Dependent Time Series Research Articles

Effects of spatial smoothing on functional brain networks.

Graph‐theoretical methods have rapidly become a standard tool in studies of the structure and function of the human brain. Whereas the structural connectome can be fairly straightforwardly mapped onto a complex network, there are more degrees of freedom in constructing networks that represent functional connections between brain areas. For functional magnetic resonance imaging (fMRI) data, such networks are typically built by aggregating the blood‐oxygen‐level dependent signal time series of voxels into larger entities (such as Regions of Interest in some brain atlas) and determining their connection strengths from some measure of time‐series correlations. Although it is evident that the outcome must be affected by how the voxel‐level time series are treated at the preprocessing stage, there is a lack of systematic studies of the effects of preprocessing on network structure. Here, we focus on the effects of spatial smoothing, a standard preprocessing method for fMRI. We apply various levels of spatial smoothing to resting‐state fMRI data and measure the changes induced in functional networks. We show that the level of spatial smoothing clearly affects the degrees and other centrality measures of functional network nodes; these changes are non‐uniform, systematic, and depend on the geometry of the brain. The composition of the largest connected network component is also affected in a way that artificially increases the similarity of the networks of different subjects. Our conclusion is that wherever possible, spatial smoothing should be avoided when preprocessing fMRI data for network analysis.

Dynamic Functional Regression with Application to the Cross-section of Returns

Motivated by testing the significance of risk factors for a cross-section of returns, we develop an inferential framework which involves function-on-scalar regression. Asymptotic theory is developed assuming the factors form a weakly dependent vector-valued time series, and the regression errors are weakly dependent functions. To accommodate the empirical behavior of the cross-section of returns and of the factors, we allow both the factors and the error functions can exhibit mild departures from stationarity. This requires new asymptotic theory which leads to several tests for the significance of function-valued regression coefficients. The new approach to the study of the significance of risk factors for a cross-section of returns complements the established Fama–French approach based on portfolio construction. It is more suitable if the statistical significance of the risk factors is to be rigorously controlled.

Associations between dynamic functional connectivity and age, metabolic risk, and cognitive performance

Advanced age is associated with reduced within-network functional connectivity, particularly within the default mode network. Most studies to date have examined age differences in functional connectivity via static indices that are computed over the entire blood-oxygen-level dependent time series. Little is known about the effects of age on short-term temporal dynamics of functional connectivity. Here, we examined age differences in dynamic connectivity as well as associations between connectivity, metabolic risk, and cognitive performance in healthy adults (N = 168; age, 18–83 years). A sliding-window k-means clustering approach was used to assess dynamic connectivity from resting-state functional magnetic resonance imaging data. Three out of 8 dynamic connectivity profiles were associated with age. Furthermore, metabolic risk was associated with the relative amount of time allocated to 2 of these profiles. Finally, the relative amount of time allocated to a dynamic connectivity profile marked by heightened connectivity between default mode and medial temporal regions was positively associated with executive functions. Thus, dynamic connectivity analyses can enrich understanding of age-related differences beyond what is revealed by static analyses.

Dependency on imported oil and its effects on current account

ABSTRACTOil price hikes can have disruptive effects on the current account balances of oil-importing developing countries, which largely depend on external energy sources for domestic output. Nonetheless, the relation between oil prices and current account has been analyzed only in a limited number of studies for the developing countries. This paper contributes to the literature by examining the dynamics of how oil prices impact the current account in Turkey for the period between 2004 and 2015. For this purpose, a rolling window analysis using an advanced resampling technique, namely maximum entropy bootstrap (meboot), for strongly dependent time series data was performed. The empirical results reveal that oil price fluctuations have considerable effects on Turkey’s current account balance. In order to curtail the current account deficit, it is crucial that Turkey redesigns its energy policies and seeks alternative energy sources.

On the memory of products of long range dependent time series

This paper derives the memory of the product series xtyt, where xt and yt are stationary long memory time series of orders dx and dy, respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of products of series with non-zero means is determined by the maximal memory of the factor series, whereas the memory is reduced if the series are mean zero.

Bootstrap methods for long-memory processes: a review

This manuscript summarized advances in bootstrap methods for long-range dependent time series data. The stationary linear long-memory process is briefly described, which is a target process for bootstrap methodologies on time-domain and frequency-domain in this review. We illustrate time-domain bootstrap under long-range dependence, moving or non-overlapping block bootstraps, and the autoregressive-sieve bootstrap. In particular, block bootstrap methodologies need an adjustment factor for the distribution estimation of the sample mean in contrast to applications to weak dependent time processes. However, the autoregressive-sieve bootstrap does not need any other modification for application to long-memory. The frequency domain bootstrap for Whittle estimation is provided using parametric spectral density estimates because there is no current nonparametric spectral density estimation method using a kernel function for the linear long-range dependent time process.

