Autocorrelation In Time Series Research Articles

Precise Fault Location in TDM-PON by Utilizing Chaotic Laser Subject to Optical Feedback

We propose a method with high spatial resolution to detect fiber faults in a time-division multiplexing passive optical network (TDM-PON). A semiconductor laser serving as the probe light source is subjected to self-feedback caused by reflection at fiber faults. The feedback will induce the laser to generate chaos. Autocorrelation of the output time series shows the external cavity signature and, therefore, indicates the distance between the laser and the fiber fault. Each branch is identified by the marker that is formed by the inserted fiber Bragg grating (FBG) providing the feedback in each branch, and the faulty branch can be distinguished by the marker that has disappeared. Our proof-of-concept experiment demonstrates the identification of the faulty branch and the location of the fault point in an optical network simultaneously. This is achieved with a 6-km feeder fiber and realizes the 8-mm spatial resolution.

Regional analysis of groundwater droughts using hydrograph classification

Abstract. Groundwater drought is a spatially and temporally variable phenomenon. Here we describe the development of a method to regionally analyse and quantify groundwater drought. The method uses a cluster analysis technique (non-hierarchical k-means) to classify standardised groundwater level hydrographs (the standardised groundwater level index, SGI) prior to analysis of their groundwater drought characteristics, and has been tested using 74 groundwater level time series from Lincolnshire, UK. Using the test data set, six clusters of hydrographs have been identified. For each cluster a correlation can be established between the mean SGI and a mean standardised precipitation index (SPI), where each cluster is associated with a different SPI accumulation period. Based on a comparison of SPI time series for each cluster and for the study area as a whole, it is inferred that the clusters are independent of the driving meteorology and are primarily a function of catchment and hydrogeological factors. This inference is supported by the observation that the majority of sites in each cluster are associated with one of the principal aquifers in the study region. The groundwater drought characteristics of the three largest clusters, which constitute ~ 80 % of the sites, have been analysed. There are differences in the distributions of drought duration, magnitude and intensity of groundwater drought events between the three clusters as a function of autocorrelation of the mean SGI time series for each cluster. In addition, there are differences between the clusters in their response to three major multi-annual droughts that occurred during the analysis period. For example, sites in the cluster with the longest SGI autocorrelation experience the greatest-magnitude droughts and are the slowest to recover from major droughts, with groundwater drought conditions typically persisting at least 6 months longer than at sites in the other clusters. Membership of the clusters is shown to be related to unsaturated zone thickness at individual boreholes. This last observation emphasises the importance of catchment and aquifer characteristics as (non-trivial) controls on groundwater drought hydrographs. The method of analysis is flexible and can be adapted to a wide range of hydrogeological settings while enabling a consistent approach to the quantification of regional differences in response of groundwater to meteorological drought.

Performing T-tests to Compare Autocorrelated Time Series Data Collected from Direct-Reading Instruments

Industrial hygienists now commonly use direct-reading instruments to evaluate hazards in the workplace. The stored values over time from these instruments constitute a time series of measurements that are often autocorrelated. Given the need to statistically compare two occupational scenarios using values from a direct-reading instrument, a t-test must consider measurement autocorrelation or the resulting test will have a largely inflated type-1 error probability (false rejection of the null hypothesis). A method is described for both the one-sample and two-sample cases which properly adjusts for autocorrelation. This method involves the computation of an “equivalent sample size” that effectively decreases the actual sample size when determining the standard error of the mean for the time series. An example is provided for the one-sample case, and an example is given where a two-sample t-test is conducted for two autocorrelated time series comprised of lognormally distributed measurements.

