Recurrence Interval Analysis Research Articles

Recurrence Interval Analysis of the US Bitcoin Market

We considered the daily price dynamics of the US Bitcoin market in the period from 2015 to 2022. In the first step, we used a singular value decomposition (SVD) entropy method for assessing time-varying informational efficiency over different time scales, from weeks to quarters. It was shown that the US Bitcoin market has been informationally efficient most of the time, except for some isolated periods where the returns exhibited deviations from the random behavior. The COVID-19 pandemic has not impacted the informational efficiency. This suggests that the Bitcoin market is unpredictable, and no reliable predictions can be obtained. A further analysis was carried out by considering the recurrence intervals for different positive and negative returns. We found that the distribution of recurrence intervals for positive and negative returns is asymmetric, with mean values higher for negative returns. We found that the distribution of recurrence intervals can be described by a stretching exponential distribution, such that the empirical and analytical hazard probabilities as functions of the elapsed time show good agreement.

Climate change projections of continental-scale streamflow across the Mississippi River Basin

A large body of scientific research has demonstrated a changing climate, which affects river flow regimes and extreme flood frequencies and magnitudes. The magnitude and frequency of extreme events are of critical importance in the evaluation of river systems to inform flood risk reduction under current and future conditions. The global climate projections from the Coupled Model Intercomparison Project, Phase 5 (CMIP5) datasets were used by the Variable Infiltration Capacity (VIC) land surface model to produce a runoff dataset, implementing a Bias-Correction Spatial Disaggregation (BCSD) approach. The resulting runoff was then used as input to the Routing Application for Parallel computatIon of Discharge (RAPID) river routing model to simulate daily flows within all 1.2 million Mississippi River Basin river reaches for years 1950 through 2099. This research effort analyzed the performance of the models for the historical time period, comparing with the observations at 64 gage locations for 16 different climate models. A recurrence interval analysis was performed to determine the 2-, 5-, 10-, 50-, 100-, 500-, and 1000-year events within both the historical and projected time periods, highlighting the relative changes predicted into the future. Anticipated seasonal changes are demonstrated by comparing monthly average streamflows for three different time periods (1951–2005, 2006–2049, and 2050–2099). Results indicate that the hydrologic conditions of the Lower Mississippi River are not stationary. Based on all 16 models considered in this study, the median of the model projections shows an 8% increase in the 100-year return period discharge at Vicksburg, Mississippi, into the future time period, although the full range of 16 models varies widely from − 11 to + 85% change in the 100-year discharge in the future.

Predicting tail events in a RIA-EVT-Copula framework

Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) in extreme value theory (EVT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these extremes. We find that the waiting time between consecutive extremes (recurrence interval) follows a q-exponential distribution, and the sizes of extremes above the thresholds (exceeding size) conform to a generalized Pareto distribution. We also find that there is a significant correlation between recurrence intervals and exceeding sizes. We thus model the joint distribution of recurrence intervals and exceeding sizes through connecting the two corresponding marginal distributions with the Frank and Ali-Mikhail-Haq (AMH) copula functions, and apply this joint distribution to estimate the hazard probability to observe another extreme in Δt time since the last extreme happened t time ago. Furthermore, an extreme predicting model based on RIA-EVT-Copula is proposed by applying a decision-making algorithm on the hazard probability. Both in-sample and out-of-sample tests reveal that this new extreme forecasting framework has better predicting performance than the forecasting model based on the hazard probability only estimated from the distribution of recurrence intervals. Our results not only shed a new light on understanding the occurring pattern of extremes in financial markets, but also improve the accuracy of predicting financial extremes for risk management.

Research on Load Fluctuation of Electronic Information Industry Based on Recurrence Interval Analysis

With the upgrading and adjustment of China's industrial structure, the load of the electronic information industry is increasingly important. The safety of production and electricity is a major concern in the electronic information industry. This paper adopts the recurrence interval analysis method to investigate the risk prediction of extreme load fluctuations and proposes a suitable risk threshold setting method for the electronic information industry. Initially, the probability distribution model of recurrence intervals is established by adding the stretched exponential distribution function to analyze the recurrence law of load fluctuations. Then, this paper introduces the conditional probability density function to verify the short-term memory effect on the fluctuations. The risk predication model is further established to estimate the risk probability of the recurrence of extreme load fluctuations. At last, a risk threshold is set for identifying abnormal operating conditions of electronic enterprises based on the risk probability. The results indicate that for the typical electronic enterprise, the risk probability of recurrence of extreme load fluctuations is greater within 20 minutes after the last extreme load fluctuation occurred. It is very likely that abnormal operating conditions will occur within the duration. Based on the analysis results, managers of electronic enterprises can better arrange safety inspections.

