scholarly journals Technical note: Stochastic simulation of streamflow time series using phase randomization

2019 ◽  
Vol 23 (8) ◽  
pp. 3175-3187 ◽  
Author(s):  
Manuela I. Brunner ◽  
András Bárdossy ◽  
Reinhard Furrer
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Long Range ◽  
Fourier Transformation ◽  
Temporal Correlation ◽  
Resource Planning ◽  
Long Range Dependence ◽  
Kappa Distribution ◽  
Simulation Approach ◽  
Phase Randomization

Abstract. Stochastically generated streamflow time series are widely used in water resource planning and management. Such series represent sets of plausible yet unobserved streamflow realizations which should reproduce the main characteristics of observed data. These characteristics include the distribution of daily streamflow values and their temporal correlation as expressed by short- and long-range dependence. Existing streamflow generation approaches have mainly focused on the time domain, even though simulation in the frequency domain provides good properties. These properties comprise the simulation of both short- and long-range dependence as well as extension to multiple sites. Simulation in the frequency domain is based on the randomization of the phases of the Fourier transformation. We here combine phase randomization simulation with a flexible, four-parameter kappa distribution, which allows for the extrapolation to as yet unobserved low and high flows. The simulation approach consists of seven steps: (1) fitting the theoretical kappa distribution, (2) normalization and deseasonalization of the marginal distribution, (3) Fourier transformation, (4) random phase generation, (5) inverse Fourier transformation, (6) back transformation, and (7) simulation. The simulation approach is applicable to both individual and multiple sites. It was applied to and validated on a set of four catchments in Switzerland. Our results show that the stochastic streamflow generator based on phase randomization produces realistic streamflow time series with respect to distributional properties and temporal correlation. However, cross-correlation among sites was in some cases found to be underestimated. The approach can be recommended as a flexible tool for various applications such as the dimensioning of reservoirs or the assessment of drought persistence. Highlights. Stochastic simulation of streamflow time series for individual and multiple sites by combining phase randomization and the kappa distribution. Simulated time series reproduce temporal correlation, seasonal distributions, and extremes of observed time series. Simulation procedure suitable for use in water resource planning and management.

scholarly journals Technical note: Stochastic simulation of streamflow time series using phase randomization

2019 ◽  
Author(s):  
Manuela I. Brunner ◽  
András Bárdossy ◽  
Reinhard Furrer
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Long Range ◽  
Fourier Transformation ◽  
Temporal Correlation ◽  
Long Range Dependence ◽  
Kappa Distribution ◽  
Simulation Approach ◽  
Daily Streamflow ◽  
Phase Randomization

Abstract. Stochastically generated streamflow time series are widely used in water resource planning and management. Such series represent sets of plausible yet unobserved streamflow realizations which should reproduce the main characteristics of observed data. These characteristics include the distribution of daily streamflow values and their temporal correlation as expressed by short- and long-range dependence. Existing streamflow generation approaches have mainly focused on the time domain, even though simulation in the frequency domain provides good properties. These properties comprise the simulation of both short- and long-range dependence, as well as extension to multiple sites. Simulation in the frequency domain is based on the randomization of the phases of the Fourier transformation. We here combine phase randomization simulation with a flexible, four-parameter Kappa distribution, which allows for the extrapolation to yet unobserved low and high flows. The simulation approach consists of seven steps: 1) fitting the theoretical Kappa distribution, 2) normalization and deseasonalization, 3) Fourier transformation, 4) random phase generation, 5) inverse Fourier transformation, 6) back transformation, and 7) simulation. The simulation approach is applicable both to individual and multiple sites. It was applied to and validated on a set of four catchments in Switzerland. Our results show that the stochastic streamflow generator based on phase randomization produces realistic streamflow time series with respect to distributional properties and temporal correlation. However, cross-correlation among sites was in some cases found to be underestimated. The approach can be recommended as a flexible tool for various applications such as the dimensioning of reservoirs or the assessment of drought persistence.

scholarly journals Stochastic simulation of streamflow and spatial extremes: a continuous, wavelet-based approach

2020 ◽  
Author(s):  
Manuela I. Brunner ◽  
Eric Gilleland
Keyword(s):  
Water Management ◽  
Time Series ◽  
Wavelet Transform ◽  
Stochastic Simulation ◽  
Drought Risk ◽  
Large Set ◽  
Kappa Distribution ◽  
Simulation Approach ◽  
Spatial Extremes ◽  
Phase Randomization