Ecosystem functional assessment based on the “optical type” concept and self-similarity patterns: An application using MODIS-NDVI time series autocorrelation

Remote sensing (RS) time series are an excellent operative source for information about the land surface across several scales and different levels of landscape heterogeneity. Ustin and Gamon (2010) proposed the new concept of “optical types” (OT), meaning “optically distinguishable functional types”, as a way to better understand remote sensing signals related to the actual functional behavior of species that share common physiognomic forms but differ in functionality. Whereas the OT approach seems to be promising and consistent with ecological theory as a way to monitor vegetation derived from RS, it received little implementation.This work presents a method for implementing the OT concept for efficient monitoring of ecosystems based on RS time series. We propose relying on an ecosystem's repetitive pattern in the temporal domain (self-similarity) to assess its dynamics. Based on this approach, our main hypothesis is that distinct dynamics are intrinsic to a specific OT. Self-similarity level in the temporal domain within a broadleaf forest class was quantitatively assessed using the auto-correlation function (ACF), from statistical time series analysis. A vector comparison classification method, spectral angle mapper, and principal component analysis were used to identify general patterns related to forest dynamics. Phenological metrics derived from MODIS NDVI time series using the TIMESAT software, together with information from the National Forest Map were used to explain the different dynamics found.Results showed significant and highly stable self-similarity patterns in OTs that corresponded to forests under non-moisture-limited environments with an adaptation strategy based on a strong phenological synchrony with climate seasonality. These forests are characterized by dense closed canopy deciduous forests associated with high productivity and low biodiversity in terms of dominant species. Forests in transitional areas were associated with patterns of less temporal stability probably due to mixtures of different adaptation strategies (i.e., deciduous, marcescent and evergreen species) and higher functional diversity related to climate variability at long and short terms. A less distinct seasonality and even a double season appear in the OT of the broadleaf Mediterranean forest characterized by an open canopy dominated by evergreen-sclerophyllous formations. Within this forest, understory and overstory dynamics maximize functional diversity resulting in contrasting traits adapted to summer drought, winter frosts, and high precipitation variability.

Statistical regularities of Carbon emission trading market: Evidence from European Union allowances

As an emerging financial market, the trading value of carbon emission trading market has definitely increased. In recent years, the carbon emission allowances have already become a way of investment. They are bought and sold not only by carbon emitters but also by investors. In this paper, we analyzed the price fluctuations of the European Union allowances (EUA) futures in European Climate Exchange (ECX) market from 2007 to 2011. The symmetric and power-law probability density function of return time series was displayed. We found that there are only short-range correlations in price changes (return), while long-range correlations in the absolute of price changes (volatility). Further, detrended fluctuation analysis (DFA) approach was applied with focus on long-range autocorrelations and Hurst exponent. We observed long-range power-law autocorrelations in the volatility that quantify risk, and found that they decay much more slowly than the autocorrelation of return time series. Our analysis also showed that the significant cross correlations exist between return time series of EUA and many other returns. These cross correlations exist in a wide range of fields, including stock markets, energy concerned commodities futures, and financial futures. The significant cross-correlations between energy concerned futures and EUA indicate the physical relationship between carbon emission and energy production process. Additionally, the cross-correlations between financial futures and EUA indicate that the speculation behavior may become an important factor that can affect the price of EUA. Finally we modeled the long-range volatility time series of EUA with a particular version of the GARCH process, and the result also suggests long-range volatility autocorrelations.

Assessment of MODIS spectral indices for determining rice paddy agricultural practices and hydroperiod

Rice agricultural practices and hydroperiod dates must be determined to obtain information on water management practices and their environmental effects. Spectral indices derived from an 8-day MODIS composite allows to identify rice phenometrics at varying degrees of success. The aims of this study were (1) to assess the dynamics of the Normalized Difference Vegetation Index (NDVI), Normalized Difference Water Index (NDWI(1) and NDWI(2)) and Shortwave Angle Slope Index (SASI) in relation to rice agricultural practices and hydroperiod, and (2) to assess the capability for these indices to detect phenometrics in rice under different flooding regimes. Two rice farming areas in Spain that are governed under different water management practices, the Ebro Delta and Orellana, were studied over a 12-year period (2001–2012). The index time series autocorrelation function was calculated to determine index dynamics in both areas. Secondly, average indices were calculated to identify significant points close to key agricultural and flooding dates, and index behaviors and capacities to identify phenometrics were assessed on a pixel level. The index autocorrelation function produced a regular pattern in both zones, being remarkably homogeneous in the Ebro Delta. It was concluded that a combination of NDVI, NDWI(1), NDWI(2) and SASI may improve the results obtained through each index. NDVI was more effective at detecting the heading date and flooding trends in the Ebro Delta. NDWI(1), NDWI(2) and SASI identified the harvest and the end of environmental flooding in the Delta, and the flooding in Orellana, more effectively. These results may set strong foundations for the development of new strategies in rice monitoring systems, providing useful information to policy makers and environmental studies.

