Long-range Dependence Behavior Research Articles

Estimating the Statistical Significance of Cross–Correlations between Hydroclimatic Processes in the Presence of Long–Range Dependence

Hydroclimatic processes such as precipitation, temperature, wind speed and dew point are usually considered to be independent of each other. In this study, the cross–correlations between key hydrological-cycle processes are examined, initially by conducting statistical tests, then adding the impact of long-range dependence, which is shown to govern all these processes. Subsequently, an innovative stochastic test that can validate the significance of the cross–correlation among these processes is introduced based on Monte-Carlo simulations. The test works as follows: observations obtained from numerous global-scale timeseries were used for application to, and a comparison of, the traditional methods of validation of statistical significance, such as the t-test, after filtering the data based on length and quality, and then by estimating the cross–correlations on an annual-scale. The proposed method has two main benefits: it negates the need of the pre-whitening data series which could disrupt the stochastic properties of hydroclimatic processes, and indicates tighter limits for upper and lower boundaries of statistical significance when analyzing cross–correlations of processes that exhibit long-range dependence, compared to classical statistical tests. The results of this analysis highlight the need to acquire cross–correlations between processes, which may be significant in the case of long-range dependence behavior.

Forecasting the Volatility of the Stock Index with Deep Learning Using Asymmetric Hurst Exponents

The prediction of the stock price index is a challenge even with advanced deep-learning technology. As a result, the analysis of volatility, which has been widely studied in traditional finance, has attracted attention among researchers. This paper presents a new forecasting model that combines asymmetric fractality and deep-learning algorithms to predict a one-day-ahead absolute return series, the proxy index of stock price volatility. Asymmetric Hurst exponents are measured to capture the asymmetric long-range dependence behavior of the S&P500 index, and recurrent neural network groups are applied. The results show that the asymmetric Hurst exponents have predictive power for one-day-ahead absolute return and are more effective in volatile market conditions. In addition, we propose a new two-stage forecasting model that predicts volatility according to the magnitude of volatility. This new model shows the best forecasting performance regardless of volatility.

On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy

The paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment. The inverse of a ν-stable subordinator is used for the time-change. The submartingale property is assumed to guarantee the net-profit condition. The long-range dependence behavior is proven. The infinite-horizon ruin probability, a specialized version of the Gerber–Shiu function, is considered and investigated. In particular, we prove that the distribution function of the infinite-horizon ruin time satisfies an integral-differential equation. The case of the dividends paid according to a multi-layer dividend strategy is also considered.

Application of Rescaled Range Analysis Method to Ship Flow in Container Ports: Time Series Structure and Long-Range Dependence Analysis

Based on the time series of the number of ships calling at the container port, this paper takes Shanghai Port and Singapore Port as examples to analyze the statistical characteristics of ship flow time series in container ports. Then, the rescaled range analysis (R/S) method is used to study the long-range dependence (LRD) of ship flow sequence structure in maritime container ports and further analyze the influence of trend component and periodic component on Hurst exponent. The results indicate that both the ship flow time series of Shanghai Port and Singapore Port show the feature of nonlinear and nonstationary from 2013 to 2017, and the data of the two ports have sudden changes in August 2016. They all show specific long-range dependence behavior, but the long-range dependence of ship flow series in Singapore Port is relatively weak. Besides, the trend component and periodic component have significant impact on the Hurst exponent of the time series. Hence the trend component and periodic component should be removed in advance for long-range dependence analysis.

