Integrated Time Series Research Articles

Model Specification Testing for Nonlinear Multivariate Cointegrating Regressions

This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that the model accommodates endogeniety. A new and simple test is proposed and the resulting asymptotic theory is established. The test statistic is constructed based on a natural distance function between a nonparametric estimate and a smoothed parametric counterpart. The asymptotic distribution of the test statistic under the parametric specification is proportional to that of a local-time random variable with a known distribution. In addition, the finite sample performance of the proposed test is evaluated through using both simulated and real data examples.

Reconstructing the temporal progression of HIV-1 immune response pathways.

Motivation: Most methods for reconstructing response networks from high throughput data generate static models which cannot distinguish between early and late response stages.Results: We present TimePath, a new method that integrates time series and static datasets to reconstruct dynamic models of host response to stimulus. TimePath uses an Integer Programming formulation to select a subset of pathways that, together, explain the observed dynamic responses. Applying TimePath to study human response to HIV-1 led to accurate reconstruction of several known regulatory and signaling pathways and to novel mechanistic insights. We experimentally validated several of TimePaths’ predictions highlighting the usefulness of temporal models.Availability and Implementation: Data, Supplementary text and the TimePath software are available from http://sb.cs.cmu.edu/timepathContact: zivbj@cs.cmu.eduSupplementary information: Supplementary data are available at Bioinformatics online.

Algebra of Integrated Time Series: Evidence from Unit Root Analysis

It is argued if xt ~ I(1) and yt ~ I(1), then running a regression xt on yt would produce spurious results because e t would generally be I(1). However, there may exist a ‘b’ such that e t = x t - by t is I(0), then running a regression x t on y t would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, x t and y t are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if x t ~ I(d x ), y t ~ I(d y ), then z t = bx t + cy t ~ I(max(d x ,d y )). In this research, we offer evidence against this proposition.

Comparison Of Cointegration Tests For Near Integrated Time Series Data With Structural Break

Sample size of data, presence of structural break, location and magnitude of potential break, and having with near integrated process might affect the performance of cointegration tests. Engle-Granger (EG) and Johansen Cointegration tests may have erroneous results since they do not take into account possible structural break unlike Gregory – Hansen (GH) cointegration test. In this study, it is argued that the suitable choice of cointegration tests is quite complex, since outcomes of these tests are very sensitive to specifying these properties. The performance of cointegration tests is compared to each other underlying properties. This study presents how standard residual based tests- Engle-Granger and Gregory-Hansen- for cointegration can be implemented if series is near integrated, that is close to a unit root process. For assessing the finite sample performance of these tests, a Monte-Carlo experiment showed that both cointegration tests have relatively better size and power properties depend on break point, break magnitude, sample size of time series and the hypothesized value of AR(1) parameter. To illustrate the findings of the paper, a financial data is analyzed. The practitioners should be careful about the hypothesized value of AR(1) parameter which represents dependency degree of the data. If the autoregressive parameters is very close to one and the break magnitude is high, any test is acceptable for moderate to large sample size. However, one might need very large sample size to have a good power and actual size of the test. Additionally, GH test becomes liberal test unlike EG test as the magnitude of structural break increases.

Nonstationary Nonlinear Quantile Regression

This study examines estimation and inference based on quantile regression for parametric nonlinear models with an integrated time series covariate. We first derive the limiting distribution of the nonlinear quantile regression estimator and then consider testing for parameter restrictions, when the regression function is specified as an asymptotically homogeneous function. We also study linear-in-parameter regression models when the regression function is given by integrable regression functions as well as asymptotically homogeneous regression functions. We furthermore propose a fully modified estimator to reduce the bias in the original estimator under a certain set of conditions. Finally, simulation studies show that the estimators behave well, especially when the regression error term has a fat-tailed distribution.