Intermittency of aeolian saltation.

Saltation motion of sand grains in a steady wind was measured using a high-speed camera at very high frequency in a wind tunnel. A Heaviside-type function was defined to quantificationally describe an inherent property of saltation, i.e. intermittency. Kurtosis and periodicity of state function are statistical manifestations of intermittency. In addition, the strong autocorrelation of time series of volume concentration clearly confirms that saltation is not a completely random process at the timescale of subsecond. Formation mechanism, especially turbulent structures responsible for intermittent saltation, remains to be revealed from the viewpoint of classical mechanics.

Influence diagnostics in log-linear integer-valued GARCH models

Integer-valued generalized autoregressive conditional heteroscedasticity (GARCH) models have played an important role in time series analysis of count data. To model negatively autocorrelated time series and to accommodate covariates without restrictions, the log-linear integer-valued GARCH model has recently been proposed as an alternative to the existing models. In this paper, we study a local influence diagnostic analysis in the log-linear integer-valued GARCH models. The slope-based diagnostic and stepwise curvature-based diagnostics in a framework of the modified likelihood displacement are proposed. Under five perturbation schemes the corresponding local influence measures are derived. Two simulated data sets and a real-world example are analyzed to illustrate our method. In addition, the fitted model for this example has a negative coefficient for one of the two covariates, which is particularly illustrative of the extra flexibility of the considered model.

Early warnings of regime shifts: evaluation of spatial indicators from a whole‐ecosystem experiment

Critical transitions between alternate ecosystem states are often preceded by increased variance and autocorrelation in time series of ecosystem properties. Analogous changes may occur in spatial statistics as ecosystems approach thresholds for critical transitions. Changes in spatial statistics near thresholds have been described using models, laboratory experiments, and remotely sensed data, but there have been no tests using deliberate manipulations of whole ecosystems in the field. We previously documented a whole‐lake manipulation resulting in a transition to predator dominance, a type of critical transition. The food web of an experimental lake was forced via cascading trophic interactions from a stable state characterized by abundant prey fish, small zooplankton, and high chlorophyll concentrations to an alternative state dominated by predatory fish, large zooplankton and low chlorophyll concentrations. Time series of zooplankton and chlorophyll concentrations provided early warning of the regime shift. Here we test if similar early warning signals were present in space by applying spatial variance and the discrete Fourier transform to spatially distributed prey fish catch data from this regime shift. Prey fish spatial distributions were monitored daily using minnow traps deployed around the lake perimeter. Added predators reduced prey fish populations and altered their spatial distributions. Increases in spatial variance and shifts to low frequency spatial variance were observed up to a year in advance of the shift. There was no response in an adjacent reference lake. Our results demonstrate that spatial signals of approaching thresholds can be detected at the ecosystem scale.

