Presence Of Long-range Dependence Research Articles

Stochastic mortality dynamics driven by mixed fractional Brownian motion

Recently, the long-range dependence (LRD) of mortality dynamics has been identified and studied in the actuarial literature. The non-Markovian feature caused by LRD can raise new challenges in actuarial valuation and risk management. This paper proposes a new modeling approach that uses a combination of independent Brownian motion and fractional Brownian motion to achieve a flexible setting on capturing the LRD in mortality dynamics. The closed-form solutions of survival probabilities are derived for valuation and hedging purposes. To obtain mortality sensitivity measures in the presence of LRD, we develop a novel derivation method using directional derivatives. Our method is flexible in the sense that it can not only reflect the effect of LRD on mortality sensitivities, but also include some existing sensitivity measures as a special case. Finally, we provide a numerical illustration to analyze the performance of different sensitivity measures in a natural hedge of mortality risk.

A long-memory analysis for the CBOE Brazil ETF volatility index

PurposeThe main goal of this paper is to investigate whether there is long-memory behavior in the CBOE Brazil ETF volatility index (named here VIXBR). As structural breaks may create a spurious long-range dependence, the presence of structural breaks is also gauged.Design/methodology/approachThe study considers the period from October 2011 to March 2021, using daily data. To test the long-memory behavior, three empirical approaches are adopted: GPH, ELW and robust GPH (RGPH) estimator. To estimate the structural break points adopted to date the subsamples, the ICSS algorithm is used.FindingsResults considering the total period (TP) and subsamples show that the breaks did not create a spurious long-memory behavior and together with the rolling estimation, reveal strong evidence of the long-range dependence in the CBOE Brazil ETF volatility index. The higher degree of persistent of the VIXBR series suggests an extended period of increased uncertainty that agents need consider when making their investment decision.Research limitations/implicationsAs possible extension of this study is to investigate the behavior of long memory and structural breaks for different frequencies (weekly, monthly, among others).Practical implicationsThe presence of long-range dependence in the CBOE Brazil ETF volatility index reveals that the past information is important for the predictability of risks, and therefore, can help to protect against market risks, which has important implications regarding the future decisions of economic agents (for example, policy makers and investors).Originality/valueBrazil is an emerging capital market (ECM) that has attracted a great deal of attention from investors and investment funds seeking to diversify its assets. This paper contributes to the empirical financial literature, by studying the long-memory behavior of the CBOE Brazil ETF volatility index, considering possible structural breaks. To the best of knowledge, this has not been done so far.

Long-Range Dependence and Multifractality of Ship Flow Sequences in Container Ports: A Comparison of Shanghai, Singapore, and Rotterdam

The prediction of ship traffic flow is an important fundamental preparation for layout and design of ports as well as management of ship navigation. However, until now, the temporal characteristics and accurate prediction of ship flow sequence in port are rarely studied. Therefore, in this study, we investigated the presence of long-range dependence in container ship flow sequences using the Multifractal Detrended Fluctuation Analysis (MF-DFA). We considered three representative container ports in the world—including Shanghai, Singapore, and Rotterdam container ports—as the study sample, from 1 January 2013 to 31 December 2017. Empirical results suggested that the ship flow sequences are deviated from normal distribution, and the sequences with different time scales exhibited varying degrees of long-range dependence. Furthermore, the ship flow sequences possessed a multifractal nature, where the larger the time scale of ship flow time series, the stronger the multifractal characteristics are. The weekly ship flow sequence in the port of Singapore owned the highest degree of multifractality. Furthermore, the multifractality presented in the ship flow sequences of container ports are due to the correlation properties as well as the probability density function of the ship flow sequences. The study outlines the importance of adopting these features for an accurate modeling and prediction for maritime ship flow series.

Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

In this paper, the presence of seasonality, stationarity, and long-range memory structures are detected in daily radon measurements in a permanent monitoring station in central Italy. The transient dynamics and the seasonality structure are identified by power spectral analysis based on the continuous wavelet transformation and a clear 1-year periodicity emerges. The stationarity in the data is assessed with the Dickey Fuller test; the decay of the estimated autocorrelation function and the estimated Hurst exponent indicate the presence of long-range dependence. All the main characteristics of the data have been properly included in a modelling structure. In particular, an autoregressive fractionally integrated moving average (ARFIMA) model is estimated and compared with the classical ARMA and ARIMA models in terms of goodness of fit and, secondarily, of forecast evaluation. An autoregressive model with a non-integer values of the differencing parameter ($d=0.278$) resulted to be the most appropriate on the basis of Akaike Information Criterion, the diagnostic on the residuals, and the Root Mean Squared Error. The results suggest that there is statistically-significant evidence for not rejecting the presence of long memory in the radon concentration. The radon measurements are better characterised as being stationary, but with long memory and so the statistical dependence decays more slowly than an exponential decay.

R-Squared-Bootstrapping for Gegenbauer-Type Long Memory

The autocorrelation of long memory processes decays much slower than that of short memory processes, e.g. autoregressive processes. Fractional integration and Gegenbauer are basic models that show long memory behavior. Many tests for long memory of the fractional integration type (at f = 0) have been developed based on test statistics (e.g. the R/S-type statistics) or parameter estimators (e.g. the GPH estimator). But, so far, no work has shown reasonable power on testing for cyclic long memory. The authors investigate a parametric bootstrap procedure with an R-squared statistic as an assessment of cyclic long memory behavior. According to simulation results, the R-squared-bootstrapping method performs excellently in detecting Gegenbauer-type processes (e.g. with long memory behavior associated with frequencies $$f\in (0,0.5]$$ ) while at the same time controlling observed significance levels. The R-squared-bootstrapping test is also applied to the Lynx data and the result suggests the presence of long range dependence.

Long range dependence in cloud servers: a statistical analysis based on Google workload trace

Analysis and characterization of cloud workloads provides crucial information for designing optimal resource management policies. In this work, we propose to analyse long range dependence nature of cloud resource workloads. Long range dependence is a phenomenon widely studied in Ethernet and Internet traffic. But there is a dearth of works that analyse long range dependence in cloud workloads. In this work, we propose to verify the presence of long range dependence in cloud workloads using autocorrelation analysis and rescaled range analysis method. In addition to experimental evidence, studies on long range dependence are incomplete without a sound theoretical justification in support of its origins in cloud workloads. In this context, we propose to analytically analyse, aggregate workload in the datacenter using different metrics like arrival, service distributions of jobs and their resource usage. For a dependable explanation of long range dependence in cloud workloads, we analyse workloads from standard real dataset of Google cluster trace. Based on the analysis, we see that analysed metrics display heavy tailed behaviour and using a mathematical formulation, we prove that aggregate workload exhibits long range dependence.

Time Varying Efficiency in Indian Sectors: An Event Study on Demonetization

The study examines the level of inefficiency present in three different sectors of India. More specifically, it applies different estimation techniques to measure the level of efficiency across the agriculture, service and manufacturing sectors by choosing twenty stocks from each of them. Since there are multiple industries belonging to a particular sector, capturing the intra-industry differential in their efficiencies is also crucial. Presence of long range dependence and the time-varying efficiency across the industries belonging to different sectors have been tested. Then, the impact of recent macroeconomic event of Demonetization on these industries have been explored using six event windows. The results confirm that the impact of this event on the industry returns are mostly negative and significant. However, the magnitude of impact varies across industries depending on the level of demand uncertainty and their cash dependence. Finally, the robustness of our findings has been checked using fixed effect panel regression which further validates the results of the event study.

Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization

This paper deals with the asymptotic behavior of random oscillatory integrals in the presence of long-range dependence. As a byproduct, we solve the corrector problem in random homogenization of onedimensional elliptic equations with highly oscillatory random coefficients displaying long-range dependence, by proving convergence to stochastic integrals with respect to Hermite processes.

Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of the US Banking Sector

This paper compares the forecasting performances of both univariate and multivariate models for realized volatilities series. We consider realized volatility measures of the returns of 13 major banks traded in the NYSE. Since our variables are characterized by the presence of long range dependence, we use several modelling approaches that are able to capture such feature. We look at the forecasting accuracy of the considered models to make inference on the underlying mechanism that has generated volatilities of the assets. Our main conclusion is that the contagion effect among the considered volatilities is small or, at least, not well captured by the considered multivariate models.

Change point estimation based on Wilcoxon tests in the presence of long-range dependence

We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are established. In the case of a constant shift height, the $1/n$ convergence rate (with $n$ denoting the number of observations), which is typical under the assumption of independent observations, is also achieved for long memory sequences. It is proved that if the change point height decreases to $0$ with a certain rate, the suitably standardized estimator converges in distribution to a functional of a fractional Brownian motion. The estimator is tested on two well-known data sets. Finite sample behaviors are investigated in a Monte Carlo simulation study.

Testing for a Change in Mean under Fractional Integration

Abstract We consider testing for the presence of a change in mean, at an unknown point in the sample, in data that are possibly fractionally integrated, and of unknown order. This testing problem has recently been considered in a number of papers, most notably Shao (2011, “A Simple Test of Changes in Mean in the Possible Presence of Long-Range Dependence.” Journal of Time Series Analysis 32:598–606) and Iacone, Leybourne, and Taylor (2013b, “A Fixed-b Test for a Break in Level at an Unknown Time under Fractional Integration.” Journal of Time Series Analysis 35:40–54) who employ Wald-type statistics based on OLS estimation and rely on a self-normalization to overcome the fact that the standard Wald statistic does not have a well-defined limiting distribution across different values of the memory parameter. Here, we consider an alternative approach that uses the standard Wald statistic but is based on quasi-GLS estimation to control for the effect of the memory parameter. We show that this approach leads to significant improvements in asymptotic local power.

Do carry trade returns show signs of long memory?

Abstract Using Hurst coefficient approaches within rescaled range, detrended fluctuation, periodogram regression and average wavelet coefficient frameworks, this article examines the dynamics of currency carry trades. Specifically, we look for evidence of long-range dependence (LRD) in carry trade returns (CTR) of thirteen developed and nine emerging markets. Our analysis provides two important insights. (a) We find strong and robust evidence of LRD for CTR in developed markets and somewhat weaker evidence in emerging markets. Considering that CTR are vital components of modern financial models, these results have far-reaching consequences because, in the presence of LRD, traditional asset pricing methods/tests are no longer valid. (b) We also show that portfolios focusing on only the most persistent carry trades (highest Hurst coefficients among the ones above 0.5) can significantly outperform their all-encompassing counterparts. This implies that Hurst coefficients contain important investment information which can be used to enhance the performance of practical carry trade strategies.

Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis

The aim of this paper is to propose an empirical strategy that allows the discrimination between true and spurious long memory behaviors. That strategy is based on the comparison between the estimated long memory parameter before and after filtering out the breaks. To date the breaks, we use the probability smoothing of the Markov Switching GARCH model of Haas et al. (2004). Application of this strategy to the crude oil, heating oil, RBOB regular gasoline and the propane futures energy with the one, two, three and four months maturities show strong evidence for the presence of long range dependence in all futures energy prices volatility11As proxy of volatility, we use the squared returns. Others proxies are used in the empirical studies such as the absolute value of returns. Our empirical studies show there are strong differences between these two proxies. time series. This result of long range dependence in the volatility is confirmed by the superiority of the FIGARCH and FIEGARCH models compared with the Markov switching GARCH models in terms of out-of-sample forecasting and value at risk (VaR) performances. Moreover, we show that the proposed empirical strategy is robust to different data frequency. Practical implications of the results for market participants are proposed and discussed.

