Temporal Dependence Structure Research Articles

Clustering time series by extremal dependence

AbstractThe goal of this paper is to characterize the temporal dependence structure on the extremes of time series and use such dependency to group them. In particular, three similarity measures to capture extremal dependence are proposed, being their performance assessed in different scenarios. This will involve the use of classical time series clustering algorithms, as well as rigorous evaluation of their performance in both simulated scenarios and real-world time series data sets. The focus will be on comparing the performance of these similarity measures with different clustering methods, and illustrate the efficacy of extremal dependence-based clustering in meteorological data. To achieve this, we will consider a dataset consisting of daily maximum temperatures recorded at 500 stations across Europe.

Copula Variational LSTM for High-Dimensional Cross-Market Multivariate Dependence Modeling.

We address a challenging problem-modeling high-dimensional, long-range dependencies between nonnormal multivariates, which is important for demanding applications such as cross-market modeling (CMM). With heterogeneous indicators and markets, CMM aims to capture between-market financial couplings and influence over time and within-market interactions between financial variables. We make the first attempt to integrate deep variational sequential learning with copula-based statistical dependence modeling and characterize both temporal dependence degrees and structures between hidden variables representing nonnormal multivariates. Our copula variational learning network weighted partial regular vine copula-based variational long short-term memory (WPVC-VLSTM) integrates variational long short-term memory (LSTM) networks and regular vine copula to model variational sequential dependence degrees and structures. The regular vine copula models nonnormal distributional dependence degrees and structures. VLSTM captures variational long-range dependencies coupling high-dimensional dynamic hidden variables without strong hypotheses and multivariate constraints. WPVC-VLSTM outperforms benchmarks, including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in terms of both technical significance and portfolio forecasting performance. WPVC-VLSTM shows a step-forward for CMM and deep variational learning.

Ridge Regression Under Dense Factor Augmented Models

This article establishes a comprehensive theory of the optimality, robustness, and cross-validation selection consistency for the ridge regression under factor-augmented models with possibly dense idiosyncratic information. Using spectral analysis for random matrices, we show that the ridge regression is asymptotically efficient in capturing both factor and idiosyncratic information by minimizing the limiting predictive loss among the entire class of spectral regularized estimators under large-dimensional factor models and mixed-effects hypothesis. We derive an asymptotically optimal ridge penalty in closed form and prove that a bias-corrected k-fold cross-validation procedure can adaptively select the best ridge penalty in large samples. We extend the theory to the autoregressive models with many exogenous variables and establish a consistent cross-validation procedure using the what-we-called double ridge regression method. Our results allow for nonparametric distributions for, possibly heavy-tailed, martingale difference errors and idiosyncratic random coefficients and adapt to the cross-sectional and temporal dependence structures of the large-dimensional predictors. We demonstrate the performance of our ridge estimators in simulated examples as well as an economic dataset. All the proofs are available in the supplementary materials, which also includes more technical discussions and remarks, extra simulation results, and useful lemmas that may be of independent interest.

Analysis of East Asia Wind Vectors Using Space–Time Cross-Covariance Models

As the risk posed by climate change becomes increasingly evident, countries across the world are constantly seeking alternative energy sources. Wind energy has substantial potential for future energy portfolios without having negative impacts on the environment. In developing nationwide and worldwide energy plans, understanding the spatio-temporal pattern of wind is crucial. We analyze wind vectors in the region of East Asia from the fifth-generation ECMWF atmospheric reanalysis. To model the wind vectors, we consider Tukey g-and-h transformation-based non-Gaussian processes, along with multivariate covariance functions. The proposed model can address non-Gaussian features and nonstationary dependence structures of wind vectors. In addition, a two-step inference scheme coupled with the composite likelihood method is applied to handle the computational issues posed by a large dataset. In the first step, we fit the temporal dependence structures of data with a location-specific non-Gaussian time series model. This allows us to remove substantial amounts of nonstationary variations in both space and time, and thus, relatively simple covariance models can handle large and complicated data in the second step. We show that the proposed method with a covariance structure reflecting the nonstationarity due to the latitude difference and the land–ocean difference leads to better predictions for wind speed as well as wind potential, which is crucial for planning wind power generation.