Algebra of Integrated Time Series: Evidence from Unit Root Analysis

It is argued if xt~I(1) and yt~I(1), then running a regression xt on yt would produce spurious results because et would generally be I(1). However, there may exist a 'b' such that et = xt - byt is I(0), then running a regression xt on yt would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, xt and yt are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if xt~I(dx), yt~I(dy), then zt = bxt cyt ~I(max(dx,dy)). In this research, we offer evidence against this proposition.

Developing indices of temporal dispersion and continuity to map natural vegetation

An accurate and updated natural vegetation map is imperative for sustainable environmental management. This paper proposed a novel natural vegetation mapping algorithm based on time series images. Several indices of temporal dispersion and continuity were established for this purpose: low density (LD), medium density (MD), high density (HD) and medium continuity (MC). These indices were developed based on the particular percentiles-determined section of the EVI2 temporal profiles obtained through continuous wavelet transform. The natural vegetation was generally characterized as with lower temporal dispersion and greater temporal continuity compared with agricultural crops. The proposed methodology incorporated the indices of temporal dispersion and continuity and was applied to 13 provinces in central East China based on 500m 8-day composite Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index with two bands (EVI2) in 2013. An overall accuracy of 92.97% was obtained when compared with 2715 ground truth sites. There was also a good agreement (kappa index=0.8049) on the distribution and areas of different vegetation types between the MODIS-estimated image and the Landsat 8 OLI interpreted data on two test regions. This study demonstrated the efficiency of the transform and metric integrated time series classification approaches in the fields of land and vegetation cover mapping.

IDENTIFICACIÓN DE MODELOS ARFIMA

Desde la introducción de los modelos fraccionalmente integrados ARFIMA para series de tiempo con memoria larga, ha surgido un gran interés en el estudio de sus propiedades y áreas de aplicación. En este modelo, el grado de la memoria está definido por el parámetro de diferenciación fraccional, el cual toma valores en un intervalo continuo de números reales. Para realizar la estimación de este parámetro y probar la existencia de memoria larga, se han propuesto distintos procedimientos en la literatura. Ahora bien, generalmente no basta con conocer si hay memoria larga en la serie de tiempo, sino que es necesario estimar adecuadamente el valor del parámetro de diferenciación fraccional, del cual depende la dinámica de largo plazo de la serie, y de la componente ARMA asociada al comportamiento de corto plazo. Esta estimación requiere de la especificación correcta del modelo ARFIMA. El objeto de este documento es el de implementar un proceso de identificación del modelo ARFIMA para series estacionarias a partir de un procedimiento paramétrico propuesto, y comparar su desempeño con métodos semiparamétricos propuestos en la literatura. Los resultados obtenidos a través de un estudio de simulación, muestran que el procedimiento propuesto tiene, en general, un mejor desempeño.

CHRONOS: a time-varying method for microRNA-mediated subpathway enrichment analysis.

In the era of network medicine and the rapid growth of paired time series mRNA/microRNA expression experiments, there is an urgent need for pathway enrichment analysis methods able to capture the time- and condition-specific 'active parts' of the biological circuitry as well as the microRNA impact. Current methods ignore the multiple dynamical 'themes'-in the form of enriched biologically relevant microRNA-mediated subpathways-that determine the functionality of signaling networks across time. To address these challenges, we developed time-vaRying enriCHment integrOmics Subpathway aNalysis tOol (CHRONOS) by integrating time series mRNA/microRNA expression data with KEGG pathway maps and microRNA-target interactions. Specifically, microRNA-mediated subpathway topologies are extracted and evaluated based on the temporal transition and the fold change activity of the linked genes/microRNAs. Further, we provide measures that capture the structural and functional features of subpathways in relation to the complete organism pathway atlas. Our application to synthetic and real data shows that CHRONOS outperforms current subpathway-based methods into unraveling the inherent dynamic properties of pathways. CHRONOS is freely available at http://biosignal.med.upatras.gr/chronos/ tassos.bezerianos@nus.edu.sg Supplementary data are available at Bioinformatics online.

