On Attempts to Use Models Incorporating Long-Range Dependence in Long-Term Volatility Forecasting

2018 ◽  
Author(s):  
Nicholas Reitter
Keyword(s):  
Long Range ◽  
Long Range Dependence ◽  
Volatility Forecasting

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.

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.

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.

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 Intelligent Network Applications Monitoring and Diagnosis Employing Software Sensing and Machine Learning Solutions

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5036
Author(s):  
Marius Minea ◽  
Cătălin Marian Dumitrescu ◽  
Viviana Laetitia Minea
Keyword(s):  
Time Series ◽  
Long Range ◽  
Network Performance ◽  
Smart Cities ◽  
Long Range Dependence ◽  
Intelligent Network ◽  
Statistical Concept ◽  
Engine Operation ◽  
Communications Networks

The article presents a research in the field of complex sensing, detection, and recovery of communications networks applications and hardware, in case of failures, maloperations, or unauthorized intrusions. A case study, based on Davis AI engine operation versus human maintenance operation is performed on the efficiency of artificial intelligence agents in detecting faulty operation, in the context of growing complexity of communications networks, and the perspective of future development of internet of things, big data, smart cities, and connected vehicles. (*). In the second part of the article, a new solution is proposed for the detection of applications faults or unauthorized intrusions in traffic of communications networks. The first objective of the proposed method is to propose an approach for predicting time series. This approach is based on a multi-resolution decomposition of the signals employing the undecimate wavelet transform (UWT). The second approach for assessing traffic flow is based on the analysis of long-range dependence (LRD) (for this case, a long-term dependence). Estimating the degree of long-range dependence is performed by estimating the Hurst parameter of the analyzed time series. This is a relatively new statistical concept in communications traffic analysis and can be implemented using UWT. This property has important implications for network performance, design, and sizing. The presence of long-range dependency in network traffic is assumed to have a significant impact on network performance, and the occurrence of LRD can be the result of faults that occur during certain periods. The strategy chosen for this purpose is based on long-term dependence on traffic, and for the prediction of faults occurrence, a predictive control model (MPC) is proposed, combined with a neural network with radial function (RBF). It is demonstrated via simulations that, in the case of communications traffic, time location is the most important feature of the proposed algorithm.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

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.

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