Adapting rainfall bias-corrections to improve hydrological simulations generated from climate model forcings

Global circulation models (GCMs) provide important insights into future climate change. Bias-correction of downscaled GCM output is integral to any hydrological investigations of climate change due to discrepancies between the statistics of downscaled GCM simulations and observations. Many bias-correction techniques have been developed to support hydrological applications. However, there have been few comparisons of the sensitivity of hydrological simulations to different bias-correction assumptions. This paper investigates the importance of two common assumptions: (i) simultaneously correcting bias at multiple time scales, and (ii) explicitly handling rainfall autocorrelation; in quantile mapping of downscaled GCM rainfall data for hydrological simulation. Four quantile mapping methods are applied to correct bias in dynamically downscaled reanalysis and historical GCM simulations of rainfall for 11 catchments in south-eastern Australia and the performance of bias-corrected rainfall and streamflow simulations is evaluated.All quantile mapping methods investigated can effectively eliminate bias in monthly and annual rainfall totals. Quantile mapping methods that consider differences in the temporal dependence (autocorrelation) structure of downscaled GCM and observed rainfall are most effective in reducing bias in rainfall sequencing statistics, such as probability of consecutive wet or dry days. Streamflow simulations of mean and high streamflow percentiles are underestimated when generated using rainfall that is corrected using quantile mapping methods that do not consider differences in the temporal dependence structure of downscaled GCM and observed rainfall. Future hydrological investigations of climate change should therefore adopt methods that explicitly consider the temporal dependence structures of downscaled GCM and observed rainfall.

Modeling the Bias of Digital Data: An Approach to Combining Digital With Official Statistics to Estimate and Predict Migration Trends

Obtaining reliable and timely estimates of migration flows is critical for advancing the migration theory and guiding policy decisions, but it remains a challenge. Digital data provide granular information on time and space, but do not draw from representative samples of the population, leading to biased estimates. We propose a method for combining digital data and official statistics by using the official statistics to model the spatial and temporal dependence structure of the biases of digital data. We use simulations to demonstrate the validity of the model, then empirically illustrate our approach by combining geo-located Twitter data with data from the American Community Survey (ACS) to estimate state-level out-migration probabilities in the United States. We show that our model, which combines unbiased and biased data, produces predictions that are more accurate than predictions based solely on unbiased data. Our approach demonstrates how digital data can be used to complement, rather than replace, official statistics.

Permutation entropy and its variants for measuring temporal dependence

SummaryPermutation entropy (PE) is an ordinal‐based non‐parametric complexity measure for studying the temporal dependence structure in a linear or non‐linear time series. Based on the PE, we propose a new measure, namely permutation dependence (PD), to quantify the strength of the temporal dependence in a univariate time series and remedy the major drawbacks of PE. We demonstrate that the PE and PD are viable and useful alternatives to conventional temporal dependence measures, such as the autocorrelation function (ACF) and mutual information (MI). Compared to the ACF, the PE and PD are not restricted in detecting the linear or quasi‐linear serial correlation in an autoregression model. Instead, they can be viewed as non‐parametric and non‐linear alternatives since they do not require any prior knowledge or assumptions about the underlying structure. Compared to MI estimated by k‐nearest neighbour, PE and PD show added sensitivity to structures of relatively weak strength. We compare the finite‐sample performance of the PE and PD with the ACF and the MI estimated by k‐nearest neighbour in a number of simulation studies to showcase their respective strengths and weaknesses. Moreover, their performance under non‐stationarity is also investigated. Using high‐frequency EUR/USD exchange rate returns data, we apply the PE and PD to study the temporal dependence structure in intraday foreign exchange.

Time-coupled day-ahead wind power scenario generation: A combined regular vine copula and variance reduction method

Advanced stochastic programming-based power system operations planning requires wind power forecast in the form of scenarios. Generating wind power scenarios reflecting the intertemporal dependence over the forecast horizon is paramount for multi-period operations planning routines. Yet, less attention has been given to such time-coupled (temporal) wind power scenario generation (SG). Recent literature shows that copula-based SG methods are suitable for typical operations planning routines like economic dispatch and unit commitment. This work proposes a new and efficient data-driven temporal wind power SG framework using regular vine copula with variance reduction. The proposed SG puts forth two contributions to improve the quality of the temporal scenarios. The first contribution is to introduce the regular vine copula to model the temporal dependence structure of the wind power forecast error, which is shown to fit the real-world data better than the existing copula models. The second contribution is to propose a uniform design-based vine copula sampling algorithm, which benefits the downstream operations planning applications with improved convergence and accuracy of the solutions. A detailed multivariate scenario evaluation using multiple metrics shows that the proposed SG improves the quality of the temporal scenarios compared to the existing benchmarks. The Diebold-Mariano statistical test also verifies the significant improvement in the quality of the wind power scenarios.