Impact of autocorrelation on functional connectivity

Although the impact of serial correlation (autocorrelation) in residuals of general linear models for fMRI time-series has been studied extensively, the effect of autocorrelation on functional connectivity studies has been largely neglected until recently. Some recent studies based on results from economics have questioned the conventional estimation of functional connectivity and argue that not correcting for autocorrelation in fMRI time-series results in “spurious” correlation coefficients. In this paper, first we assess the effect of autocorrelation on Pearson correlation coefficient through theoretical approximation and simulation. Then we present this effect on real fMRI data. To our knowledge this is the first work comprehensively investigating the effect of autocorrelation on functional connectivity estimates. Our results show that although FC values are altered, even following correction for autocorrelation, results of hypothesis testing on FC values remain very similar to those before correction. In real data we show this is true for main effects and also for group difference testing between healthy controls and schizophrenia patients. We further discuss model order selection in the context of autoregressive processes, effects of frequency filtering and propose a preprocessing pipeline for connectivity studies.

Interaction network based early-warning indicators of vegetation transitions

Changes in vegetation patterns in semi-arid regions can precede the abrupt transition to bare soil. Here, complex network techniques are used to develop novel early-warning indicators for these desertification transitions. These indicators are applied to results from a local positive feedback vegetation model and are compared to classical indicators, such as the autocorrelation and variance of biomass time series. A quantitative measure is also introduced to evaluate the quality of the early-warning indicators. Based on this measure, the network-based indicators are superior to the classical ones, being more sensitive to the presence of the transition point.

HAC Corrections for Strongly Autocorrelated Time Series

Applied work routinely relies on heteroscedasticity and autocorrelation consistent (HAC) standard errors when conducting inference in a time series setting. As is well known, however, these corrections perform poorly in small samples under pronounced autocorrelations. In this article, I first provide a review of popular methods to clarify the reasons for this failure. I then derive inference that remains valid under a specific form of strong dependence. In particular, I assume that the long-run properties can be approximated by a stationary Gaussian AR(1) model, with coefficient arbitrarily close to one. In this setting, I derive tests that come close to maximizing a weighted average power criterion. Small sample simulations show these tests to perform well, also in a regression context.

Testing the detectability of spatio–temporal climate transitions from paleoclimate networks with the START model

Abstract. A critical challenge in paleoclimate data analysis is the fact that the proxy data are heterogeneously distributed in space, which affects statistical methods that rely on spatial embedding of data. In the paleoclimate network approach nodes represent paleoclimate proxy time series, and links in the network are given by statistically significant similarities between them. Their location in space, proxy and archive type is coded in the node attributes. We develop a semi-empirical model for Spatio-Temporally AutocoRrelated Time series, inspired by the interplay of different Asian Summer Monsoon (ASM) systems. We use an ensemble of transition runs of this START model to test whether and how spatio–temporal climate transitions could be detectable from (paleo)climate networks. We sample model time series both on a grid and at locations at which paleoclimate data are available to investigate the effect of the spatially heterogeneous availability of data. Node betweenness centrality, averaged over the transition region, does not respond to the transition displayed by the START model, neither in the grid-based nor in the scattered sampling arrangement. The regionally defined measures of regional node degree and cross link ratio, however, are indicative of the changes in both scenarios, although the magnitude of the changes differs according to the sampling. We find that the START model is particularly suitable for pseudo-proxy experiments to test the technical reconstruction limits of paleoclimate data based on their location, and we conclude that (paleo)climate networks are suitable for investigating spatio–temporal transitions in the dependence structure of underlying climatic fields.

At What Time of Day Do Daily Extreme Near-Surface Wind Speeds Occur?

Abstract The timing of daily extreme wind speeds from 10 to 200 m is considered using 11 yr of 10-min averaged data from the 213-m tower at Cabauw, the Netherlands. This analysis is complicated by the tendency of autocorrelated time series to take their extreme values near the beginning or end of a fixed window in time, even when the series is stationary. It is demonstrated that a simple averaging procedure using different base times to define the day effectively suppresses this “edge effect” and enhances the intrinsic nonstationarity associated with diurnal variations in boundary layer processes. It is found that daily extreme wind speeds at 10 m are most likely in the early afternoon, whereas those at 200 m are most likely in between midnight and sunrise. An analysis of the joint distribution of the timing of extremes at these two altitudes indicates the presence of two regimes: one in which the timing is synchronized between these two layers, and the other in which the occurrence of extremes is asynchronous. These results are interpreted physically using an idealized mechanistic model of the surface layer momentum budget.