Modeling Long Memory in Volatility for Spot Price of Lentil with Multi-step Ahead Out-of-sample Forecast Using AR-FIGARCH Model

The potential presence of long memory (LM) properties in return and volatility of the spot price of lentil in Indore market has been investigated. Geweke and Porter-Hudak (1983) (GPH) method has been applied to test for presence of long range dependence in the volatility processes for the series. Stationarity of the series has been tested using Augmented Dickey-Fuller (ADF) unit root test and Philips-Peron (PP) unit root test. It is observed that both the log returns as well as squared log returns series are stationary at level but there is a significant presence of long memory in squared log return series. Accordingly, AR-FIGARCH model was applied for forecasting the volatility of lentil price. To this end, window based evaluation of forecasting is carried out with the help of Mean squares prediction error (MSPE), Root MSPE (RMSPE), Mean absolute prediction error (MAPE) and Relative MAPE (RMAPE). The residuals of the fitted models were used for diagnostic checking. Out-of sample forecast of volatility has been computed for 1st June-31st July, 2015 along with the percentage deviation from the actual price. The maximum deviation has been found to be 2.55%. The R software package has been used for data analysis.

Multiscaling and Stock Market Efficiency in China

China has taken important steps to reform its economy and capital markets in the past 20 years. Despite these efforts there is a lack of quantitative evidence on how these measures have impacted price returns in the stock exchanges. The purpose of this research was to determine the randomness of Chinese equity returns and to measure the scaling property of volatility over time. The main assumption of the Efficient Market Hypothesis is that security returns follow the path of a random walk and that volatility scales with the square root of time. This notion was tested by analyzing daily stock returns of the Shanghai- and Shenzhen Composite Indexes between 1990 and 2013. The Kolmogorov–Smirnov (KS) test rejected the log-normal distribution and random walk hypothesis. The measured Hurst exponents revealed a multiscaling property of fractal Brownian motion and indicated the presence of long-range dependence. The findings also showed that the degree of persistence and cycle length has reduced over time.

Evidence of Long Memory in the Indian Stock Market

This article tests the small sample properties of three approaches in estimating the long-range dependence measure (the R/S approach, the R/S-AL approach and the Detrending Moving Average (DMA) approach) using Monte Carlo simulation experiments. We use simulated series of Gaussian noise and fractional Gaussian noise of varying lengths (252, 504, 1008, 2016 and 4032) which approximately represents daily data series of 1 year, 2 years, 4 years, 8 years and 16 years period. We observe a pronounced reduction in the variance and the mean absolute error under the DMA approach when the sample size increases, which indicates that the DMA approach performs better than the R/S and the R/S-AL approaches. In addition, we test for the presence of long memory in daily data from the Indian stock market. In particular, we examine the dynamic nature of market efficiency in the Indian stock market by using a moving sub-sample window of 1,008 observations (approximately 4 years of daily data). Our findings support the presence of long-range dependence in the Indian stock market. Furthermore, S&P CNX Nifty shows a highly dynamic behaviour in its efficiency characteristics.

