Multivariate Time Series Models Research Articles

The Devil Is in the Tail Dependence: An Assessment of Multivariate Copula‐Based Frameworks and Dependence Concepts for Coastal Compound Flood Dynamics

AbstractA hurricane event can often produce both intense rainfall and a storm tide that can cause a major compound flooding threat to coastlines. This paper examined applications of multivariate copula‐based time series models using data observed during Hurricane Irma (2017) along the coastlines of Florida, Georgia, and South Carolina, United States. Multivariate time series models were developed using bivariate copulas wherein storm tide and rainfall data were modeled using LOWESS‐based autoregressive moving average (ARMA). n samples of observed data were then synthesized using a Monte Carlo approach in which the empirical copula and the parametric estimate of the copula were obtained to approximate two‐sided p‐values using the Rosenblatt probability integral transform method. Analysis suggested that proper selection of the underlying LOWESS‐based ARMA model was the crucial aspect for modeling compound flooding wherein Archimedean, Elliptical, and Extreme Value copulas all offered consistent flexibility in terms of dependence modeling. As a backdrop to compound flood probabilities, this research also outlined both theoretical and applied frameworks for the calculation of non‐exceedance probabilities in a multidimensional environment using classical isofrequency probability assumptions for the “AND” (a bivariate joint probability) and Survival Kendall definitions. Random realizations from storm copulas combined with multivariate non‐exceedance probability definitions ultimately showed there were periods of temporal yet cyclical high intensities that lasted 1–2 hr. Lastly, a discussion is presented on the broader application of the proposed methodology within the field of engineering design and risk management which may serve as a catalyst for the continued research in compound flooding.

Covid-19 impact on Cryptocurrencies market using Multivariate Time Series Models

The ever-growing volume of cryptocurrency transactions indicates the importance to understand the new cryptocurrency market. Many research works have demonstrated the unique features of cryptocurrency market compared to other asset markets. Under the impact of Covid-19, the cryptocurrency market may display more differential features. We analyse these differential features of the cryptocurrency market by studying their return persistence, return asymmetry, interdependency, and volatility spillover. The vector autoregressive moving average model with variance gamma innovations is proposed to capture these features before and during the pandemic outbreak. We consider four cryptocurrencies, namely Bitcoin, Ripple, Dash, and Litecoin which have top market capitalisation. For model estimation, we apply the computational efficient expectation/conditional maximisation algorithm. We interpret the results concerning their technological setups.

A Comparison of Multivariate and Univariate Time Series Models Applied in Tree Sap Flux Analyses

AbstractAccurate model predictions of the tree sap flux in sapwood are critical for forestry water management, primarily due to data availability limitations. Time series models have been used in tree sap flux analyses since 2005. Classic autoregressive models such as the ARIMA (autoregressive integrated moving average), ARIMAX (ARIMA with exogenous variables), SARIMA (seasonal ARIMA) and SARIMAX (seasonal ARIMAX) models are designed and tested for two common exotic species (Eucalyptus citriodora Hook. f. and Acacia auriculaeformis A. Chun) in dry and wet seasons in South China. The performance of the models is assessed with a scoring system for integrating six statistical indices. The results show that taking both seasonal term and exogenous variables into account could improve day sap flux prediction accuracy.

Quantile hidden semi-Markov models for multivariate time series.

This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states’ sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11222-022-10130-1.

Understanding the transmission dynamics of a large-scale measles outbreak in Southern Vietnam