Self-rated health: patterns in the journeys of patients with multi-morbidity and frailty.

Self-rated health (SRH) is a single measure predictor of hospital utilization and health outcomes in epidemiological studies. There have been few studies of SRH in patient journeys in clinical settings. Reduced resilience to stressors, reflected by SRH, exposes older people (complex systems) to the risk of hospitalization. It is proposed that SRH reflects rather than predicts deteriorations and hospital use; with low SRH autocorrelation in time series. The aim was to investigate SRH fluctuations in regular outbound telephone calls (average biweekly) to patients by Care Guides. Descriptive case study using quantitative autoregressive techniques and qualitative case analysis on SRH time series. Fourteen participants were randomly selected from the Patient Journey Record System (PaJR) database. The PaJR database recorded 198 consecutively sampled older multi-morbid patients journeys in three primary care settings. Analysis consisted of triangulation of SRH (0 very poor - 6 excellent) patterns from three analyses: SRH graduations associations with service utilization; time series modelling (autocorrelation, and step ahead forecast); and qualitative categorization of deteriorations. Fourteen patients reported mean SRH 2.84 (poor-fair) in 818 calls over 13 ± 6.4 months of follow-up. In 24% calls, SRH was poor-fair and significantly associated with hospital use. SRH autocorrelation was low in 14 time series (-0.11 to 0.26) with little difference (χ(2) = 6.46, P = 0.91) among them. Fluctuations between better and worse health were very common and poor health was associated with hospital use. It is not clear why some patients continued on a downward trajectory, whereas others who destabilized appeared to completely recover, and even improved over time. SRH reflects an individual's complex health trajectory, but as a single measure does not predict when and how deteriorations will occur in this study. Individual patients appear to behave as complex adaptive systems. The dynamics of SRH and its influences in destabilizations warrant further research.

A two-step framework for over-threshold modelling of environmental extremes

Abstract. The evaluation of the probability of occurrence of extreme natural events is important for the protection of urban areas, industrial facilities and others. Traditionally, the extreme value theory (EVT) offers a valid theoretical framework on this topic. In an over-threshold modelling (OTM) approach, Pickands' theorem, (Pickands, 1975) states that, for a sample composed by independent and identically distributed (i.i.d.) values, the distribution of the data exceeding a given threshold converges through a generalized Pareto distribution (GPD). Following this theoretical result, the analysis of realizations of environmental variables exceeding a threshold spread widely in the literature. However, applying this theorem to an auto-correlated time series logically involves two successive and complementary steps: the first one is required to build a sample of i.i.d. values from the available information, as required by the EVT; the second to set the threshold for the optimal convergence toward the GPD. In the past, the same threshold was often employed both for sampling observations and for meeting the hypothesis of extreme value convergence. This confusion can lead to an erroneous understanding of methodologies and tools available in the literature. This paper aims at clarifying the conceptual framework involved in threshold selection, reviewing the available methods for the application of both steps and illustrating it with a double threshold approach.

Autocorrelation and cross-correlation in time series of homicide and attempted homicide

We propose in this paper to establish the relationship between homicides and attempted homicides by a non-stationary time-series analysis. This analysis will be carried out by Detrended Fluctuation Analysis (DFA), Detrended Cross-Correlation Analysis (DCCA), and DCCA cross-correlation coefficient, ρDCCA(n). Through this analysis we can identify a positive cross-correlation between homicides and attempted homicides. At the same time, looked at from the point of view of autocorrelation (DFA), this analysis can be more informative depending on time scale. For short scale (days), we cannot identify auto-correlations, on the scale of weeks DFA presents anti-persistent behavior, and for long time scales (n>90 days) DFA presents a persistent behavior. Finally, the application of this new type of statistical analysis proved to be efficient and, in this sense, this paper can contribute to a more accurate descriptive statistics of crime.

