values, often employing methods such as regression analysis, moving averages, or time series analysis.
lightbulbAbout this topic
Trend estimation is a statistical technique used to analyze and predict the direction and magnitude of changes in data over time. It involves identifying patterns within historical data to forecast future values, often employing methods such as regression analysis, moving averages, or time series analysis.

Key research themes

1. How can non-parametric Mann-Kendall family tests be adapted to account for autocorrelation and seasonality in trend estimation?

This research area focuses on enhancing the robustness of non-parametric Mann-Kendall trend tests when applied to environmental, climatic, and hydrological time series data that commonly exhibit serial correlation and seasonal patterns. Original Mann-Kendall tests assume independence of data points, but many real-world series violate this due to autocorrelation or seasonality, leading to distorted trend inferences. Modifications and python implementations have been developed to address these issues, enabling statistically reliable trend detection.

Key finding: This paper presents 'pyMannKendall', a comprehensive Python package implementing 11 variants of the Mann-Kendall test including modifications that correct for serial autocorrelation and seasonality effects, such as the... Read more
Key finding: By comparing four Mann-Kendall test variants—MK1 (original), MK2 (correcting for lag-1 autocorrelation), MK3 (correcting long-term persistence), and MK4 (incorporating Hurst phenomenon)—this study demonstrates that neglecting... Read more
Key finding: Utilizing Sen's slope estimator and Mann-Kendall trend test—both robust non-parametric methods insensitive to outliers and distributional assumptions—this study identifies statistically significant increasing trends in annual... Read more
Key finding: Among Mann-Kendall and Sen's slope methods, the study introduces Sen's Innovative Trend Method (ITM), which outperforms traditional non-parametric tests by effectively capturing trends in low, medium, and high quantiles of... Read more
Key finding: This paper reveals that running trend analyses based on overlapping windowed least squares slopes (based on Mann-Kendall-inspired methods) alone poorly summarize underlying time series characteristics, especially under... Read more

2. What advanced stochastic and renewal process models improve parameter estimation and trend detection in time series with repairable systems or event data?

This research area investigates sophisticated stochastic point process models such as trend renewal processes (TRP) and heterogeneous trend-renewal processes that model repairable systems and failure events with complex trends and unobserved heterogeneity. Estimation methodologies that accommodate unknown renewal distributions or nonparametric approaches have been developed to enhance flexibility and applicability of trend and failure intensity estimation, important for reliability engineering and event forecasting in various domains.

Key finding: This work develops a nonparametric estimation approach for trend-renewal processes without assuming a known form for the renewal failure rate, complementing maximum likelihood methods dependent on fixed trend functions.... Read more
Key finding: In the scenario where the renewal distribution is unknown, maximum likelihood estimation is infeasible for TRPs. This paper proposes three alternative estimation methods that do not require knowledge of the renewal... Read more
Key finding: Beyond its hydrological and climatological applications, the pyMannKendall package supports multivariate Mann-Kendall testing, enhancing ability to analyze multiple correlated parameters, which parallels needs in modeling... Read more

3. How can multivariate and state-space modeling improve extraction and estimation of common stochastic trends in economic and industrial time series?

This theme covers the use of multivariate signal extraction techniques, such as the Hodrick-Prescott filter and state-space models with Kalman filtering, to identify latent common stochastic trends that govern multiple related time series. These methods address challenges like nonstationarity, cointegration, and model parameter estimation, enabling robust trend extraction for macroeconomic indicators, industrial production, and financial variables.

Key finding: This paper generalizes the univariate Hodrick–Prescott filter to a multivariate setting through a VARMA framework and introduces the 'Moment Estimation Through Aggregation' (META) technique for parameter estimation. The... Read more
Key finding: Focusing on state-space models with a single latent integrated stochastic trend, the paper establishes the consistency and asymptotic mixed normality of maximum likelihood estimators via Kalman filtering, even under... Read more
Key finding: Presenting incremental computation algorithms for correlation and related measures, this work offers scalable tools that can be used alongside state-space or multivariate trend extraction methods to process large, rapidly... Read more

