Trend Analysis

Harvey, Andrew

doi:10.1002/9780470057339.vat025

Cited by 4 publications

(5 citation statements)

References 29 publications

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“…1 Harvey (2006) gives two definitions for "trend". In much of the statistical literature a trend is conceived of as that part of a series which changes relatively slowly (smoothly) over time.…”

Section: Stationarity and Trend Methodsmentioning

confidence: 99%

Inferences on weather extremes and weather-related disasters: a review of statistical methods

Visser

Petersen

2012

Clim. Past

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Abstract. The study of weather extremes and their impacts, such as weather-related disasters, plays an important role in research of climate change. Due to the great societal consequences of extremes -historically, now and in the future -the peer-reviewed literature on this theme has been growing enormously since the 1980s. Data sources have a wide origin, from century-long climate reconstructions from tree rings to relatively short (30 to 60 yr) databases with disaster statistics and human impacts.When scanning peer-reviewed literature on weather extremes and its impacts, it is noticeable that many different methods are used to make inferences. However, discussions on these methods are rare. Such discussions are important since a particular methodological choice might substantially influence the inferences made. A calculation of a return period of once in 500 yr, based on a normal distribution will deviate from that based on a Gumbel distribution. And the particular choice between a linear or a flexible trend model might influence inferences as well.In this article, a concise overview of statistical methods applied in the field of weather extremes and weather-related disasters is given. Methods have been evaluated as to stationarity assumptions, the choice for specific probability density functions (PDFs) and the availability of uncertainty information. As for stationarity assumptions, the outcome was that good testing is essential. Inferences on extremes may be wrong if data are assumed stationary while they are not. The same holds for the block-stationarity assumption. As for PDF choices it was found that often more than one PDF shape fits to the same data. From a simulation study the conclusion can be drawn that both the generalized extreme value (GEV) distribution and the log-normal PDF fit very well to a variety of indicators. The application of the normal and Gumbel distributions is more limited. As for uncertainty, it is advisable to test conclusions on extremes for assumptions underlying the modelling approach. Finally, it can be concluded that the coupling of individual extremes or disasters to climate change should be avoided.

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Section: Stationarity and Trend Methodsmentioning

confidence: 99%

Inferences on weather extremes and weather-related disasters: a review of statistical methods

Visser

Petersen

2012

Clim. Past

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“…In the present application, the so‐called smooth trend model was chosen to model the trends

L_{t, d}, d \in false{1, \dots, D false}

. This model is well known in the econometric literature for its reasonable flexibility and parsimony (Durbin and Koopman (), chapter 3, and Harvey ()). The smooth trend model (or the integrated random walk) can be defined by the following two equations for series d :

\begin{matrix} L_{t, d} = L_{t - 1, d} + R_{t - 1, d,} \\ R_{t, d} = R_{t - 1, d} + {italicη}_{R, t, d}, \end{matrix}

where the state variables

L_{t, d}

and

R_{t, d}

are the level and slope of the d th series respectively.…”

Section: Structural Time Series Models and Methods Employedmentioning

confidence: 99%

Multivariate State Space Approach to Variance Reduction in Series with Level and Variance Breaks Due to Survey Redesigns

Bollineni‐Balabay¹,

Brakel²,

Palm

2015

Journal of the Royal Statistical Society Series A: Statistics in Society

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Statistics Netherlands applies a design-based estimation procedure to produce road transportation figures. Frequent survey redesigns caused discontinuities in these series which obstruct the comparability of figures over time. Reductions in the sample size and changes in the sample design resulted in variance breaks and unacceptably large sampling errors in the recent part of the series. Both problems are addressed and solved simultaneously. Discontinuities and small sample sizes are accounted for by using a multivariate structural time series model that borrows strength over time and space. The paper illustrates an increased precision when we move from univariate models to a multivariate model where the domains are jointly modelled. This increase is especially significant in the most recent period when sample sizes become smaller, with standard errors of the design-based estimator of the target variables being reduced by 40-70% with the model-based approach.

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“…Furthermore, the definition of “trend” is not unique. In section 2.1, we have formulated two definitions: (i) trends are seen as a smooth signal where the smoothness is chosen to filter out shorter‐term (decadal) natural fluctuations, and (ii) trends may be viewed in terms of prediction where the estimated trend is conceived as that part of the series which, when extrapolated, provides the clearest indication of the future long‐term movements in the series [ Harvey , ]. And both definitions are pretty vague: what is “smoothness” or what are “long‐term movements”?…”

Section: Preliminariesmentioning

confidence: 99%

“…The estimated trend is conceived as that part of the series which, when extrapolated, provides the clearest indication of the future long-term movements in the series. This application of trends is very popular in fields such as business planning, financial market analyses, and econometrics [e.g., Harvey, 1989Harvey, , 2001Makridakis and Hibon, 2000;Armstrong, 2001;Soyer and Hogarth, 2012]. Forecasting by extrapolation is sometimes applied in short-term weather prediction, and it has shown up recently in the ''sea level debate,'' described in the introduction.…”

Section: Why Estimating Trends?mentioning

confidence: 99%

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A review of trend models applied to sea level data with reference to the “acceleration‐deceleration debate”

2015

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Global sea levels have been rising through the past century and are projected to rise at an accelerated rate throughout the 21st century. This has motivated a number of authors to search for already existing accelerations in observations, which would be, if present, vital for coastal protection planning purposes. No scientific consensus has been reached yet as to how a possible acceleration could be separated from intrinsic climate variability in sea level records. This has led to an intensive debate on its existence and, if absent, also on the general validity of current future projections. Here we shed light on the controversial discussion from a methodological point of view. To do so, we provide a comprehensive review of trend methods used in the community so far. This resulted in an overview of 30 methods, each having its individual mathematical formulation, flexibilities, and characteristics. We illustrate that varying trend approaches may lead to contradictory acceleration‐deceleration inferences. As for statistics‐oriented trend methods, we argue that checks on model assumptions and model selection techniques yield a way out. However, since these selection methods all have implicit assumptions, we show that good modeling practices are of importance too. We conclude at this point that (i) several differently characterized methods should be applied and discussed simultaneously, (ii) uncertainties should be taken into account to prevent biased or wrong conclusions, and (iii) removing internally generated climate variability by incorporating atmospheric or oceanographic information helps to uncover externally forced climate change signals.

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Trend Analysis

Cited by 4 publications

References 29 publications

Inferences on weather extremes and weather-related disasters: a review of statistical methods

Inferences on weather extremes and weather-related disasters: a review of statistical methods

Multivariate State Space Approach to Variance Reduction in Series with Level and Variance Breaks Due to Survey Redesigns

A review of trend models applied to sea level data with reference to the “acceleration‐deceleration debate”

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