Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (04) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (4) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob.34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

scholarly journals PERAMALAN JUMLAH PENUMPANG KERETA API MENGGUNAKAN METODE ARIMA, INTERVENSI DAN ARFIMA (Studi Kasus : Penumpang Kereta Api Kelas Lokal EkonomiDAOP IV Semarang)

2018 ◽  
Vol 7 (1) ◽  
pp. 96-109
Author(s):  
Helmi Panjaitan ◽  
Alan Prahutama ◽  
Sudarno Sudarno
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Time Series Data ◽  
Moving Average ◽  
Step Function ◽  
Local Economy ◽  
Stationary Time Series ◽  
Series Data ◽  
Short Term

Autoregressive Integrated Moving Average (ARIMA) is stationary time series model after differentiation. Differentiation value of ARIMA method is an integer so it is only able to model in the short term. The best model using ARIMA method is ARIMA([13]; 1; 0) with an MSE value of 1,870844. The Intervention method is a model for time series data which in practice has extreme fluctuations both up and down. In the data plot the number of train passengers was found to be extreme fluctuation. The data used was from January 2009 to June 2017 where fluctuation up significantly in January 2016 (T=85 to T=102) so the intervention model that was suspected was a step function. The best model uses the Intervention step function is ARIMA ([13]; 1; 1) (b=0; s=18; r=0) with MSE of 1124. Autoregressive Fractionally Integrated Moving Average (ARFIMA) method is a development of the ARIMA method. The advantage of the ARFIMA method is the non-integer differentiation value so that it can overcome long memory effect that can not be solve with the ARIMA method. ARFIMA model is capable of modeling high changes in the long term (long term persistence) and explain long-term and short-term correlation structures at the same time. The number of local economy class train passengers in DAOP IV Semarang contains long memory effects, so the ARFIMA method is used to obtain the best model. The best model obtained is the ARMA(0; [1,13]) model with the differential value is 0,367546, then the model can be written into ARFIMA (0; d; [1,13]) with an MSE value of 0,00964. Based on the analysis of the three methods, the best method of analyzing the number of local economy class train passengers in DAOP IV Semarang is the ARFIMA method with the model is ARFIMA (0; 0,367546; [1,13]). Keywords: Train Passengers, ARIMA, Intervention, ARFIMA, Forecasting

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 Variability and Confidence Intervals for the Mean of Climate Data with Short- and Long-Range Dependence

2018 ◽  
Vol 31 (15) ◽  
pp. 6135-6156 ◽  
Author(s):  
Matthew C. Bowers ◽  
Wen-wen Tung
Keyword(s):  
Confidence Intervals ◽  
Long Range ◽  
Long Memory ◽  
Long Range Dependence ◽  
Climate Data ◽  
Temperature State ◽  
Correlation Structures ◽  
The Mean ◽  
Error Bars ◽  
Mean State

This paper presents an adaptive procedure for estimating the variability and determining error bars as confidence intervals for climate mean states by accounting for both short- and long-range dependence. While the prevailing methods for quantifying the variability of climate means account for short-range dependence, they ignore long memory, which is demonstrated to lead to underestimated variability and hence artificially narrow confidence intervals. To capture both short- and long-range correlation structures, climate data are modeled as fractionally integrated autoregressive moving-average processes. The preferred model can be selected adaptively via an information criterion and a diagnostic visualization, and the estimated variability of the climate mean state can be computed directly from the chosen model. The procedure was demonstrated by determining error bars for four 30-yr means of surface temperatures observed at Potsdam, Germany, from 1896 to 2015. These error bars are roughly twice the width as those obtained using prevailing methods, which disregard long memory, leading to a substantive reinterpretation of differences among mean states of this particular dataset. Despite their increased width, the new error bars still suggest that a significant increase occurred in the mean temperature state of Potsdam from the 1896–1925 period to the most recent period, 1986–2015. The new wider error bars, therefore, communicate greater uncertainty in the mean state yet present even stronger evidence of a significant temperature increase. These results corroborate a need for more meticulous consideration of the correlation structures of climate data—especially of their long-memory properties—in assessing the variability and determining confidence intervals for their mean states.

