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Mario Trottini, Maria Isabel, Vigo Aguiar, and Santiago Belda Palazón

1. Introduction Running trends analysis (RTA) is one of several methods used in climate research to analyze univariate time series and time series association. For a given time series { y t }, observed at n equally spaced points in time t 1 , t 2 , …, t n , RTA involves defining n − L + 1 overlapping time windows ( W 1 , W 2 , …, W n − L +1 ) each with exactly L consecutive time points (2 ≤ L ≤ n − 1), and then evaluating the least squares estimates of the trend for each time

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Robert Lund, Xiaolan L. Wang, Qi Qi Lu, Jaxk Reeves, Colin Gallagher, and Yang Feng

1. Introduction A changepoint is a time at which the structural pattern of a time series changes. Instrumentation/observer changes, station location changes, and changes in observation practices are frequent culprits behind changepoints. In many cases, the changepoint time and cause are documented and it is reasonably straightforward to statistically adjust (homogenize) the series for the effects of the changepoint. Unfortunately, many changepoint times are undocumented. While undocumented

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Colin Gallagher, Robert Lund, and Michael Robbins

1. Introduction Changepoint features can drastically alter inferences made from a climatic time series. For example, Fig. 1 shows how trend estimates change when changepoint information is incorporated or neglected. This example considers annually averaged temperatures recorded at New Bedford, Massachusetts, from 1812 to 1999. The figure reports two statistical regression fits: 1) a line, which has a positive slope of 1.366°C century −1 , and 2) a “piecewise line” that allows for four mean

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Claire Vincent, Gregor Giebel, Pierre Pinson, and Henrik Madsen

wind farm was shown to fluctuate with an amplitude of up to 100 MW in 15–20 min. The construction of the second Horns Rev wind farm, with a capacity of more than 200 MW in close proximity to the existing turbines (as shown in Fig. 1 ), is expected to exacerbate these problems. The aim of this work is to apply a statistical method called the Hilbert–Huang transform to describe the time evolving variability information in wind speed time series. The applicability of the method to studying the

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Andrea Toreti, Franz G. Kuglitsch, Elena Xoplaki, and Jürg Luterbacher

1. Introduction Long instrumental time series of climate variables are often affected by abrupt changes caused by climatic and/or nonclimatic factors. In a time series context, the identification of abrupt changes is equivalent to the subdivision of a series into segments characterized by homogeneous statistical features (e.g., mean and higher-order moments). Time series segmentation or changepoint detection is a broad topic involving several application fields, such as, for example

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Ying Pan and Edward G. Patton

1. Introduction Stationary time series are required to precisely estimate time-averaged statistics. Without prior knowledge of a variable’s characteristics, a stationarity measure should desirably remain invariant to applying a constant offset to the variable. Statistical techniques satisfying this requirement include the integral time scale ( Lumley and Panofsky 1964 ), the reverse arrangement test ( Kendall et al. 1979 ), the run test ( Brownlee 1965 ), and the nonstationarity ratio ( Mahrt

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Gerald L Potter, George J. Huffman, David T. Bolvin, Michael G. Bosilovich, Judy Hertz, and Laura E. Carriere

of these events. Such an analysis could make these reanalysis and observational datasets more useful for determining naturally occurring variations and trends in the time series. Here, we report on a simple method that utilizes a time series of histogram anomalies of precipitation that is sensitive to changes in the dataset, whether genuine or artificial, which we name the Histogram Anomaly Time Series (HATS). Data To demonstrate the usefulness of HATS, we use the repackaged Modern

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Christopher D. Curtis

1. Introduction Time series simulation plays an important role in developing new weather radar signal processing algorithms. Having simulated data that accurately represent the weather signal characteristics is essential. In this paper, a few modifications to conventional simulators will be introduced to improve both accuracy and performance. The focus will be on simulating single-polarization weather radar data using a Gaussian spectral model for the weather (or ground clutter) signal

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Yanfei Kang, Danijel Belušić, and Kate Smith-Miles

1. Introduction Time series can be regarded as progressions of various shapes in time. In a broader geophysical context, shapes, or events, are embedded in various levels of noise that are usually of a certain type or color. The motions in the atmosphere exhibit scale interactions such that the power spectra usually decrease with scale as a negative power of the wavenumber. This is the characteristic shared with red noise, and as a result, atmospheric time series are frequently modeled using a

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Alexander Gluhovsky and Ernest Agee

1. Introduction Time series obtained from various observational and modeling activities may provide crucial information for understanding and predicting atmospheric and climatic variability. However, traditional methods of time series analysis involving linear parametric models are “based on certain probabilistic assumptions about the nature of the physical process that generates the time series of interest. Such mathematical assumptions are rarely, if ever, met in practice” ( Ghil et al. 2002

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