Investigating large-amplitude protein loop motions as extreme events using recurrence interval analysis

We investigate large amplitude motions of the two key residues ASP49 and PHE142 in β-lactamase inhibitor protein BLIP as extreme events, using recurrence interval analysis. The recurrence intervals for distance returns between the centers of mass of these two residues over a period of 300 ns are calculated. We find that the probability distribution functions for these recurrence intervals above a range of positive threshold q>0, Pq(τ), show limited scaling with the mean recurrence interval τavgat each respective threshold as Pq(τ)=1τavgf(τ∕τavg). Half of the scaled distributions are fitted by a power law t−γ at the significance level of 1%, with γ’s ranging from 1.72 to 1.79 for the corresponding thresholds. A stretched exponential fit exp−(ττavg)γ, fails at the 1% significance level for all of the scaled distributions. The scaled distributions also show short term and long term memory behavior, which is removed by shuffling the distance return time series.

Forecasting extreme atmospheric events with a recurrence-interval-analysis-based autoregressive conditional duration model

With most city dwellers in China subjected to air pollution, forecasting extreme air pollution spells is of paramount significance in both scheduling outdoor activities and ameliorating air pollution. In this paper, we integrate the autoregressive conditional duration model (ACD) with the recurrence interval analysis (RIA) and also extend the ACD model to a spatially autoregressive conditional duration (SACD) model by adding a spatially reviewed term to quantitatively explain and predict extreme air pollution recurrence intervals. Using the hourly data of six pollutants and the air quality index (AQI) during 2013–2016 collected from 12 national air quality monitoring stations in Beijing as our test samples, we attest that the spatially reviewed recurrence intervals have some general explanatory power over the recurrence intervals in the neighbouring air quality monitoring stations. We also conduct a one-step forecast using the RIA-ACD(1,1) and RIA-SACD(1,1,1) models and find that 90% of the predicted recurrence intervals are smaller than 72 hours, which justifies the predictive power of the proposed models. When applied to more time lags and neighbouring stations, the models are found to yield results that are consistent with reality, which evinces the feasibility of predicting extreme air pollution events through a recurrence-interval-analysis-based autoregressive conditional duration model. Moreover, the addition of a spatial term has proved effective in enhancing the predictive power.

A New Perspective on Improving Hospital Energy Administration Based on Recurrence Interval Analysis

Based on 15-min high-frequency power load data from a Chinese hospital, by adopting recurrence interval analysis, an attempt is made to provide a new perspective for improving hospital energy administration in electrical efficiency and safety. Initially, the definition of extreme fluctuation of the power load, as well as the recurrence interval, is given. Next, the stretched exponential distribution function is provided, which fits quite well with the probability density distribution of recurrence intervals. Then, tests on recurrence intervals, including scaling behavior and short-term and long-term memory effect are conducted. At last, a risk estimation method of VaR is proposed for hospital energy administrator to forecast risk probability. Results clearly indicate that the recurrence interval analysis (RIA) method works well on forecasting extreme power load fluctuation in hospital. However, there is no evidence to support the existence of the long-term memory effect of recurrence intervals, which means that hospital energy management plans have to be continuously fixed and updated with time. Some relevant applicant suggestions are provided for the energy administrator at the end of this paper.

Recurrence Interval Analysis on Electricity Consumption of an Office Building in China

The energy management of office buildings has been a rising concern for owners, researchers, and energy suppliers. The volatility of power load in office buildings threatens energy consumption and risks device security. This paper investigates the load fluctuation patterns in an office building based on user data, using recurrence interval analysis for different thresholds. The recurrence intervals of volatility are fitted by stretched exponential distribution, from which the probability density function is derived. Then, the short-term and long-term memory effect on the fluctuations are learned by conditional probability density function and multifractal detrended fluctuation analysis, respectively. A hazard function is further established to analyze the risk estimation of load volatility and derive the value at risk (VaR). Thus, a functional relationship has been established between average recurrence interval and threshold. The methodology and analysis results addressed in this paper help to understand load fluctuation patterns and aid in the design of energy consumption strategies in office buildings. According to the results of our research, conclusions and management suggestions are provided at the end of this paper.