Temporal cross-correlation between influenza-like illnesses and invasive pneumococcal disease in The Netherlands.

BackgroundWhile the burden of community‐acquired pneumonia and invasive pneumococcal disease (IPD) is still considerable, there is little insight in the factors contributing to disease. Previous research on the lagged relationship between respiratory viruses and pneumococcal disease incidence is inconclusive, and studies correcting for temporal autocorrelation are lacking.ObjectivesTo investigate the temporal relation between influenza‐like illnesses (ILI) and IPD, correcting for temporal autocorrelation.MethodsWeekly counts of ILI were obtained from the Sentinel Practices of NIVEL Primary Care Database. IPD data were collected from the Dutch laboratory‐based surveillance system for bacterial meningitis from 2004 to 2014. We analysed the correlation between time series, pre‐whitening the dependent time series with the best‐fit seasonal autoregressive integrated moving average (SARIMA) model to the independent time series. We performed cross‐correlations between ILI and IPD incidences, and the (pre‐whitened) residuals, in the overall population and in the elderly.ResultsWe found significant cross‐correlations between ILI and IPD incidences peaking at lags ‐3 overall and at 1 week in the 65+ population. However, after pre‐whitening, no cross‐correlations were apparent in either population group.ConclusionOur study suggests that ILI occurrence does not seem to be the major driver of IPD incidence in The Netherlands.

LTR-MDTS structure - a structure for multiple dependent time series prediction

The subject of research presented in this paper is to model a neural network structure and appropriate training algorithm that is most suited for multiple dependent time series prediction / deduction. The basic idea is to take advantage of neural networks in solving the problem of prediction of synchronized basketball referees? movement during a basketball action. Presentation of time series stemming from the aforementioned problem, by using traditional Multilayered Perceptron neural networks (MLP), leads to a sort of paradox of backward time lapse effect that certain input and hidden layers nodes have on output nodes that correspond to previous moments in time. This paper describes conducted research and analysis of different methods of overcoming the presented problem. Presented paper is essentially split into two parts. First part gives insight on efforts that are put into training set configuration on standard Multi Layered Perceptron back propagation neural networks, in order to decrease backwards time lapse effects that certain input and hidden layers nodes have on output nodes. Second part of paper focuses on the results that a new neural network structure called LTR - MDTS provides. Foundation of LTR - MDTS design relies on a foundation on standard MLP neural networks with certain, left-to-right synapse removal to eliminate aforementioned backwards time lapse effect on the output nodes.

Method of Dynamic VaR and CVaR Risk Measures Forecasting for Long Range Dependent Time Series on the Base of the Heteroscedastic Model

The paper proposes a new method of dynamic VaR and CVaR risk measures forecasting. The method is designed for obtaining the forecast estimates of risk measures for volatile time series with long range dependence. The method is based on the heteroskedastic time series model. The FIGARCH model is used for volatility modeling and forecasting. The model is reduced to the AR model of infinite order. The reduced system of Yule-Walker equations is solved to find the autoregression coefficients. The regression equation for the autocorrelation function based on the definition of a long-range dependence is used to get the autocorrelation estimates. An optimization procedure is proposed to specify the estimates of autocorrelation coefficients. The procedure for obtaining of the forecast values of dynamic risk measures VaR and CVaR is formalized as a multi-step algorithm. The algorithm includes the following steps: autoregression forecasting, innovation highlighting, obtaining of the assessments for static risk measures for residuals of the model, forming of the final forecast using the proposed formulas, quality analysis of the results. The proposed method is applied to the time series of the index of the Tokyo stock exchange. The quality analysis using various tests is conducted and confirmed the high quality of the obtained estimates.

Fixed-b Inference for Testing Structural Change in a Time Series Regression

This paper addresses tests for structural change in a weakly dependent time series regression. The cases of full structural change and partial structural change are considered. Heteroskedasticity-autocorrelation (HAC) robust Wald tests based on nonparametric covariance matrix estimators are explored. Fixed-b theory is developed for the HAC estimators which allows fixed-b approximations for the test statistics. For the case of the break date being known, the fixed-b limits of the statistics depend on the break fraction and the bandwidth tuning parameter as well as on the kernel. When the break date is unknown, supremum, mean and exponential Wald statistics are commonly used for testing the presence of the structural break. Fixed-b limits of these statistics are obtained and critical values are tabulated. A simulation study compares the finite sample properties of existing tests and proposed tests.