Analysis of groundwater drought building on the standardised precipitation index approach

Abstract. A new index for standardising groundwater level time series and characterising groundwater droughts, the Standardised Groundwater level Index (SGI), is described. The SGI builds on the Standardised Precipitation Index (SPI) to account for differences in the form and characteristics of groundwater level and precipitation time series. The SGI is estimated using a non-parametric normal scores transform of groundwater level data for each calendar month. These monthly estimates are then merged to form a continuous index. The SGI has been calculated for 14 relatively long, up to 103 yr, groundwater level hydrographs from a variety of aquifers and compared with SPI for the same sites. The relationship between SGI and SPI is site specific and the SPI accumulation period which leads to the strongest correlation between SGI and SPI, qmax, varies between sites. However, there is a consistent positive linear correlation between a measure of the range of significant autocorrelation in the SGI series, mmax, and qmax across all sites. Given this correlation between SGI mmax and SPI qmax, and given that periods of low values of SGI can be shown to coincide with previously independently documented droughts, SGI is taken to be a robust and meaningful index of groundwater drought. The maximum length of groundwater droughts defined by SGI is an increasing function of mmax, meaning that relatively long groundwater droughts are generally more prevalent at sites where SGI has a relatively long autocorrelation range. Based on correlations between mmax, average unsaturated zone thickness and aquifer hydraulic diffusivity, the source of autocorrelation in SGI is inferred to be dependent on dominant aquifer flow and storage characteristics. For fractured aquifers, such as the Cretaceous Chalk, autocorrelation in SGI is inferred to be primarily related to autocorrelation in the recharge time series, while in granular aquifers, such as the Permo–Triassic sandstones, autocorrelation in SGI is inferred to be primarily a function of intrinsic saturated flow and storage properties of aquifer. These results highlight the need to take into account the hydrogeological context of groundwater monitoring sites when designing and interpreting data from groundwater drought monitoring networks.

Parsimonious Fitting of Long-Range Dependent Network Traffic Using ARMA Models

ARMA models are well-suited for capturing auto-correlations of time series. However, in the context of network traffic modeling they are rarely used for their often claimed inappropriateness for fitting Long Range Dependence (LRD) processes. This letter provides evidence that LRD effects can be well approximated by ARMA models; but only the classical fitting algorithms are inappropriate for this task. Accordingly, we propose a novel algorithm, which deploys a multi-scale fitting procedure. It achieves high accuracy up to an arbitrary cut-off lag, yielding parsimonious ARMA models. Our findings encourage a stronger integration of the ARMA framework into the field of network traffic modeling.

Impact of climatic change on streamflow in the upper reaches of the Minjiang River, China

Characteristics of hydroclimatic change in the upper reaches of the Minjiang River are analysed using data collected over the past 50 years. The effect of autocorrelation of time series on trend analysis is removed by adopting a pre-whitening technique. Long-term hydrometeorological trend and abrupt changes are analysed by the Mann-Kendall test. The results were validated by the linear trend and Spearman methods. Correlations between runoff change with air temperature and with precipitation were studied with the Pearson method. The results clearly show that average air temperature in the upper reaches of the river is increasing, and precipitation decreasing, with differences in spatio-temporal distribution. Runoff change has a clear positive correlation with precipitation. Meteorological change, especially in precipitation, is the key governing influence of runoff volume. The annual runoff decrease, especially the decrease of inflow in spring and autumn and earlier appearance and longer duration of the low-flow season, will impact greatly on irrigation and municipal water supply. Therefore, relevant measures and further study are necessary.Editor Z.W. Kundzewicz; Associate editor Q. ZhangCitation Huang, X.R., Zhao, J.W., Li, W.H., and Jiang, H.X., 2013. Impact of climatic change on streamflow in the upper reaches of the Minjiang River, China. Hydrological Sciences Journal, 59 (1), 154–164.