ObjectivesSouthern Vietnam experienced a large measles outbreak of over 26,000 cases during 2018-2020. We aimed to understand and quantify the measles spread in space-time dependence and the transmissibility during the outbreak. MethodsMeasles surveillance reported cases between January 2018 and June 2020, vaccination coverage, and population data at provinicial level were used. To illustrate the spatio-temporal pattern of disease spread, we employed the endemic-epidemic multivariate time series model decomposing measles risk additively into autoregressive, spatio-temporal, and endemic components. Likelihood-based estimation procedures were performed to determine the time-varying reproductive number Re of measles. ResultsOur analysis showed that the incidence of measles was associated with vaccination coverage heterogeneity and spatial interaction between provincial units. The risk of infections was dominated by between-province transmission (36.1% to 78.8%), followed by local endogenous transmission (4.1% to 61.5%). In contrast, the endemic behavior had a relatively small contribution (2.4% to 33.4%) across provinces. In the exponential phase of the epidemic, Re was above the threshold with a maximum value of 2.34 (95% CI: 2.20-2.46). ConclusionLocal vaccination coverage and human mobility are important factors contributing to the measles dynamics in Southern Vietnam, and the high risk of inter-provincial transmission is of most concern. Strengthening the disease surveillance is recommended, and further research is essential to understand the relative contribution of population immunity and control measures in measles epidemics.

Modeling and inference for multivariate time series of counts based on the INGARCH scheme

Modeling multivariate time series of counts using the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) scheme is proposed. The key idea is to model each component of the time series with a univariate INGARCH model, where the conditional distribution is modeled with a one-parameter exponential family distribution, and to use a (nonlinear) parametric function of all components to recursively produce the conditional means. It is shown that the proposed multivariate INGARCH (MINGARCH) model is strictly stationary and ergodic. For inference, the quasi-maximum likelihood estimator (QMLE) and the minimum density power divergence estimator (MDPDE) for robust estimation are adopted, and their consistency and asymptotic normality are verified. As an application, the change point test based on the QMLE and MDPDE is illustrated. The Monte Carlo simulation study and real data analysis using the number of weekly syphilis cases in the United States are conducted to confirm the validity of the proposed method.

Reaction to the COVID-19 pandemic in Seoul with biostatistics.

This paper discusses our collaboration work with government officers in the health department of Seoul during the COVID-19 pandemic. First, we focus on short-term forecasting for the number of new confirmed cases and severe cases. Second, we focus on understanding how much of the current infections has been affected by external influx from neighborhood areas or internal transmission within the area. This understanding may be important because it is linked to the government policy determining non-pharmaceutical interventions. To obtain the decomposition of the effect, districts of Seoul should be considered simultaneously, and multivariate time series models are used. Third, we focus on predicting the number of new weekly confirmed cases for each district in Seoul. This detailed prediction may be important to the government policy on resource allocation. We consider an ensemble method to overcome poor prediction performance of simple models. This paper presents the methodological details and analysis results of the study.

Exponentially Weighted Multivariate HAR Model with Applications in the Stock Market

This paper considers a multivariate time series model for stock prices in the stock market. A multivariate heterogeneous autoregressive (HAR) model is adopted with exponentially decaying coefficients. This model is not only suitable for multivariate data with strong cross-correlation and long memory, but also represents a common structure of the joint data in terms of decay rates. Tests are proposed to identify the existence of the decay rates in the multivariate HAR model. The null limiting distributions are established as the standard Brownian bridge and are proven by means of a modified martingale central limit theorem. Simulation studies are conducted to assess the performance of tests and estimates. Empirical analysis with joint datasets of U.S. stock prices illustrates that the proposed model outperforms the conventional HAR models via OLSE and LASSO with respect to residual errors.

Infinite hidden Markov models for multiple multivariate time series with missing data.

Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper, we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sampling and dynamic programming, to sample the hidden states, and a Bayesian multiple imputation algorithm to impute missing data. In simulation studies, our model excels in estimating hidden states and state-specific means and imputing observations that are missing at random or below the limit of detection. We validate our imputation approach on data from the Fort Collins Commuter Study. We show that the estimated hidden states improve imputations for data that are missing at random compared to existing approaches. In a case study of the Fort Collins Commuter Study, we describe the inferential gains obtained from our model including improved imputation of missing data and the ability to identify shared patterns in activity and exposure among repeated sampling days for individuals and among distinctindividuals.