A study on the variations in long-range dependence of solar energetic particles during different solar cycles

2018 ◽  
Vol 13 (S340) ◽  
pp. 47-48
Author(s):  
V. Vipindas ◽  
Sumesh Gopinath ◽  
T. E. Girish
Keyword(s):  
Long Range ◽  
Long Memory ◽  
Hurst Exponent ◽  
High Energy ◽  
Energetic Particles ◽  
Solar Energetic Particles ◽  
Long Range Dependence ◽  
Solar Cycles ◽  
Self Similarity ◽  
High Energy Particles

AbstractSolar Energetic Particles (SEPs) are high-energy particles ejected by the Sun which consist of protons, electrons and heavy ions having energies in the range of a few tens of keVs to several GeVs. The statistical features of the solar energetic particles (SEPs) during different periods of solar cycles are highly variable. In the present study we try to quantify the long-range dependence (or long-memory) of the solar energetic particles during different periods of solar cycle (SC) 23 and 24. For stochastic processes, long-range dependence or self-similarity is usually quantified by the Hurst exponent. We compare the Hurst exponent of SEP proton fluxes having energies (>1MeV to >100 MeV) for different periods, which include both solar maximum and minimum years, in order to find whether SC-dependent self-similarity exist for SEP flux.

Correlation models with long-range dependence

2002 ◽  
Vol 39 (2) ◽  
pp. 370-382 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Memory ◽  
Short Range ◽  
Sufficient Conditions ◽  
Long Range Dependence ◽  
Simple Method ◽  
Summable Sequence ◽  
Correlation Models ◽  
Necessary And Sufficient

This paper is concerned with the correlation structure of a stationary discrete time-series with long memory or long-range dependence. Given a sequence of bounded variation, we obtain necessary and sufficient conditions for a function generated from the sequence to be a proper correlation function. These conditions are applied to derive various slowly decaying correlation models. To obtain correlation models with short-range dependence from an absolutely summable sequence, a simple method is introduced.

Power-law correlations and other models with long-range dependence on a lattice

2003 ◽  
Vol 40 (3) ◽  
pp. 690-703 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Long Range ◽  
Power Law ◽  
Correlation Functions ◽  
Short Range ◽  
Long Range Dependence ◽  
Correlation Model ◽  
Double Sequences ◽  
Exact Power ◽  
Stationary Random Field ◽  
Dependent Correlation

This paper introduces long-range dependence for a stationary random field on a plane lattice, derives an exact power-law correlation model and other models with long-range dependence on the lattice, and explores the close connection between short-range dependent correlation functions and absolutely summable double sequences.

MODELING NETWORK TRAFFIC USING CAUCHY CORRELATION MODEL WITH LONG-RANGE DEPENDENCE

2005 ◽  
Vol 19 (17) ◽  
pp. 829-840 ◽  
Author(s):  
MING LI ◽  
S. C. LIM
Keyword(s):  
Long Range ◽  
Network Traffic ◽  
Traffic Engineering ◽  
Single Parameter ◽  
Traffic Modeling ◽  
Long Range Dependence ◽  
Correlation Model ◽  
Traffic Time Series ◽  
Fractal Properties

Much attention has been given to the long-range dependence and fractal properties in network traffic engineering, and these properties are also widely observed in many fields of science and technologies. Traffic time series is conventionally characterized by its fractal dimension D, which is a measure for roughness, and by the Hurst parameter H, which is a measure for long-range dependence, see for examples (Refs. 10–12). Each property has been traditionally modeled and explained by self-affine random functions, such as fractional Gaussian noise (FGN)1,10–13,18,22–28 and fractional Brownian motion (FBM),6,7 where a linear relationship between D and H, say D = 2 - H for one-dimensional series, links the two properties. The limitation of single parameter models (e.g., FGN) in long-range dependent (LRD) traffic modeling has been noticed as can be seen from Refs. 1, 18 and 25. Hence, models which can provide good fitting of LRD traffic for both short-term lags and long-term ones are worth studying due to the importance of accurate models of traffic in network communications.13 This letter utilizes a statistical model called the Cauchy correlation model to model LRD traffic. This model characterizes D and H separately, and it allows any combination of two within the constraint of LRD condition. It is a new power-law correlation model for LRD traffic modeling with its local and global behavior decoupling. Its flexibility in data modeling in comparison with a single parameter model of FGN is briefly discussed, and applications to LRD traffic modeling demonstrated.