Nonlinear autocorrelation function of functional time series

In functional time series analysis, the functional autocorrelation function (fACF) plays an important role in revealing the temporal dependence structures underlying the dynamics and identifying the lags at which substantial correlation exists. However, akin to its counterpart in the univariate case, the fACF is restricted by linear structure and can be misleading in reflecting nonlinear temporal dependence. This paper proposes a nonlinear alternative to the fACF for analyzing the temporal dependence in functional time series. We consider linear and nonlinear data generating processes: a functional autoregressive process and a functional generalized autoregressive conditional heteroskedasticity process. We demonstrate that when the process exhibits linear temporal structures, the inference obtained from our proposed nonlinear fACF is consistent with that from the fACF. When the underlying process exhibits nonlinear temporal dependence, our nonlinear fACF has a superior capability in uncovering the nonlinear structure that the fACF misleads. An empirical data analysis highlights its applications in unveiling nonlinear temporal structures in the daily curves of the intraday volatility dynamics of the foreign exchange rate.

On seasonal functional modeling under strong dependence, with applications to mechanically ventilated breathing activity

Breathing effort in mechanical ventilation is commonly estimated by airway pressure. More advanced methods involve transdiaphragmatic pressure measurements (Pdi) or surface electromyography (sEMG) of the respiratory muscles. To study whether inspiratory efforts may be predicted by the noninvasive sEMG method, a model is proposed for time series with a stochastically changing periodic component. The model can be interpreted as a functional time series or a process based on a state space representation, with a flexible temporal dependence structure in the parameter process and the residuals, including long memory, short memory or antipersistence. An application to Pdi and sEMG measurements shows the potential usefulness of the method in the context of monitoring patients undergoing mechanical ventilation.

Spatiotemporal Modeling of Nursery Habitat Using Bayesian Inference: Environmental Drivers of Juvenile Blue Crab Abundance

Nursery grounds provide conditions favorable for growth and survival of juvenile fish and crustaceans through abundant food resources and refugia, and enhance secondary production of populations. While small-scale studies remain important tools to assess nursery value of structured habitats and environmental factors, targeted applications that unify survey data over large spatial and temporal scales are vital to generalize inference of nursery function, identify highly productive regions, and inform management strategies. Using 21 years of spatio-temporally indexed survey data (i.e., water chemistry, turbidity, blue crab, and predator abundance) and GIS information on potential nursery habitats (i.e., seagrass, salt marsh, and unvegetated shallow bottom), we constructed five Bayesian hierarchical models with varying spatial and temporal dependence structures to infer variation in nursery habitat value for young juveniles (20–40 mm carapace width) of the blue crabCallinectes sapiduswithin three tributaries (James, York and Rappahannock Rivers) in lower Chesapeake Bay. Out-of-sample predictions of juvenile blue crab counts from a model considering fully nonseparable spatiotemporal dependence outperformed predictions from simpler models. Salt marsh surface area and turbidity were the strongest determinants of crab abundance (positive association in both cases). Highest crab abundances occurred near the turbidity maximum where relative salt marsh area was greatest. Relative seagrass area, which has been emphasized as the most valuable nursery in studies conducted at small spatial scales, was not associated with high crab abundance within the three tributaries. Hence, salt marshes should be considered a key nursery habitat for the blue crab, even where extensive seagrass beds occur. The patterns between juvenile blue crab abundance and environmental variables also indicated that identification of nurseries should be based on investigations at broad spatial and temporal scales incorporating multiple potential nursery habitats, and based on statistical analyses that address spatial and temporal statistical dependence.