Sustainable Energy Consumption in Northeast Asia: A Case from China’s Fuel Oil Futures Market

The sustainable energy consumption in northeast Asia has a huge impact on regional stability and economic growth, which gives price volatility research in the energy market both theoretical value and practical application. We select China’s fuel oil futures market as a research subject and use recurrence interval analysis to investigate the price volatility pattern in different thresholds. We utilize the stretched exponential function to fit the pattern of the recurrence intervals of price fluctuations and find that the probability density functions of the recurrence intervals in different thresholds do not show the scaling behavior. Then the conditional probability density function and detrended fluctuation analysis prove that there is short-term and long-term correlation. Last, we use a hazard function to introduce the recurrence intervals into the (value at risk) VaR calculation and establish a functional relationship between the mean recurrence interval and the threshold. Following this result, we also shed light on policy discussion for hedgers and government.

The Recurrence Interval Difference of Power Load in Heavy/Light Industries of China

The significant fluctuation of industrial electricity consumption has a high impact on power load, which makes the research on recurrence intervals between extreme events of theoretical and practical significance. The study uses a high-frequency data of heavy and light industries and employs recurrence interval analysis in different thresholds. We find that the reoccurrence interval of volatility can fit with the stretched exponential function and the probability density functions of recurrence intervals in various thresholds shows a scaling behavior. Then, the conditional probability density function and the multifractal detrended fluctuation analysis demonstrate the existence of short-range correlation, long-range correlation, and multifractal properties, respectively. We further construct a hazard function, introduce recurrence intervals into VaR calculation and establish a functional relationship between average recurrence interval and threshold. Following this result, we also shed light on policy discussion for multi-industrial electricity supply management.

Short term prediction of extreme returns based on the recurrence interval analysis

Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals—the waiting time between consecutive extremes—we show that these extreme returns are predictable in the short term. Examining a range of different types of returns and thresholds we find that recurrence intervals follow a q-exponential distribution, which we then use to theoretically derive the hazard probability . Maximizing the usefulness of extreme forecasts to define an optimized hazard threshold, we indicate a financial extreme occurring within the next day when the hazard probability is greater than the optimized threshold. Both in-sample tests and out-of-sample predictions indicate that these forecasts are more accurate than a benchmark that ignores the predictive signals. This recurrence interval finding deepens our understanding of reoccurring extreme returns and can be applied to forecast extremes in risk management.

Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets

Forecasting extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between successive volatilities exceeding a certain threshold Q, which has a one-to-one correspondence with the expected recurrence time . We find that the recurrence intervals with large are well approximated by the stretched exponential distribution for all stocks. Thus, an analytical formula for determining the hazard probability that a volatility above Q will occur within a short interval if the last volatility exceeding Q happened t periods ago can be directly derived from the stretched exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above Q based on the hazard probability. Using the ‘receiver operator characteristic’ analysis, we find that this prediction method efficiently forecasts the occurrence of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and quantify more accurately financial risks in stock markets.

Risk estimation of CSI 300 index spot and futures in China from a new perspective

We investigate the statistical behavior and application in risk estimation of recurrence intervals between high-frequency returns that are either larger than a given positive threshold or smaller than a negative threshold for the stock index and stock index futures markets in China. By studying the probability density function of recurrence intervals, we find symmetric profiles for both the positive and negative occurrence thresholds, which can be fitted with stretched exponential functions. The probability density function further scales with the mean interval as the unified functional form for different thresholds. We further study the dependence of the conditional probability density function and the scaled mean condition recurrence interval on the previous recurrence interval, and demonstrate the existence of short memory in recurrence intervals. The result from detrended fluctuation analysis exhibits long-term correlations, where the detrended fluctuation function decays as an exponential function, with an exponent between 0.5 and 1. Based on the results of the analysis of recurrence intervals, we construct a hazard function and define a loss probability in order to evaluate risk in financial markets. To our surprise, a crossover is found in the loss probability plot of the stock index and its futures market, which sheds light on the issue of value at risk (VaR) overestimation (underestimation) based on recurrence interval analysis of complex financial markets. The study would enable one to improve risk estimation and is useful for management of risks in financial markets.