A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images.

We describe two modifications that parallelize and reorganize caching in the well-known Greedy Equivalence Search (GES) algorithm for discovering directed acyclic graphs on random variables from sample values. We apply one of these modifications, the Fast Greedy Search (FGS) assuming faithfulness, to an i.i.d. sample of 1,000 units to recover with high precision and good recall an average degree 2 directed acyclic graph (DAG) with one million Gaussian variables. We describe a modification of the algorithm to rapidly find the Markov Blanket of any variable in a high dimensional system. Using 51,000 voxels that parcellate an entire human cortex, we apply the FGS algorithm to Blood Oxygenation Level Dependent (BOLD) time series obtained from resting state fMRI.

Testing for Symmetry in Weakly Dependent Time Series

I propose a test of symmetry for a stationary time series based on the difference between the dispersion above the central tendency of the series with that below it. The test has many attractive features: it is applicable to dependent processes, it has a familiar form, it can be implemented using regression, and it has a standard Gaussian limiting distribution under the null of symmetry. The finite sample properties of the test are examined via Monte Carlo simulation and suggest that it is more powerful than competing tests in the literature for the DGPs considered. I apply the test to investigate business cycle asymmetry in sectoral data and confirm previous findings that asymmetry is more often detected in goods-producing sectors than service-related sectors.

Brain Network Architecture and Global Intelligence in Children with Focal Epilepsy.

The biologic basis for intelligence rests to a large degree on the capacity for efficient integration of information across the cerebral network. We aimed to measure the relationship between network architecture and intelligence in the pediatric, epileptic brain. Patients were retrospectively identified with the following: 1) focal epilepsy; 2) brain MR imaging at 3T, including resting-state functional MR imaging; and 3) full-scale intelligence quotient measured by a pediatric neuropsychologist. The cerebral cortex was parcellated into approximately 700 gray matter network "nodes." The strength of a connection between 2 nodes was defined by the correlation between their blood oxygen level-dependent time-series. We calculated the following topologic properties: clustering coefficient, transitivity, modularity, path length, and global efficiency. A machine learning algorithm was used to measure the independent contribution of each metric to the intelligence quotient after adjusting for all other metrics. Thirty patients met the criteria (4-18 years of age); 20 patients required anesthesia during MR imaging. After we accounted for age and sex, clustering coefficient and path length were independently associated with full-scale intelligence quotient. Neither motion parameters nor general anesthesia was an important variable with regard to accurate intelligence quotient prediction by the machine learning algorithm. A longer history of epilepsy was associated with shorter path lengths (P = .008), consistent with reorganization of the network on the basis of seizures. Considering only patients receiving anesthesia during machine learning did not alter the patterns of network architecture contributing to global intelligence. These findings support the physiologic relevance of imaging-based metrics of network architecture in the pathologic, developing brain.

Identifying differences in brain activities and an accurate detection of autism spectrum disorder using resting state functional-magnetic resonance imaging : A spatial filtering approach.

This paper presents a new approach for detecting major differences in brain activities between Autism Spectrum Disorder (ASD) patients and neurotypical subjects using the resting state fMRI. Further the method also extracts discriminative features for an accurate diagnosis of ASD. The proposed approach determines a spatial filter that projects the covariance matrices of the Blood Oxygen Level Dependent (BOLD) time-series signals from both the ASD patients and neurotypical subjects in orthogonal directions such that they are highly separable. The inverse of this filter also provides a spatial pattern map within the brain that highlights those regions responsible for the distinguishable activities between the ASD patients and neurotypical subjects. For a better classification, highly discriminative log-variance features providing the maximum separation between the two classes are extracted from the projected BOLD time-series data. A detailed study has been carried out using the publicly available data from the Autism Brain Imaging Data Exchange (ABIDE) consortium for the different gender and age-groups. The study results indicate that for all the above categories, the regional differences in resting state activities are more commonly found in the right hemisphere compared to the left hemisphere of the brain. Among males, a clear shift in activities to the prefrontal cortex is observed for ASD patients while other parts of the brain show diminished activities compared to neurotypical subjects. Among females, such a clear shift is not evident; however, several regions, especially in the posterior and medial portions of the brain show diminished activities due to ASD. Finally, the classification performance obtained using the log-variance features is found to be better when compared to earlier studies in the literature.