Abstract. Stochastically generated streamflow time series are used for various water management and hazard estimation applications. They provide realizations of plausible but yet unobserved streamflow time series with the same temporal and distributional characteristics as the observed data. However, the representation of non-stationarities and spatial dependence among sites remains a challenge in stochastic modeling. We investigate whether the use of frequency-domain instead of time-domain models allows for the joint simulation of realistic, continuous streamflow time series at daily resolution and spatial extremes at multiple sites. To do so, we propose the stochastic simulation approach called Phase Randomization Simulation using wavelets PRSim.wave which combines an empirical spatio-temporal model based on the wavelet transform and phase randomization with the flexible four-parameter kappa distribution. The approach consists of five steps: (1) derivation of random phases, (2) fitting of kappa distribution, (3) wavelet transform, (4) inverse wavelet transform, and (5) transformation to kappa distribution. We apply and evaluate PRSim.wave on a large set of 671 catchments in the contiguous United States. We show that this approach allows for the generation of realistic time series at multiple sites exhibiting short- and long-range dependence, non-stationarities, and unobserved extreme events. Our evaluation results strongly suggest that the flexible, continuous simulation approach is potentially valuable for a diverse range of water management applications where the reproduction of spatial dependencies is of interest. Examples include the development of regional water management plans, the estimation of regional flood or drought risk, or the estimation of regional hydropower potential among others.

scholarly journals Stochastic simulation of streamflow and spatial extremes: a continuous, wavelet-based approach

2020 ◽  
Vol 24 (8) ◽  
pp. 3967-3982 ◽  
Author(s):  
Manuela I. Brunner ◽  
Eric Gilleland
Keyword(s):  
Water Management ◽  
Time Series ◽  
Wavelet Transform ◽  
Stochastic Simulation ◽  
Kappa Distribution ◽  
Simulation Approach ◽  
Spatial Extremes ◽  
Temporal Model ◽  
Spatio Temporal ◽  
Phase Randomization

Abstract. Stochastically generated streamflow time series are used for various water management and hazard estimation applications. They provide realizations of plausible but as yet unobserved streamflow time series with the same temporal and distributional characteristics as the observed data. However, the representation of non-stationarities and spatial dependence among sites remains a challenge in stochastic modeling. We investigate whether the use of frequency-domain instead of time-domain models allows for the joint simulation of realistic, continuous streamflow time series at daily resolution and spatial extremes at multiple sites. To do so, we propose the stochastic simulation approach called Phase Randomization Simulation using wavelets (PRSim.wave) which combines an empirical spatio-temporal model based on the wavelet transform and phase randomization with the flexible four-parameter kappa distribution. The approach consists of five steps: (1) derivation of random phases, (2) fitting of the kappa distribution, (3) wavelet transform, (4) inverse wavelet transform, and (5) transformation to kappa distribution. We apply and evaluate PRSim.wave on a large set of 671 catchments in the contiguous United States. We show that this approach allows for the generation of realistic time series at multiple sites exhibiting short- and long-range dependence, non-stationarities, and unobserved extreme events. Our evaluation results strongly suggest that the flexible, continuous simulation approach is potentially valuable for a diverse range of water management applications where the reproduction of spatial dependencies is of interest. Examples include the development of regional water management plans, the estimation of regional flood or drought risk, or the estimation of regional hydropower potential. Highlights. Stochastic simulation of continuous streamflow time series using an empirical, wavelet-based, spatio-temporal model in combination with the parametric kappa distribution. Generation of stochastic time series at multiple sites showing temporal short- and long-range dependence, non-stationarities, and spatial dependence in extreme events. Implementation of PRSim.wave in R package PRSim: Stochastic Simulation of Streamflow Time Series using Phase Randomization.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

scholarly journals Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Entropy ◽  
2016 ◽  
Vol 18 (1) ◽  
pp. 23 ◽  
Author(s):  
Qing Li ◽  
Steven Liang ◽  
Jianguo Yang ◽  
Beizhi Li
Keyword(s):  
Time Series ◽  
Long Range ◽  
Chaotic Time Series ◽  
Long Range Dependence ◽  
Vibration Intensity ◽  
Bearing Vibration

Representative Time Series Fractal Analysis of the Traffic Flows of a Dedicated High-Speed Link

2021 ◽  
Author(s):  
Ginno Millan ◽  
manuel vargas ◽  
Guillermo Fuertes
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Long Range Dependence ◽  
Traffic Flows ◽  
Speed Computer

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link exhibited fractal behavior since the Hurst exponent was in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between -0.5, 0. Based on these results, it is ideal to characterize both the singularities of the fractal traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyzes, the fact that the traffic flows of current computer networks exhibited fractal behavior with a long-range dependence was reaffirmed.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

scholarly journals Broadband log-periodogram regression of time series with long-range dependence

1999 ◽  
Vol 27 (4) ◽  
pp. 1415-1439 ◽  
Author(s):  
Eric Moulines ◽  
Philippe Soulier
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Range Dependence

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

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