Degree Of Long-range Dependence Research Articles

Profitability of private equity: mean reversion and transitory shocks

This paper deals with the analysis of the statistical properties of the profitability yielded by Private Equity from a fractionally integrated viewpoint. Using quarterly data from 1981q2 to 2021q3, the results support the hypothesis of stationarity and mean reversion in all cases; however, we observe differences in the degree of persistence across regions, Europe being the closest to short memory while the US shows the highest degree of long range dependence and thus the longer lasting effects of shocks. Some policy recommendations of the results obtained are included at the end of the manuscript.

Frequency-Domain Evidence for Climate Change

The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since conventional tests of hypotheses about the memory parameter, which measures the degree of long-range dependence, are typically based on asymptotic arguments and are therefore of limited practical value in case of small or medium sample sizes, we employ a new small-sample test as well as a related estimator for the memory parameter. To safeguard against false positive findings, simulation studies are carried out to examine the suitability of the employed methods and hemispheric datasets are used to check the robustness of the empirical findings against low-frequency natural variability caused by oceanic cycles. Overall, our frequency-domain analysis provides strong evidence of non-stationarity, which is consistent with previous results obtained in the time domain with models allowing for stochastic or deterministic trends.

One model is not enough: Heterogeneity in cryptocurrencies’ multifractal profiles

This letter studies of the multifractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that cryptocurrencies have different degree of long range dependence, and –more importantly – follow different stochastic processes. Some of them follow models closer to monofractal fractional Gaussian noises, while others exhibit complex multifractal dynamics. Regarding the source of multifractality, our results are mixed. Time series shuffling produces a reduction in the level of multifractality, but not enough to offset it. We find an association of kurtosis with multifractality.

One Model Is Not Enough: Heterogeneity in Cryptocurrencies’ Multi-fractal Profiles

This letter studies of the multi-fractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that cryptocurrencies have different degree of long range dependence, and — more importantly — follow different stochastic processes. Some of them follow models closer to mono-fractal fractional Gaussian noises, while others exhibit complex multi-fractal dynamics. Regarding the source of multi-fractality, our results are mixed. Time series shuffling produces a reduction in the level of multi-fractality, but not enough to offset it. We find an association of kurtosis with multi-fractality.

Application of Wavelet-Based Maximum Likelihood Estimator in Measuring Market Risk for Fossil Fuel

Energy commodity prices are inherently volatile, since they are determined by the volatile global demand and supply of fossil fuel extractions, which in the long-run will affect the observed climate patterns. Measuring the risk associated with energy price changes, therefore, ultimately provides us with an important tool to study the economic drivers of climate changes. This study examines the potential use of long-memory estimation methods in capturing such risk. In particular, we are interested in investigating the energy markets’ efficiency at the aggregated level, using a novel wavelet-based maximum likelihood estimator (waveMLE). We first compare the performance of various conventional estimators with this new method. Our simulated results show that waveMLE in general outperforms these previously well-established estimators. Additionally, we document that while energy returns realizations follow a white-noise and are generally independent, volatility processes exhibits a certain degree of long-range dependence.

Classification of acoustic noise signals using wavelet spectrum based support vector machine

Harsh noises come from air-conditioning units are chronic complaining issues to their users. Individual perceptions of noise levels have been generally quantified by means of subjective evaluation such as a jury test. This article proposes a classification approach to acoustic noise signals using a wavelet spectrum analysis. We derive energy spectrums of noise signals using a discrete wavelet transform at pre-specified window length. The energy spectrums are a linear form and represented by a Hurst parameter as an informative summary of long-range dependent signal data. The Hurst parameter controls the self-similarity scaling as well as the degree of long-range dependence. We estimate the Hurst parameter through the least squares regression of sample energy against a resolution level in the wavelet spectral domain. In the context of multi-class classification problem, the classification of noise signals is performed by a nonlinear support vector machine (SVM) for parameter estimates of linear energy profiles containing the Hurst parameter. In an application example of air-conditioner noise signals, empirical results show that the proposed method offers the higher level of accuracy in acoustic noise sound classification.

Do global CO2 emissions from fossil-fuel consumption exhibit long memory? a fractional-integration analysis

ABSTRACTIn this article we use an autoregressive fractionally integrated moving average approach to measure the degree of fractional integration of aggregate world CO2 emissions and its five components – coal, oil, gas, cement, and gas flaring. We find that all variables are stationary and mean reverting, but exhibit long-term memory. Our results suggest that both coal and oil combustion emissions have the weakest degree of long-range dependence, while emissions from gas and gas flaring have the strongest. With evidence of long memory, we conclude that transitory policy shocks are likely to have long-lasting effects, but not permanent effects. Accordingly, permanent effects on CO2 emissions require a more permanent policy stance. In this context, if one were to rely only on testing for stationarity and non-stationarity, one would likely conclude in favour of non-stationarity, and therefore that even transitory policy shocks have permanent effects. Our fractional-integration analysis highlights that this is not the case.