Inference for impulse response coefficients from multivariate fractionally integrated processes

ABSTRACTThis article considers a multivariate system of fractionally integrated time series and investigates the most appropriate way for estimating Impulse Response (IR) coefficients and their associated confidence intervals. The article extends the univariate analysis recently provided by Baillie and Kapetanios (2013), and uses a semiparametric, time domain estimator, based on a vector autoregression (VAR) approximation. Results are also derived for the orthogonalized estimated IRs which are generally more practically relevant. Simulation evidence strongly indicates the desirability of applying the Kilian small sample bias correction, which is found to improve the coverage accuracy of confidence intervals for IRs. The most appropriate order of the VAR turns out to be relevant for the lag length of the IR being estimated.

Are international economic and financial co-movements characterized by asymmetric co-integration?

Purpose – The recent economic crises have attracted attention to the issue of international equity co-movements and correlations. Using data from 1980 to 2010, the authors examine the international co-movements of both real economic activity, as reflected in industrial production and the gross domestic product (GDP), and financial activity, as reflected in equity market returns. While classic symmetric co-integration tests do not reject the hypothesis of no co-integration, the authors find evidence of asymmetric co-integration in these three variables between the USA and the rest of the Group of Seven (G7) countries. The momentum threshold autoregressive (M-TAR) model captures the nature of the asymmetry most effectively and is the most applicable model for adjustment to long-term equilibrium. This model suggests that the path of adjustment to long-run equilibrium is somewhat different when the price differential is decreasing than when it is increasing. These findings imply that the benefits of asset diversification for investors with a long horizon might be limited in scope. Design/methodology/approach – This work is based on the theory of integrated time series. The authors use symmetric and asymmetric co-integration tests to market indices, as well as to monthly industrial production statistics and quarterly data about the GDP. In line with the financial economic literature, the authors select the GDP as a proxy that reflects the real economy and share prices to mirror the financial sector of the economy. Because no monthly data exist about GDP, the authors use instead the industrial production. Both variables cover the period from January 1980 to June 2010. Findings – The overall findings demonstrate that the USA and the rest of the G7 countries are not symmetrically co-integrated with respect to the GDP. Indeed, they are asymmetrically co-integrated. These findings may explain the additional important result that the majority of equity markets are also asymmetrically co-integrated with the USA. Research limitations/implications – The co-movements of the equity markets and real economic activity imply that the benefits of asset diversification for investors with a long horizon might be limited in scope. In the short run, however, portfolio diversification can be more beneficial due to the short-term fluctuations that may derive from the asymmetric correction process. Originality/value – Prior research on co-movements has focused mainly on studying the correlations among international equity markets by analyzing conditional correlations or using symmetric co-integration methods; the authors test the existence of a long-term relationship between economic variables with respect to the USA and the rest of the G7 countries using a threshold co-integration model.

High‐Performance Integrated Control of water quality and quantity in urban water reservoirs

AbstractThis paper contributes a novel High‐Performance Integrated Control framework to support the real‐time operation of urban water supply storages affected by water quality problems. We use a 3‐D, high‐fidelity simulation model to predict the main water quality dynamics and inform a real‐time controller based on Model Predictive Control. The integration of the simulation model into the control scheme is performed by a model reduction process that identifies a low‐order, dynamic emulator running 4 orders of magnitude faster. The model reduction, which relies on a semiautomatic procedural approach integrating time series clustering and variable selection algorithms, generates a compact and physically meaningful emulator that can be coupled with the controller. The framework is used to design the hourly operation of Marina Reservoir, a 3.2 Mm3 storm‐water‐fed reservoir located in the center of Singapore, operated for drinking water supply and flood control. Because of its recent formation from a former estuary, the reservoir suffers from high salinity levels, whose behavior is modeled with Delft3D‐FLOW. Results show that our control framework reduces the minimum salinity levels by nearly 40% and cuts the average annual deficit of drinking water supply by about 2 times the active storage of the reservoir (about 4% of the total annual demand).

