α-stable laws for noncoding regions in DNA sequences

Crato, Nuno; Linhares, Raquel Romes; Lopes, Sílvia da Silva

doi:10.1080/02664760903406447

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…Another procedure to detect long‐range dependence is the detrended fluctuation analysis (DFA) proposed by Peng et al [1992]. Crato et al [2010] give a full description and technical details of the DFA method, while Crato et al [2011] report an application to DNA sequences and Livina et al [2003] apply the DFA to measure the correlation properties of river flow fluctuations. To apply the DFA method to the original and deseasonalized Ladário time series we considered two different values of g ( n ) [for details, see Crato et al , 2010], where n = 1092 is the sample size.…”

Section: Preliminary Analysis Of the Ladário Time Seriesmentioning

confidence: 99%

Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models

Prass

Bravo

Clarke

et al. 2012

Water Resources Research

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[1] The paper compares forecasts of mean monthly water levels up to six months ahead at Ladário, on the Upper Paraguay River, Brazil, estimated from two long-range dependence models. In one of them, the marked seasonal cycle was removed and a fractionally differenced model was fitted to the transformed series. In the other, a seasonal fractionally differenced model was fitted to water levels without transformation. Forecasts from both models for periods up to six months ahead were compared with forecasts given by simpler ''short-range dependence'' Box-Jenkins models, one fitted to the transformed series, the other a seasonal autoregressive moving average (ARMA) model. Estimates of parameters in the four models (two ''long-range dependence'', two ''short-range dependence'') were updated at six-monthly intervals over a 20 year period, and forecasts were compared using root mean square errors (rmse) between water-level forecasts and observed levels. As judged by rmse, performances of the two long-range dependence models, and of the ARMA (1,1) short-range dependence model, were very similar; all three out-performed the seasonal short-range dependence ARMA model. There was evidence that all models performed better during recession periods, than on the hydrograph rising limb.

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Section: Preliminary Analysis Of the Ladário Time Seriesmentioning

confidence: 99%

Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models

Prass

Bravo

Clarke

et al. 2012

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…The aÀstable distribution is considered as the generalization of the Gaussian one. Although the first application of this distribution appeared in the work of Mandelbrot [16], where the financial time series were analyzed, the aÀstable distributions and processes have found various applications, including economy [17][18][19][20][21][22][23], physics [24][25][26][27], signal processing [28][29][30][31], computer science [32][33][34][35], geology and geophysics [36][37][38], biology [39][40][41][42], and many other fields. The aÀstable distributions are also considered for climate data modelling, see, e.g., [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Application of non-Gaussian multidimensional autoregressive model for climate data prediction

Broszkiewicz-Suwaj

Wyłomańska

2021

Int J Adv Eng Sci Appl Math

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From the point of view of agriculture, ecology, or environmental engineering, the capability of forecasting meteorological variables in the long and short term is crucial. Short-term forecasts enabling the planning of field work in agriculture, management of mass events, or tourism are important, while long-term forecasts related to advancing climate change are also very interesting. In the literature, there are known many approaches that can be used to forecast climate time series. The most common is based on the statistical modelling of the corresponding data, and the prediction is made on the fitted model. There are known one-dimensional approaches, where single variables are modeled separately; however, in the last decade, there appears a new trend which assumes the importance of the relationship between different time series. This is the approach considered in this paper. We propose to examine the climate data (temperature and precipitation) using the multidimensional vector autoregressive model (VAR). However, because in the time series we observe non-Gaussian behaviour, the classical VAR model can not be applied and the multidimensional Gaussian noise is replaced by the $$\alpha -$$ α - stable one. This model was previously analyzed by the authors in the context of financial data description where also non-Gaussian characteristics are observed. The main goal of this paper is to answer the question whether there are reasons to go from the Gaussian model to the generalized models, like $$\alpha -$$ α - stable based. The second purpose is to link total precipitation data with temperature time series. In the classical approach, precipitation was treated as a variable not correlated with temperature, which, as we will show in the paper, is inconsistent with reality. We hope the presented in this paper results open new areas of interest related to climate data modelling and prediction.

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Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations

Karling

Lopes

Souza

2023

Journal of Multivariate Analysis

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α-stable laws for noncoding regions in DNA sequences

Cited by 7 publications

References 21 publications

Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models

Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models

Application of non-Gaussian multidimensional autoregressive model for climate data prediction

Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations

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