All papers in Trend Estimation

The problem of correcting the tide gauge records for the vertical land motion upon which the gauges are settled has only been partially solved. At best, the analyses so far have included model corrections for one of the many processes... more
We propose a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on nonparametric trend estimation and autoregressive approximation for some noise process. The bootstrap... more
We propose a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on nonparametric trend estimation and autoregressive approximation for some noise process. The bootstrap... more
We used hourly counts of Red-tailed Hawks (Bufeo jumaicensis) migrating at Hawk Mountain during the autumns of 1992, 1993, and 1994, to examine the possibility that the extent to which time of day and local weather parameters affected the... more
ABsTRAcr.--Cold-front passage has long been associated with south-bound raptor migration in northeastern North America. We used Hawk Mountain Sanctuary's 55-year database to calculate abundance indices of 14 raptor species at the site.... more
Las investigaciones sobre el comportamiento de caza y dieta del gavilán de cooper (Astur cooperii) en México son escasas, por lo que falta mayor información y observaciones al respecto. En este trabajo presentamos la primera observación... more
Background: Several compounds contained in coffee have been found to suppress carcinogenesis in experimental studies. We conducted a dose-response meta-analysis to assess the impact of coffee consumption on the risk of endometrial cancer.... more
In 2005 the National Research Council (NRC) analyzed right-to-carry (RTC) laws, also known as shall-issue laws, which relax the requirements necessary to acquire a permit to carry a concealed weapon. The NRC essentially concluded that the... more
This paper describes the key features of the Moroccan business cycles during the period 1980:q1-2012:q1. In particular, this paper identifies the chronologies in classical and growth cycles (expansion and contraction phases and full... more
We present a detailed analysis of a rare cross‐taxa native species phenology dataset (plant flowering, insect first sighting, and amphibian first sighting) from Mohonk Lake, NY. This dataset is highly unusual in North America for its... more
There is no single reference dataset of long-term global upper-air temperature observations, although several groups have developed datasets from radiosonde and satellite observations for climate-monitoring purposes. The existence of... more
Establishing status and trend for an endangered species is critical to recovery, especially when it is faced with a nascent extinction agent. We calculated, with hierarchical log-linear change-point models, hibernaculum-level population... more
Along with coauthors, John J. Donohue of the Stanford Law School regularly releases empirical research finding that certain laws concerning the carrying of firearms, those known as right-to-carry or RTC laws, increase violent crime. We... more
BioOne Complete (complete.BioOne.org) is a full-text database of 200 subscribed and open-access titles in the biological, ecological, and environmental sciences published by nonprofit societies, associations, museums, institutions, and... more
BioOne Complete (complete.BioOne.org) is a full-text database of 200 subscribed and open-access titles in the biological, ecological, and environmental sciences published by nonprofit societies, associations, museums, institutions, and... more
by Laurie Goodrich and 
1 more
ABSTRACr.-Counts of migrating hawks were initiated in 1934 at Hawk Mountain and, except for 1943-1945, have continued to the present. We analyzed the data from 1934-1986 by a standardized sample period appropriate for each species. Counts... more
Two count sites. Given coordinates are for site at Cardel, where counts were made from atop a fi ve-story hotel in the middle of the city. In Chichicaxtle (19°21′N, 96°28′W), counts were made from a 7-m tower near a soccer fi eld.
Between 1981 and 2003, 269 visits were made to 72 caves in Indiana to count hibernating bats. Nearly 2,000,000 bats of seven species were counted: Indiana myotis (Myotis sodalis), little brown myotis (M. lucifugus), northern myotis (M.... more
The ARIMA-model-based methodology of programs TRAMO and SEATS is applied for seasonal adjustment and trend-cycle estimation of the exports, imports, and balance of trade Japanese series. The programs are used in an automatic mode, and the... more
Shipping and shipping services are a key industry of great importance to the economy of Cyprus and the wider European Union. Assessment, management and future steering of the industry, and its associated economy, is carried out by a range... more
This book is a review and description of the state-of-the-art methods of tree-ring analy~is with specific emphasis on applications in the environmental sciences. Traditionally, methods of tree-ring analysis, or more properly in this case... more
The issue of a possible tide gauge datum discontinuity at Brest, caused by the bombing of the city in August 1944, is discussed. This issue is very important, as many scientists have used this long record to derive a long‐term sea level... more
The main aim of this communication is to present data on the status of 4 species of Accipitridae-Goshawk, Sparrowhawk, Lewant Sparrowhawk and Shikra at the territory of Georgia. Data were collected as a part of complex studies of birds of... more