Random Number Generator with Long-Range Dependence and Multifractal Behavior Based on Memristor

Random number generators are used in areas such as encryption and system modeling, where some of these exhibit fractal behaviors. For this reason, it is interesting to make use of the memristor characteristics for the random number generation. Accordingly, the objective of this article is to evaluate the performance of a chaotic memristive system as a random number generator with fractal behavior and long-range dependence. To achieve the above, modeling memristor and its corresponding chaotic systems is performed, from which a random number generator is constructed. Subsequently, the Hurst parameter for the detection of long-range dependence is estimated and a fractal analysis of the synthesized data is performed. Finally, a comparison between the model proposed in the research and the β-MWM algorithm is made. The results obtained show that the data synthesized from the proposed generator have a variable Hurst parameter and both monofractal and multifractal behavior. The main contribution of this research is the proposal of a new model for the synthesis of traces with long-range dependence and fractal behavior based on the non-linearity of the memristor.

Network anomaly detection using a cross‐correlation‐based long‐range dependence analysis

SummaryThe detection of anomalies in network traffic is an important task in today's Internet. Among various anomaly detection methods, the techniques based on examination of the long‐range dependence (LRD) behavior of network traffic stands out to be powerful. In this paper, we reveal anomalies in aggregated network traffic by examining the LRD behavior based on the cross‐correlation function of the bidirectional control and data planes traffic. Specifically, observing that the conventional cross‐correlation function has a low measure of dissimilarity between the two planes, which leads to a reduced anomaly detection performance, we propose a modification of the cross‐correlation function to mitigate this issue. The performance of the proposed method is analyzed using a relatively recent Internet traffic captured at King Saud University. The results demonstrate that using the modified cross‐correlation function has the ability to detect low volume and short duration attacks. It also compensates for some misdetections exhibited by using the autocorrelation structures of the bidirectional traffic of the control, data, and WHOLE (combined control and data) planes traffic.

Are shocks on the returns and volatility of cryptocurrencies really persistent?

This letter questions the true nature (true versus spurious) of the Long Range Dependence (LRD) behavior observed in the returns and volatility series of four Cryptocurrencies (CC). Using a robust approach, this letter shows that the LRD behavior exhibited by the returns and volatility series of Bitcoin, Litecoin, and Ripple is a true behavior, and not a statistical artifact. As for Ethereum, the results show that the true LRD is only supported for the volatility series. Our results confirm the inefficiency of all the considered markets, with the exception of Ethereum.

Analysis of Bursty Impulsive Noise in Low-Voltage Indoor Power Line Communication Channels: Local Scaling Behaviour

Power line communication (PLC) channels are prone to multipath propagation due to impedance mismatch, and impulsive noise whose characteristics are still not well established in the literature. Moreover, measurements show that this impulsive noise appear in bursts, non-Gaussian and cyclostationary and as such cannot be modeled as the convenient additive white Gaussian noise (AWGN). Transceivers optimized for AWGN may not necessarily perform well for the PLC noise. Therefore, investigating the characteristics of PLC noise is very important for accurate modeling of the same. This study presents multifractal analysis of bursty impulsive noise measured from power line networks from three different environments. We employ multifractal detrended fluctuation analysis, which is a well-developed multifractal analysis technique for non-stationary time series data and easy to implement to analyze measured noise data. Results show that power line noise exhibits both long-range dependence (LRD) and multifractal scaling behavior with different strengths depending on the environments where they were captured. The multiscaling behavior is due to long-range correlation inherent in the power line noise. The source of this local multiscaling behavior is determined by analysis a shuffled series of the original data captured from the power network. Multifractal analysis is able to show clearly both the strengths and frequency of occurrence of bursts occurring in PLC noise which can then be applied in accurate modeling of the noise. The significance of these results is that new power line noise models should be developed that captures both LRD and multifractal scaling for more accurate performance evaluation of power line communication systems. The existing noise models though able to replicate temporal dependence of PLC noise, are not able to capture this local scaling behavior which results show is inherent in PLC noise.