DYNAMIC PANEL ANDERSON-HSIAO ESTIMATION WITH ROOTS NEAR UNITY

Limit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson–Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample sizen→ ∞. But whenT→ ∞, either for fixednor asn→ ∞, IV is$\sqrt T$consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy asn→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T) → ∞ with no restriction on the divergence rates ofnandT.When the common autoregressive root$\rho = 1 + c/\sqrt T$the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is$\sqrt n$consistent for fixedTand$\sqrt {nT}$consistent with limit distributionN(0, 4) when (n,T) → ∞ sequentially or jointly. These results are robust for common roots of the formρ= 1+c/Tγfor allγ∈ (0, 1) and joint convergence holds. Limit normality holds but the variance changes whenγ= 1. Whenγ> 1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.

Reliability forecasting for operators’ situation assessment in digital nuclear power plant main control room based on dynamic network model

With the technical development of computer hardware and software, digitalization is a trend in large-scale complex systems such as nuclear power plants (NPPs). It changes the way main control room (MCR) operators interact with systems. Faced with these technical changes, operators need to continue improving their situation assessment (SA) reliability level. In addition to evaluate operators’ SA reliability, managers and shift supervisors also want to forecast their SA reliability level. There have been many studies with respect to operators’ SA, but most of them are static analysis method and cannot be applied to predict operators’ SA reliability. So, on the basis of different forecasting approaches and observation data, how to predict the operators’ SA reliability level has became a problem that many analyst interest in. In this paper, first we identified the influence factors associated with SA reliability, and then we developed the SA reliability model, finally we proposed a reliability forecasting model by integrating time series forecasting method with dynamic network model (DNM). Our experiment verification focused on steam generator tube rupture (SGTR) event, using the forecasting model, we demonstrated how to predict operators’ SA reliability during the course, and the prediction results are consistent with measurement results.

Mapping paddy rice planting area in wheat-rice double-cropped areas through integration of Landsat-8 OLI, MODIS, and PALSAR images.

As farmland systems vary over space and time (season and year), accurate and updated maps of paddy rice are needed for studies of food security and environmental problems. We selected a wheat-rice double-cropped area from fragmented landscapes along the rural–urban complex (Jiangsu Province, China) and explored the potential utility of integrating time series optical images (Landsat-8, MODIS) and radar images (PALSAR) in mapping paddy rice planting areas. We first identified several main types of non-cropland land cover and then identified paddy rice fields by selecting pixels that were inundated only during paddy rice flooding periods. These key temporal windows were determined based on MODIS Land Surface Temperature and vegetation indices. The resultant paddy rice map was evaluated using regions of interest (ROIs) drawn from multiple high-resolution images, Google Earth, and in-situ cropland photos. The estimated overall accuracy and Kappa coefficient were 89.8% and 0.79, respectively. In comparison with the National Land Cover Data (China) from 2010, the resultant map better detected changes in the paddy rice fields and revealed more details about their distribution. These results demonstrate the efficacy of using images from multiple sources to generate paddy rice maps for two-crop rotation systems.

A comparative study of shallow groundwater level simulation with three time series models in a coastal aquifer of South China

Accurate and reliable groundwater level forecasting models can help ensure the sustainable use of a watershed’s aquifers for urban and rural water supply. In this paper, three time series analysis methods, Holt–Winters (HW), integrated time series (ITS), and seasonal autoregressive integrated moving average (SARIMA), are explored to simulate the groundwater level in a coastal aquifer, China. The monthly groundwater table depth data collected in a long time series from 2000 to 2011 are simulated and compared with those three time series models. The error criteria are estimated using coefficient of determination (R2), Nash–Sutcliffe model efficiency coefficient (E), and root-mean-squared error. The results indicate that three models are all accurate in reproducing the historical time series of groundwater levels. The comparisons of three models show that HW model is more accurate in predicting the groundwater levels than SARIMA and ITS models. It is recommended that additional studies explore this proposed method, which can be used in turn to facilitate the development and implementation of more effective and sustainable groundwater management strategies.