Golden Eagles (Aquila chrysaetos) and their diets have been studied extensively in North America and beyond. There have, however, been minimal studies of this species conducted in the state of Arizona, and none within Walnut Canyon... more
We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a... more
Point counts are a common method for sampling avian distribution and abundance. Although methods for estimating detection probabilities are available, many analyses use raw counts and do not correct for detectability. We use a removal... more
Another note on the use of logarithmic time trend
Establishing status and trend for an endangered species is critical to recovery, especially when it is faced with a nascent extinction agent. We calculated, with hierarchical log-linear change-point models, hibernaculum-level population... more
Long-term, ground based in-situ observations of ozone (O 3) and its precursor gases nitrogen dioxide (NO 2) and carbon monoxide (CO) from the four sites Hohenpeissenberg and Zugspitze (D), Sonnblick (A) and Jungfraujoch (CH) are presented... more
Urbanization is rapidly altering ecosystems worldwide, presenting both challenges and opportunities for biodiversity conservation. Birds of prey, as top predators and indicators of environmental health, are particularly sensitive to... more
The paper describes the applied seasonal adjustment procedures used for analysis of the financial time series compiled by SBP. We have applied the X-12-ARIMA method in adjusting five important financial series- currency in circulation,... more
The Instituto Español de Oceanografía (IEO, Spanish Institute of Oceanography) has maintained different monitoring programs in the Spanish Mediterranean waters (Western Mediterranean) since 1992. All these monitoring programs were unified... more
The climate change context has raised new problems in the computation of temperature return levels (RLs) in using the statistical extreme value theory. This arises since it is not yet possible to accept the hypothesis that the series of... more
Quantifying how Canada’s water yield has changed over time is an important component of the water accounts maintained by Statistics Canada. This study evaluates the movement in the series of annual water yield estimates for Southern... more
Global climate change has affected avian migration patterns and nesting phenology. Changes in one phase of a bird's cycle will most likely affect other stages, but few studies focus simultaneously on multiple life-history events. We used... more
We investigated the influence of military training on the abundance and behavior of raptors at a military training area in the Snake River Birds of Prey National Conservation Area in Idaho during the breeding seasons of 1991-1994. Raptor... more
The paper analyzes the recent trends in the occurrence of frost days in Bosnia and Herzegovina. Trends during the 1961-2015 periods were determined based on data from fourteen meteorological stations. MAKESENS procedure, which uses the... more
We give a general condition for disturbance covariance matrices in the general linear regression model which ensures that, in the limit, ordinary least squares is as efficient as generalized least squares as the disturbance covariance... more
Resumen.-Reproducción y estado del Elanio Pico Ganchudo (Chondrohierax uncinatus mirus).-Del 2000 al 2006, estudiamos al Elanio Pico Ganchudo (Chondrohierax uncinatus mirus), una subespecie endémica y en peligro de la isla Grenada. Los... more
Swainson's Hawks (Buteo swainsoni; Aguilucho Langostero) were captured and banded in La Pampa, Argentina from 28 November 1996 through 25 January 1997. We collected morphometric measurements to determine if hawks gained weight on the... more
BioOne Complete (complete.BioOne.org) is a full-text database of 200 subscribed and open-access titles in the biological, ecological, and environmental sciences published by nonprofit societies, associations, museums, institutions, and... more
Quantifying how Canada’s water yield has changed over time is an important component of the water accounts maintained by Statistics Canada. This study evaluates the movement in the series of annual water yield estimates for Southern... more
An NBER working paper by Donohue, Aneja, and Weber (DAW) estimates the impact of right-to-carry (RTC) laws and finds using data from 1979–2014 that RTC laws lead to significant increases in violent crime whether one adopts a traditional... more
NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
Quantifying how Canada’s water yield has changed over time is an important component of the water accounts maintained by Statistics Canada. This study evaluates the movement in the series of annual water yield estimates for Southern... more
New World vultures are typically diurnal with only rare nocturnal activity reported. Tabor and McAllister (1988) observed nocturnal flight by Turkey Vultures (Cathartes aura) during migration, and Mandel and Bildstein (2007) observed... more
New World vultures are typically diurnal with only rare nocturnal activity reported. Tabor and McAllister (1988) observed nocturnal flight by Turkey Vultures (Cathartes aura) during migration, and Mandel and Bildstein (2007) observed... more
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