Anomaly Detection Based on LRD Behavior Analysis of Decomposed Control and Data Planes Network Traffic Using SOSS and FARIMA Models

The detection of anomalies in network traffic, such as low volume attacks and abnormalities, has become a pressing problem in today’s large volume of Internet traffic. To this end, various anomaly detection techniques have been developed, including techniques based on long-range dependence (LRD) behavior estimation of network traffic. However, the existing LRD-based techniques analyze the aggregated WHOLE (control plus data) traffic, which might not be sufficient to detect short-duration and low-volume attacks and abnormalities in the traffic. This is because such anomalies might pass unnoticed in large volume of the normal background traffic. To address this issue, we propose a method that examines the LRD behavior of control and data planes traffic separately, which improves the detection efficacy. For LRD behavior analysis, the proposed method integrates the correlation structures of second-order self-similar and fractional autoregressive integrated moving average models. The performance of the proposed method is empirically evaluated and validated over a relatively recent real Internet traffic captured at King Saud University’s network. The analysis and results demonstrate that the proposed method efficiently detects such low volume and short duration attacks and abnormalities in the traffic, which would not be detected by merely analyzing the aggregated WHOLE traffic without decomposing it into control and data planes traffic.

Long-range dependence and time-clustering behavior in pedestrian movement patterns in stampedes: The Love Parade case-study

Abstract Pedestrian stampede happened more and more often during these years, such as Love Parade disaster in Germany 2010, trampling in Shanghai bund 2014 and crowd stampede in pilgrimages. Love Parade disaster 2010 stands out for well recorded videos, which are HD quality and available for researchers. There were totally seven surveillance cameras capturing the whole festival progress and the video we study is just before the disaster happened. Pedestrian motion was special and a small disturbance would lead the group to an avalanche in this kind of critical situation. Here we focus on the individual movement pattern. The trajectories of each pedestrian involved were extracted by a mean-shift algorithm. We analyzed the space–time patterns of the pedestrians involved in the Love Parade stampede by using the detrended fluctuation analysis and the coefficient of variation. Our results reveal that the pedestrians’ movement in crowd-quakes is persistent in space, globally time-clusterized but locally regular or quasi-periodic behavior. Pedestrian movement was treated as stop and go state by point process-based representation. When the threshold increases, this means that the “go” state is longer and pedestrians keep on walking in several consecutive time frames; this is difficult in crowded situations and lead to special time-clustering behavior of the sequence of “go” events. The study reveals pedestrian motion characteristics in critical situations, which will enhance the understanding of pedestrian behaviors and supply early warning features for not only Love Parade Disaster, but also other similar large events.

Fluctuation dynamics in US interest rates and the role of monetary policy

This paper presents empirical evidence suggesting that the degree of long-range dependence in interest rates depends on the conduct of monetary policy. We study the term structure of interest rates for the US and find evidence that global Hurst exponents change dramatically according to Chairman Tenure in the Federal Reserve Board and also with changes in the conduct of monetary policy. In the period from 1960s until the monetarist experiment in the beginning of the 1980s interest rates had a significant long-range dependence behavior. However, in the recent period, in the second part of the Volcker tenure and in the Greenspan tenure, interest rates do not present long-range dependence behavior. These empirical findings cast some light on the origins of long-range dependence behavior in financial assets.

The long-range dependence behavior of the term structure of interest rates in Japan

This paper presents an empirical evidence suggesting that Japanese interest rates for different maturities possess long-range dependence in both mean and volatility. For long-term bonds, predictability in the term structure of interest rates increases with maturity, suggesting that there exists a term premium. Furthermore, the dynamics of short-term interest rates (6 months) is very different from longer term bonds, as the former are anti-persistent, which implies that the zero-interest rate policy is perceived to be temporary.