Dynamic efficiency of stock markets and exchange rates

We use generalized Hurst exponents to investigate long-range dependence across countries that have implemented an inflation targeting monetary policy regime and have a floating currency regime. We show that the degree of long-range dependence has changed after the 2008 crisis for equity markets but not as much for exchange rate markets. We compare results for developed and emerging economies and find that there still are some important differences but not as they were before the crisis. We also include an additional set of relevant countries and find that our results are more pronounced for inflation targeters. We discuss several implications of these results.

Hurst Index of Functions of Long-Range-Dependent Markov Chains

A positive recurrent, aperiodic Markov chain is said to be long-range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long-range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queueing networks, source compression, and finance.

Hurst Index of Functions of Long-Range-Dependent Markov Chains

A positive recurrent, aperiodic Markov chain is said to be long-range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long-range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queueing networks, source compression, and finance.

A wavelet based investigation of long memory in stock returns

Using a wavelet-based maximum likelihood fractional integration estimator, we test long memory (return predictability) in the returns at the market, industry and firm level. In an analysis of emerging market daily returns over the full sample period, we find that long-memory is not present and in approximately twenty percent of 175 stocks there is evidence of long memory. The absence of long memory in the market returns may be a consequence of contemporaneous aggregation of stock returns. However, when the analysis is carried out with rolling windows evidence of long memory is observed in certain time frames. These results are largely consistent with that of detrended fluctuation analysis. A test of firm-level information in explaining stock return predictability using a logistic regression model reveal that returns of large firms are more likely to possess long memory feature than in the returns of small firms. There is no evidence to suggest that turnover, earnings per share, book-to-market ratio, systematic risk and abnormal return with respect to the market model is associated with return predictability. However, degree of long-range dependence appears to be associated positively with earnings per share, systematic risk and abnormal return and negatively with book-to-market ratio.

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.

An improved Hurst parameter estimator based on fractional Fourier transform

A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically possesses long-range dependence with known Hurst parameters to test the accuracy of the proposed Hurst parameter estimator. For justifying the advantage of the proposed estimator, some other existing Hurst parameter estimation methods, such as wavelet-based method and a global estimator based on dispersional analysis, are compared. The proposed estimator can process the very long experimental time series locally to achieve a reliable estimation of the Hurst parameter.

A hierarchical clustering scheme approach to assessment of IP-network traffic using detrended fluctuation analysis

This paper presents an approach to the assessment of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view in analyzing the degree of long-range dependence (LRD) of IP-network traffic, we use a hierarchical clustering scheme, which provides a way to classify high-dimensional data with a tree-like structure. Also, in the LRD-based analysis, we employ detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in non-stationary time-series signals. Based on sequential measurements of IP-network traffic at two locations, this paper derives corresponding values for the LRD-related parameter α that reflects the degree of LRD of measured data. In performing the hierarchical clustering scheme, we use three parameters: the α value, average throughput, and the proportion of network traffic that exceeds 80% of network bandwidth for each measured data set. We visually confirm that the traffic data can be classified in accordance with the network traffic properties, resulting in that the combined depiction of the LRD and other factors can give us an effective assessment of network conditions at different times.

Long-range dependence in interest rates and monetary policy

This Letter studies the dynamics of Brazilian interest rates for short-term maturities. The Letter employs developed techniques in the econophysics literature and tests for long-range dependence in the term structure of these interest rates for the last decade. Empirical results suggest that the degree of long-range dependence has changed over time due to changes in monetary policy, specially in the short-end of the term structure of interest rates. Therefore, we show that it is possible to identify monetary arrangements using these techniques from econophysics.

Time-varying long-range dependence in US interest rates

Abstract This paper presents empirical evidence of time-varying long-range dependence for 1, 3, 5 and 10 years interest rates for the US. Based on the local Whittle method empirical results suggest that the degree of long-range dependence in the US interest rates has significantly decreased over time.

Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence

Abstract. We consider semiparametric estimation in time‐series regression in the presence of long‐range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain‐weighted least squares estimates, which includes both narrow‐band ordinary least squares and narrow‐band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time‐series regression with long‐range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long‐range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite‐sample performance of the generalized least squares estimate and the feasible estimate.

Stock market prices and long-range dependence

Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit long-range dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the modified rescaled adjusted range or R/S statistic that was proposed by Lo [17] as a test for long-range dependence with good robustness properties under “extra” short-range dependence. Our main conclusion is that because the modified R/S statistic shows a strong preference for accepting the null hypothesis of no long-range dependence, irrespective of whether long-range dependence is present in the data or not, Lo's acceptance of the hypothesis for the CRSP data (i.e., no long-range dependence in stock market prices) is less conclusive than is usually regarded in the econometrics literature. In fact, upon further analysis of the data, we find empirical evidence of long-range dependence in stock price returns, but because the corresponding degree of long-range dependence (measured via the Hurst parameter H) is typically very low (i.e., H-values around 0.60), the evidence is not absolutely conclusive.