Most powerful test against a sequence of high dimensional local alternatives

We develop a powerful quadratic test for the overall significance of many covariates in a dense regression model in the presence of nuisance parameters. By equally weighting the sample moments, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a non-parametric error distribution and weakly exogenous nuisance variables, in particular autoregressors in many applications. Using random matrix theory, we show that the test has the optimal asymptotic testing power among a large class of competitors against local alternatives whose coordinates are dense in the eigenbasis of the high dimensional sample covariance matrix among regressors. The asymptotic results are adaptive to the covariates’ cross-sectional and temporal dependence structure and do not require a limiting spectral law of their sample covariance matrix. In the most general case, the nuisance estimation may play a role in the asymptotic limit and we give a robust modification for these irregular scenarios. Monte Carlo studies suggest a good power performance of our proposed test against high dimensional dense alternative for various data generating processes. We apply the test to detect the significance of over one hundred exogenous variables in the FRED-MD database for predicting the monthly growth in the US industrial production index.

A Stepwise and Dynamic C-Vine Copula–Based Approach for Nonstationary Monthly Streamflow Forecasts

AbstractIn recent years, the stationary assumption of hydroclimatic variables as well as their temporal and spatial dependence structure have been challenged due to anthropogenic and climate change...

The development of a novel nonstationary meteorological and hydrological drought index using the climatic and anthropogenic indices as covariates

Hydrometeorological variables such as precipitation and runoff are not necessarily stationary under change environment due to anthropogenic influences and climate change. Therefore, the assumption of stationary of standardized drought indices cannot necessarily be applied in the future. The novelty of this study is to develop a nonstationary multivariate standardized drought index, entitled the Nonstationary Meteorological and Hydrological Drought Index (NMHDI), as an improvement of the Meteorological and Hydrological Drought Index (MHDI). The method used consisted of three parts: (1) simulation of the nonstationary marginal distribution of precipitation data using climatic indices as covariates; (2) the nonstationary probability model fitted to runoff data using the climatic and anthropogenic indices as covariates and; (3) using the time-varying copula model to describe the temporal dependence structure of precipitation and runoff, following which the NMHDI was calculated. The performances of the NMHDI and MHDI was compared at the Huaxian station in Weihe River Basin, western China for the period 1961–2010 to illustrate the capabilities of the NMHDI. Moreover, bivariate frequency analysis was conducted using the two indices. The results indicated that the nonstationary model showed better performance in reproducing the variations in precipitation and runoff data and their dependence structure over time as compared with stationary one. The NMHDI identified more frequent extreme droughts. The improved performance of the NMHDI was attributed to its ability to respond to the continuously changing environment. In addition, the MHDI and NMHDI estimated significantly different recurrence periods. The proposed NMHDI provides a novel approach to comprehensive drought monitoring, and can provide valuable information for drought management policymaking under a changing environment.

The conditional distance autocovariance function

AbstractThe partial autocorrelation function (PACF) is often used in time series analysis to identify the extent of the lag in an autoregressive model. However, the PACF is only suitable for detecting linear correlations. This article proposes the conditional distance autocovariance function (CDACF), which is zero if and only if measured time series components are conditionally independent. Due to the lack of this property, traditional tools for measuring partial correlations such as the PACF cannot work well for nonlinear sequences. Based on the CDACF, we introduce a tool known as an integrated conditional distance autocovariance function (ICDACF), which can test conditional temporal dependence structures of a sequence and estimate the order of an autoregressive process. Simulation studies reveal that the ICDACF can detect the conditional dependence of nonlinear autoregressive models efficiently while controlling for type‐I error rates. Finally, an analysis of a Bitcoin price dataset using the ICDACF demonstrates that our method has considerable advantages over other state‐of‐the‐art methods.

PAC-Bayes Bounds on Variational Tempered Posteriors for Markov Models.

Datasets displaying temporal dependencies abound in science and engineering applications, with Markov models representing a simplified and popular view of the temporal dependence structure. In this paper, we consider Bayesian settings that place prior distributions over the parameters of the transition kernel of a Markov model, and seek to characterize the resulting, typically intractable, posterior distributions. We present a Probably Approximately Correct (PAC)-Bayesian analysis of variational Bayes (VB) approximations to tempered Bayesian posterior distributions, bounding the model risk of the VB approximations. Tempered posteriors are known to be robust to model misspecification, and their variational approximations do not suffer the usual problems of over confident approximations. Our results tie the risk bounds to the mixing and ergodic properties of the Markov data generating model. We illustrate the PAC-Bayes bounds through a number of example Markov models, and also consider the situation where the Markov model is misspecified.