Regularized Estimation of Linear Functionals of Precision Matrices for High-Dimensional Time Series

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d. samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. It is shown that the convergence rates depend on the degree of temporal dependence and the moment conditions of the underlying linear processes. The Dantzig-selector estimator is applied to the sparse Markowitz portfolio allocation and the optimal linear prediction for time series, in which the ratio consistency when compared with an oracle estimator is established. The effect of dependence and innovation moment conditions is further illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real fMRI dataset and to portfolio optimization on a financial dataset.

How Much Information Does Dependence Between Wavelet Coefficients Contain?

ABSTRACTThis article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short- as well as long-range dependent time series is assumed. We focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic. To this end, we derive asymptotic distributional properties of the sample variance for a time series that is synthesized, ignoring some or all dependence between wavelet coefficients. We show that the second-order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent Gaussian case. This holds true even if the dependency is correct within each level and only the dependence between levels is ignored. In the case of sample autocovariances and sample autocorrelations at lag one, we indicate that first-order properties are erroneous. In a second step, we investigate several nonparametric bootstrap schemes in the wavelet domain, which take more and more dependence into account until finally the full dependency is mimicked. We obtain very similar results, where only a bootstrap mimicking the full covariance structure correctly can be valid asymptotically. A simulation study supports our theoretical findings for the wavelet domain bootstraps. For long-range-dependent time series with long-memory parameter d > 1/4, we show that some additional problems occur, which cannot be solved easily without using additional information for the bootstrap. Supplementary materials for this article are available online.

A complete convergence theorem for stationary regularly varying multivariate time series

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof of the invariance principle for the corresponding partial maximum process.

Testing for Change‐Points in Long‐Range Dependent Time Series by Means of a Self‐Normalized Wilcoxon Test

We propose a testing procedure based on the Wilcoxon two‐sample test statistic in order to test for change‐points in the mean of long‐range dependent data. We show that the corresponding self‐normalized test statistic converges in distribution to a non‐degenerate limit under the hypothesis that no change occurred and that it diverges to infinity under the alternative of a change‐point with constant height. Furthermore, we derive the asymptotic distribution of the self‐normalized Wilcoxon test statistic under local alternatives, that is, under the assumption that the height of the level shift decreases as the sample size increases. Regarding the finite sample performance, simulation results confirm that the self‐normalized Wilcoxon test yields a consistent discrimination between hypothesis and alternative and that its empirical size is already close to the significance level for moderate sample sizes.

Dynamic Bayesian Network Modeling of the Interplay between EGFR and Hedgehog Signaling.

Aberrant activation of sonic Hegdehog (SHH) signaling has been found to disrupt cellular differentiation in many human cancers and to increase proliferation. The SHH pathway is known to cross-talk with EGFR dependent signaling. Recent studies experimentally addressed this interplay in Daoy cells, which are presumable a model system for medulloblastoma, a highly malignant brain tumor that predominately occurs in children. Currently ongoing are several clinical trials for different solid cancers, which are designed to validate the clinical benefits of targeting the SHH in combination with other pathways. This has motivated us to investigate interactions between EGFR and SHH dependent signaling in greater depth. To our knowledge, there is no mathematical model describing the interplay between EGFR and SHH dependent signaling in medulloblastoma so far. Here we come up with a fully probabilistic approach using Dynamic Bayesian Networks (DBNs). To build our model, we made use of literature based knowledge describing SHH and EGFR signaling and integrated gene expression (Illumina) and cellular location dependent time series protein expression data (Reverse Phase Protein Arrays). We validated our model by sub-sampling training data and making Bayesian predictions on the left out test data. Our predictions focusing on key transcription factors and p70S6K, showed a high level of concordance with experimental data. Furthermore, the stability of our model was tested by a parametric bootstrap approach. Stable network features were in agreement with published data. Altogether we believe that our model improved our understanding of the interplay between two highly oncogenic signaling pathways in Daoy cells. This may open new perspectives for the future therapy of Hedghog/EGF-dependent solid tumors.

Nonparametric multiple change point estimation in highly dependent time series

Given a heterogeneous time-series sample, the objective is to find points in time, called change points, where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown stationary ergodic distributions. No modelling, independence or mixing assumptions are made. A novel, computationally efficient, nonparametric method is proposed, and is shown to be asymptotically consistent in this general framework. The theoretical results are complemented with experimental evaluations.