Asymmetric long memory volatility in the PIIGS economies

PurposeThe main purpose of this paper is to examine the asymmetry and long memory properties in the volatility of the stock indices of the PIIGS economies (Portugal, Ireland, Italy, Greece and Spain).Design/methodology/approachThe paper utilizes the wavelets approach (based on Haar, Daubechies‐4, Daubechies‐12 and Daubechies‐20 wavelets) and the GARCH class of models (namely, ARFIMA (p,d′,q)‐GARCH (1,1), IGARCH (1,1), FIGARCH (1,d,0), FIGARCH (1,d,1), EGARCH (1,1) and FIEGARCH (1,d,1)) to accomplish the desired goals.FindingsThe findings provide evidence in support of the presence of long range dependence in the various proxies of volatility of the PIIGS economies. The results from the wavelet approach also support the Taylor effect in the volatility proxies. The results show that ARFIMA (p,d′,q)‐FIGARCH (1,d,0) model specification is better able to capture the long memory property of conditional volatility than the conventional GARCH and IGARCH models. In addition, the ARFIMA (p,d′,q)‐FIEGARCH (1,d,1) model is better able to capture the asymmetric long memory feature in the conditional volatility.Originality/valueThis paper has both methodological and empirical originality. On the methodological side, the study applies the wavelet technique on the major proxies of volatility (squared returns, absolute returns, logarithm squared returns and the range) because the wavelet‐based estimator exhibits superior properties in modeling the behavior of the volatility of stock returns. On the empirical side, the paper finds asymmetry and long range dependence in the conditional volatility of the stock returns in PIIGS economies using the GARCH family of models.

Wavelet Spectrum for Investigating Statistical Characteristics of UDP-Based Internet Traffic

In this paper, we consider statistical characteristics of real User Datagram Protocol (UDP) traffic. Four main issues in the study include(i) the presence of long rangedependence (LRD) in the UDP traffic,(ii) the marginal distribution of the UDP traces,(iii) dependence structure of wavelet coefficients,(iv) and performance evaluation of the Hurst parameter estimation based on different numbers of vanishing moments of the mother wavelet . By analyzing a large set of real traffic data, it is evident that the UDP Internet traffic reveals the LRD properties with considerably high non-stationary processes.Furthermore, it exhibits non-Gaussian marginal distributions. However, by increasing the number of vanishing moments,it is impossible to achieve reduction fromLRD to become a short range dependence. Thus, it can be shown that there is no significant difference in performance estimation of the Hurst parameter for different numbers of vanishing moments of the mother wavelet.

What can wavelets reveal about SOFIX?

The current paper investigates the major index of the Bulgarian Stock Exchange with respect to the presence of long- range dependence and principal predictability of the index. The wavelet transform is utilized in order to carry out the investigation since it is a well-suited tool for the analysis of fractal processes and sheds additional light to the term structure of the index. In recent papers Lomev and co-writers (1-3) confirm the presence of long-range dependence (LRD) of SOFIX on other East-European stock exchange indexes. The presence of LRD is closely related to persistency, that is, positive values are likely to be followed by positive values and negative values are likely to be followed by negative values. The latter implies that the chance to predict correctly the future direction of the process is greater than 50%. Actually, the problem of predictability of SOFIX has been already investigated by Lomev and Ivanov (4) and it turns out that the index is predictable. From this point of view the current paper utilizes the wavelet transform in two directions. Firstly, LRD presence for SOFIX is detected. Secondly, wavelet-based forecasts are developed for the index, in order to test it for principal predictability and to investigate its term structure. A good reasoning behind the application of the wavelet transform is that it is a proper tool for the analysis of financial data. On one hand financial data incorporates information about decisions and actions taken by market participants, operating over different time horizons and on the other hand the wavelet transform of some series decomposes the original sequence over a range of frequency scales. The wavelet transform may be continuous or discrete; however for empirical purposes the discrete wavelets transform (DWT) is preferred. Different algorithms are developed for the implementation of DWT, each one having its advantages and drawbacks. A detailed discussion may be found for example in (5), (6). The current investigation utilizes the triangle algorithm of Mallat (7) for the detection of LRD and the a trous wavelet transform (6) for prediction purposes.

A simple test of changes in mean in the possible presence of long-range dependence

We propose a simple testing procedure to test for a change point in the mean of a possibly long-range dependent time series. Under the null hypothesis, the series is stationary with long-range dependence and our test statistic converges to a non-degenerate distribution, whereas under the alternative, the series has a change point in the mean and the test statistic diverges to infinity. We demonstrate the good size and power properties of our test via simulations and illustrate its usefulness by analysing two real data sets.