CDREM: inferring dynamic combinatorial gene regulation.

Genes are often combinatorially regulated by multiple transcription factors (TFs). Such combinatorial regulation plays an important role in development and facilitates the ability of cells to respond to different stresses. While a number of approaches have utilized sequence and ChIP-based datasets to study combinational regulation, these have often ignored the combinational logic and the dynamics associated with such regulation. Here we present cDREM, a new method for reconstructing dynamic models of combinatorial regulation. cDREM integrates time series gene expression data with (static) protein interaction data. The method is based on a hidden Markov model and utilizes the sparse group Lasso to identify small subsets of combinatorially active TFs, their time of activation, and the logical function they implement. We tested cDREM on yeast and human data sets. Using yeast we show that the predicted combinatorial sets agree with other high throughput genomic datasets and improve upon prior methods developed to infer combinatorial regulation. Applying cDREM to study human response to flu, we were able to identify several combinatorial TF sets, some of which were known to regulate immune response while others represent novel combinations of important TFs.

Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the potential to invalidate the use of these methods. Using new tests constructed within a more general heteroskedastic fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed to be robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the asymptotic tests do not admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. A Monte Carlo simulation study demonstrates that very significant improvements in finite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments.

A CONSISTENT NONPARAMETRIC TEST ON SEMIPARAMETRIC SMOOTH COEFFICIENT MODELS WITH INTEGRATED TIME SERIES

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

The relation between structural and functional connectivity patterns in complex brain networks

ObjectiveAn important problem in systems neuroscience is the relation between complex structural and functional brain networks. Here we use simulations of a simple dynamic process based upon the susceptible–infected–susceptible (SIS) model of infection dynamics on an empirical structural brain network to investigate the extent to which the functional interactions between any two brain areas depend upon (i) the presence of a direct structural connection; and (ii) the degree product of the two areas in the structural network. MethodsFor the structural brain network, we used a 78×78 matrix representing known anatomical connections between brain regions at the level of the AAL atlas (Gong et al., 2009). On this structural network we simulated brain dynamics using a model derived from the study of epidemic processes on networks. Analogous to the SIS model, each vertex/brain region could be in one of two states (inactive/active) with two parameters β and δ determining the transition probabilities. First, the phase transition between the fully inactive and partially active state was investigated as a function of β and δ. Second, the statistical interdependencies between time series of node states were determined (close to and far away from the critical state) with two measures: (i) functional connectivity based upon the correlation coefficient of integrated activation time series; and (ii) effective connectivity based upon conditional co-activation at different time intervals. ResultsWe find a phase transition between an inactive and a partially active state for a critical ratio τ=β/δ of the transition rates in agreement with the theory of SIS models. Slightly above the critical threshold, node activity increases with degree, also in line with epidemic theory. The functional, but not the effective connectivity matrix closely resembled the underlying structural matrix. Both functional connectivity and, to a lesser extent, effective connectivity were higher for connected as compared to disconnected (i.e.: not directly connected) nodes. Effective connectivity scaled with the degree product. For functional connectivity, a weaker scaling relation was only observed for disconnected node pairs. For random networks with the same degree distribution as the original structural network, similar patterns were seen, but the scaling exponent was significantly decreased especially for effective connectivity. ConclusionsEven with a very simple dynamical model it can be shown that functional relations between nodes of a realistic anatomical network display clear patterns if the system is studied near the critical transition. The detailed nature of these patterns depends on the properties of the functional or effective connectivity measure that is used. While the strength of functional interactions between any two nodes clearly depends upon the presence or absence of a direct connection, this study has shown that the degree product of the nodes also plays a large role in explaining interaction strength, especially for disconnected nodes and in combination with an effective connectivity measure. The influence of degree product on node interaction strength probably reflects the presence of large numbers of indirect connections.