Most Powerful Test against High Dimensional Local Alternatives

We propose a powerful quadratic test for the overall significance of many weak exogenous variables in a dense autoregressive model. By shrinking the classical weighting matrix on the sample moments to be identity, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a non-parametric error distribution and estimation of the autoregressive coefficients. Using random matrix theory, we show that the test has the optimal asymptotic testing power among a large class of competitors against local dense alternatives whose direction is free in the eigenbasis of the sample covariance matrix among regressors. The asymptotic results are adaptive to the predictors' cross-sectional and temporal dependence structure, and do not require a limiting spectral law of their sample covariance matrix. The method extends beyond autoregressive models, and allows more general nuisance parameters. Monte Carlo studies suggest a good power performance of our proposed test against high dimensional dense alternative for various data generating processes. We apply our tests to detect the overall significance of over one hundred exogenous variables in the latest FRED-MD database for predicting the monthly growth in the US industrial production index.

Risk management via contemporaneous and temporal dependence structures with applications

This paper presents the estimation methods of the Bayesian Graphical Vector Auto-regression with and without innovations such as external regressors (BG-VAR(X)) and Bayesian Graphical Systems Equation Modelling with and without exogenous variables (BG-SEM(X)), which are developed to examine risk network structures embedded in multivariate time series. This methodical approach allows for the analysis of various dynamics and persistence in the multivariate time series in terms of risk propagation. For instance, both the BG-SEMX and BG-VARX can reveal the within-day and across-day major risk transmitters as well as risk recipients from other univariate time series, which better explain risk contagion using complex network models. In addition, the procedures for models with and without exogenous variables have been explored, which shows that the former produce more network structures compared to the latter and therefore depict their influential role. This approach, therefore, provides a platform for future research in terms of extension of the method to encompass different types of multivariate data with additional innovations that might aid feasible analysis and the design of policy instruments and the implementation of relevant policy implications.•Development and application of innovative network models that enhances the efficient analysis of multivariate time series data.•Estimation of intra-day and inter-day interconnection from a daily multivariate time series data and their dynamics and persistence from contagion analysis viewpoint.

Advanced Statistical Learning on Short Term Load Process Forecasting

Short Term Load Forecast (STLF) is necessary for effective scheduling, operation optimization trading, and decision-making for electricity consumers. Modern and efficient machine learning methods are recalled nowadays to manage complicated structural big datasets, which are characterized by having a nonlinear temporal dependence structure. We propose different statistical nonlinear models to manage these challenges of hard type datasets and forecast 15-min frequency electricity load up to 2-days ahead. We show that the Long-short Term Memory (LSTM) and the Gated Recurrent Unit (GRU) models applied to the production line of a chemical production facility outperform several other predictive models in terms of out-of-sample forecasting accuracy by the Diebold-Mariano (DM) test with several metrics. The predictive information is fundamental for the risk and production management of electricity consumers.

Fuzzy Postprocessing to Advance the Quality of Continental Seasonal Hydrological Forecasts for River Basin Management

AbstractStreamflow forecasting services driven by seasonal meteorological forecasts from dynamic prediction systems deliver valuable information for decision-making in the water sector. Moving beyond the traditional river basin boundaries, large-scale hydrological models enable a coordinated, efficient, and harmonized anticipation and management of water-related risks (droughts, floods). However, the use of forecasts from such models at the river basin scale remains a challenge, depending on how the model reproduces the hydrological features of each particular river basin. Consequently, postprocessing of forecasts is a crucial step to ensure usefulness at the river basin scale. In this paper we present a methodology to postprocess seasonal streamflow forecasts from large-scale hydrological models and advance their quality for local applications. It consists of fuzzy logic systems that bias-adjust seasonal forecasts from a large-scale hydrological model by comparing its modeled streamflows with local observations. The methodology is demonstrated using forecasts from the pan-European hydrological model E-HYPE at the Jucar River basin (Spain). Fuzzy postprocessed forecasts are compared to postprocessed forecasts derived from a quantile mapping approach as a benchmark. Fuzzy postprocessing was able to provide skillful streamflow forecasts for the Jucar River basin, keeping most of the skill of raw E-HYPE forecasts and also outperforming quantile-mapping-based forecasts. The proposed methodology offers an efficient one-to-one mapping between large-scale modeled streamflows and basin-scale observations preserving its temporal dependence structure and can adapt its input set to increase the skill of postprocessed forecasts.