Analysis of the clinical features of 436 cases of recurrence hand, foot and mouth disease

Objective To analyze the clinical characteristics and treatment methods of recurrence hand,foot and mouth disease (HFMD).Methods The clinical data of 436 HFMD patients were retrospectively analyzed.The characteristics of clinical manifestations,laboratory tests were analyzed.Results There were a total of 211 patients,accounting for 48.4％,the recurrence age was 2 to 5 years old.All relapsed patients rash appeared in the hand,foot and mouth or buttocks,there were 104 cases of rash appeared in elbow and knee,9 cases appeared in the torso.The recurrence patients proned to occur respiratory system,digestive system,cardiovascular system and nervous system complications.Respiratory complications were the most common,accounting for about 76.4％,followed by the digestive system,accounting for 18.5％.The distribution of relapse in children with time to recurrence and recurrence in-terval analysis found mainly in April to June,a total of 251 patients,the total relapse proportion was 57.6％ ;time in-terval was more common between 3 months to 12 months,a total of 326 cases of recurrence,accounting for 74.8％.Conclusion Clinical manifestations are not typical in recurrence HFMD patients,most are ordinary,less critically illpatients,it is easy to merge the respiratory system,digestive system complications.Early detection and diagnosis is the key to the treatment. Key words: Hand, foot and mouth disease; Recurrence; Enterovirus; Therapies, investigational

Estimation of surface water quality in a Yazoo River tributary using the duration curve and recurrence interval approach

Pollution of surface water with harmful chemicals and eutrophication of rivers and lakes with excess nutrients are serious environmental concerns. This study estimated surface water quality in a stream within the Yazoo River Basin (YRB), Mississippi, USA, using the duration curve and recurrence interval analysis techniques. Data from the US Geological Survey (USGS) surface water monitoring station located in Deer Creek east of Leland from the YRB were selected for the analysis. Results showed that the water quality constituents, namely water temperature, specific conductivity (SC) and dissolved oxygen (DO), in this stream were found not to be the major concerns as the percentages of the time when these constituents did not meet their criteria were very low. Our results further revealed that the water temperature and SC increased as time elapsed, indicating the potential global warming and contamination impacts in this stream. In contrast, the DO and pH decreased as time elapsed, postulating a potential increase in biochemical oxygen demand and an acidic trend in this stream. Over the last decade, the average recurrence intervals when the water temperature, SC, and DO did not meet their criteria or minimum conditions were around 1 year. Using a target DO value of 429 kg d−1 proposed by the Mississippi Department of Environmental Quality, results from this study showed that there was about 25% of the time when the DO load did not meet the target value. This study suggests that the duration curve and recurrence interval analysis techniques are useful statistical tools for water quality trend estimation.

Recurrence interval analysis of high-frequency financial returns and its application to risk estimation

We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures, including the Kolmogorov–Smirnov (KS) statistic, the weighted KS statistic and the Cramér–von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds q. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability Wq(Δt,t), value-at-risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.

Recurrence interval analysis of trading volumes

We study the statistical properties of the recurrence intervals τ between successive trading volumes exceeding a certain threshold q. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2009. Similar to the recurrence interval distribution of the price returns, the tail of the recurrence interval distribution of the trading volumes follows a power-law scaling, and the results are verified by the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cramér-von Mises criterion. The measurements of the conditional probability distribution and the detrended fluctuation function show that both short-term and long-term memory effects exist in the recurrence intervals between trading volumes. We further study the relationship between trading volumes and price returns based on the recurrence interval analysis method. It is found that large trading volumes are more likely to occur following large price returns, and the comovement between trading volumes and price returns is more pronounced for large trading volumes.

Record Precipitation Totals from the Coastal New England Rainstorm of 20–21 October 1996

This paper analyses the 20–21 October 1996 rainstorm along the coastal zone of New England in terms of its synoptic setting and its temporal and spatial patterns, and assesses its recurrence interval. The event was primarily generated by an intense cutoff low aloft, with an associated frontal boundary at the surface, both of which slowly drifted across New England. Storm rainfall totals ranged as high as 488 mm, which fell just short of the all-time greatest storm event ever recorded in New England, but statewide 1-day precipitation records were set in Maine and New Hampshire. Recurrence interval analysis revealed that this event was in gross excess of a 100-yr rainfall event and may be greater than a 400-yr event in this region.