Height Extrapolation of Wind Data

1985 ◽  
Vol 107 (1) ◽  
pp. 10-14 ◽  
Author(s):  
A. S. Mikhail
Keyword(s):  
Wind Speed ◽  
Power Law ◽  
Wind Data ◽  
Power Law Model ◽  
Short Term ◽  
Shape Factors ◽  
Wind Speeds ◽  
Average Wind ◽  
Modified Power Law

Various models that are used for height extrapolation of short and long-term averaged wind speeds are discussed. Hourly averaged data from three tall meteorological towers (the NOAA Erie Tower in Colorado, the Battelle Goodnoe Hills Tower in Washington, and the WKY-TV Tower in Oklahoma), together with data from 17 candidate sites (selected for possible installation of large WECS), were used to analyze the variability of short-term average wind shear with atmospheric and surface parameters and the variability of the long-term Weibull distribution parameter with height. The exponents of a power-law model, fit to the wind speed profiles at the three meteorological towers, showed the same variability with anemometer level wind speed, stability, and surface roughness as the similarity law model. Of the four models representing short-term wind data extrapolation with height (1/7 power law, logarithmic law, power law, and modified power law), the modified power law gives the minimum rms for all candidate sites for short-term average wind speeds and the mean cube of the speed. The modified power-law model was also able to predict the upper-level scale factor for the WKY-TV and Goodnoe Hills Tower data with greater accuracy. All models were not successful in extrapolation of the Weibull shape factors.

scholarly journals Long-range dependence in coastal framework geology: Asymmetries and implications for barrier island resiliency

2018 ◽  
Author(s):  
Phillipe Wernette ◽  
Chris Houser ◽  
Bradley Weymer ◽  
Mark Everett ◽  
Michael Bishop ◽  
...  
Keyword(s):  
Long Range ◽  
Coastal Management ◽  
Moving Average ◽  
Barrier Island ◽  
Long Range Dependence ◽  
The North ◽  
Arfima Models ◽  
Societal Pressure ◽  
Dune Morphology

Abstract. Barrier island transgression is influenced by the alongshore variation in beach and dune morphology, which determines the amount of sediment moved landward through washover. While several studies have demonstrated how variations in dune morphology affect island response to storms, the reasons for that variation and the implications for island management remain unclear. This paper builds on previous research by demonstrating that the framework geology can influence beach and dune morphology asymmetrically alongshore. The influence of relict paleo-channels on beach and dune morphology on Padre Island National Seashore, Texas was quantified by isolating the long-range dependence (LRD) parameter in autoregressive fractionally-integrated moving average (ARFIMA) models. ARFIMA models were fit across all scales and a moving window approach was used to examine how LRD varied with computational scale and location along the island. The resulting LRD matrices were plotted by latitude to place the results in context of previously identified variations in the framework geology. Results indicate that the LRD is not constant alongshore for all surface morphometrics. Many flares in the LRD plots correlate to relict infilled paleo-channels in the framework geology, indicating that the framework geology has a significant influence on the morphology of PAIS. Barrier island surface morphology LRD is strongest at large paleo-channels and decreases to the north. The spatial patterns in LRD surface morphometrics and framework geology variations demonstrate that the influence of paleo-channels in the framework geology can be asymmetric where the alongshore sediment transport gradient was unidirectional during island development. The asymmetric influence of framework geology on coastal morphology has long-term implications for coastal management activities because it dictates the long-term behavior of a barrier island. Coastal management projects should first seek to understand how the framework geology influences coastal processes in order to more effectively balance long-term natural variability with short-term societal pressure.

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