Multiscale Fitting Procedure Using Markov Modulated Poisson Processes

This paper proposes a parameter fitting procedure using Markov Modulated Poisson Processes (MMPPs) that leads to accurate estimates of queuing behavior for network traffic exhibiting long-range dependence behavior. The procedure matches both the autocovariance and marginal distribution of the counting process. A major feature is that the number of states is not fixed a priori, and can be adapted to the particular trace being modeled. The MMPP is constructed as a superposition of L 2-MMPPs and one M-MMPP. The 2-MMPPs are designed to match the autocovariance and the M-MMPP to match the marginal distribution. Each 2-MMPP models a specific time-scale of the data. The procedure starts by approximating the autocovariance by a weighted sum of exponential functions that model the autocovariance of the 2-MMPPs. The autocovariance tail can be adjusted to capture the long-range dependence characteristics of the traffic, up to the time-scales of interest to the system under study. The procedure then fits the M-MMPP parameters in order to match the marginal distribution, within the constraints imposed by the autocovariance matching. The number of states is also determined as part of this step. The final MMPP with M2 L states is obtained by superposing the L 2-MMPPs and the M-MMPP. We apply the inference procedure to traffic traces exhibiting long-range dependence and evaluate its queuing behavior through simulation. Very good results are obtained, both in terms of queuing behavior and number of states, for the traces used, which include the well-known Bellcore traces.

Optimization and phase transitions in a chaotic model of data traffic.

Ohira and Sawatari [Phys. Rev E 58, 193 (1998)] introduced a simple model for a packet-switching network which was extended by Solé and Valverde [Physica A 289, 595 (2001)]. Both models used Poisson-like traffic sources. Solé and Valverde demonstrated that long-range dependence (LRD) in autocorrelation behavior can be seen in the queue length dynamics at a given node. Actual network traffic sources are known to exhibit long-range autocorrelation. To simulate the real case more closely, we have studied the effect of introducing LRD behavior at an earlier stage. We replaced the Poisson-like sources with LRD sources, modeled using chaotic maps. As was seen in the previous models, a phase transition occurs as the traffic load on a network is increased and the network changes to a congested state where the time taken for delivery of packets increases dramatically and throughput collapses. The paper reports extensive numerical results from our simulations using both Poisson and LRD sources. It demonstrates the natural network-induced LRD when sources are purely Poisson and shows strong enhancement when LRD sources are added. The model is adapted to include congestion control mechanisms and their impact is considered.

MPEG Traffic Generation Matching Intra- and Inter-GoP Correlation

VBR-compressed video traffic is expected to consti tute the majority of the B-ISDN network load in the immediate future. At the moment, the MPEG coding scheme is widely used for many types of ap plications. On account of the high burstiness and periodicity of the traffic generated by an MPEG en coder, it is crucial to obtain a model for the genera tion of sequences with the same statistical charac teristics of real MPEG traces. In this paper, after demonstrating that intra-GOP correlation, that is, the correlation between frames belonging to the same GoP', has to be taken into account, an accu rate model allowing the generation of an MPEG like trace is proposed. Moreover, as the MPEG traf fic has been demonstrated to be self-similar, that is, it presents a long-range dependence (LRD), the proposed algorithm applies a method based on the Fast Fourier Transform in order to generate self- similar traces. This algorithm allows generation of a trace, imposing the short-range dependence and LRD behavior and the probability density function of any given video sequence.

On the characterization of VBR MPEG streams

We present a comprehensive model for variable-bit-rate MPEG video streams. This model captures the bit-rate variations at multiple time scales. Long-term variations are captured by incorporating scene changes, which are most noticeable in the fluctuations of I frames. The size of an I frame is modeled by the sum of two random components: a scene-related component and an AR(2) component that accounts for the fluctuations within a scene. Two random processes of i.i.d. rvs are used to model the sizes of P and B frames, respectively. The complete model is then obtained by intermixing the three sub-models according to a given GOP pattern. It is shown that the composite model exhibits long-range dependence (LRD) in the sense that its autocorrelation function is non-summable. The LRD behavior is caused by the repetitive GOP pattern which induces periodic cross-correlations between different types of frames. Using standard statistical methods, we successfully fit our model to several empirical video traces. We then study the queueing performance for video traffic at a statistical multiplexer. The results show that the model is sufficiently accurate in predicting the queueing performance for real video streams.