The Impact of Google Trends on the Tourist Arrivals: A Case of Antalya Tourism

With the growth of the tourism industry, tourism demand forecasting has become an important research topic. Recently researches have shown that Google Trends(GT) data with the help of Google can positively affect the forecast of tourist arrivals. However, the use of this data directly can cause some errors. This article provides suggestions on how the calculation differences according to the same time at different time intervals in GT data (which is obtained on an hourly, daily, monthly and yearly basis) can be eliminated. In this study, it is aimed to examine the effect of GT data for Antalya, Turkey's favorite tourist destination by the Russians. In addition, the multivariate time series models are used to see separately and together the effects of international trade (IT), weather conditions (WC) and number of flights (FN) variables on tourism data, as well as GT data. As a result, it has been seen that the tourist arrival can be forecasted better with the GT (AGT) data, which is recommended to be used by adjusted.

MULTIVARIATE TIME SERIES ANALYSIS IN MODELLING MALARIA CASES IN JIMETA METROPOLIS OF ADAMAWA STATE, NIGERIA

Sub-Sahara Africa harbours most of the Malaria burden including Nigeria. There are scanty studies that aim at modelling these cases particularly in the study area. This study therefore, focused on a multivariate time series model for malaria cases among the residents in Jimeta metropolis of Adamawa State. A secondary data on reported malaria cases for adults, pregnant women and children was collected from January 2011 to December 2020 on monthly basis from medical records at the specialist Hospital, Jimeta, Yola, Adamawa State. The vector autoregressive (VAR) model was employed for modelling. A descriptive analysis was performed on the data. The lag order selection for stationary VAR model suggest lag three as the optimal lag for VAR model with malaria cases among children, adult and pregnant women. To assess how well the model fit the data set, AIC of 26.9458 for model with lag (3) was best. The Breusch-Godfrey LM test for residual serial correlation of VAR model suggest no autocorrelation at each lag, there is no problem of autocorrelation, since the associated p-value is greater than the conventional 0.05 level of significance. Jarque-Bera test shows that the residuals are not normally distributed and the forecast made showed that, rates of malaria cases are higher among adult followed by children and then pregnant women.

Endoscopic optical coherence tomography angiography using inverse SNR-amplitude decorrelation features and electrothermal micro-electro-mechanical system raster scan.

Angiogenesis is closely associated with tumor development and progression. Endoscopic optical coherence tomography angiography (OCTA) enables rapid inspection of mucosal 3D vasculature of inner organs in the early-stage tumor diagnosis; however, it is limited by instabilities of the optical signal and beam scanning. In the phase-unstable swept source OCTA (SS-OCTA), amplitude decorrelation was used to compute the motion-induced changes as motion contrast. The influence of the random noise-induced amplitude fluctuations on decorrelation was characterized as a function of inverse signal-to-noise ratio (SNR) with a multi-variate time series (MVTS) model and statistical analysis. Then, the noise-induced decorrelation artifacts in static tissue regions were eliminated by applying a flow mask based on the statistical relation between inverse SNR (iSNR) and amplitude decorrelation (IDa), which was named IDa-OCTA. In addition, a distal stepwise raster scan was realized with a low-voltage electrothermal micro-electro-mechanical system (ET-MEMS)-based catheter for endoscopic imaging, whereby the stable and repeatable B-scans at each step suppressed the decorrelation noise induced by the spatial mismatch between paired scans. The derived IDa relation was validated through numerical simulation and flow phantom experiments. In vivo human buccal mucosa imaging was performed to demonstrate the endoscopic IDa-OCTA imaging. In this, the subsurface structure and vasculature were visualized in a rapid and depth-resolved manner. The rapid 3D vasculature visualization realized by the endoscopic IDa-OCTA improves the diagnosis of early tumors in internal organs.

Multivariate time series and regression models for forecasting annual maintenance costs of EPDM roofing systems

The scope of this study focuses on developing and comparing the performances of Vector Autoregession (VAR) time series and multivariate linear regression (MLR) models in predicting the annual maintenance costs of Ethylene Propylene Diene Monomer (EPDM) roofing systems. To accomplish the objective of this study, two prediction models that utilized VAR time series and MLR methodologies were developed to enable a comparison of their performances. These two models were developed in four main phases that focused on data collection, data analysis, model development, and validation. The data collection and analysis phases focused on collecting and analyzing historical data of 16 different EPDM roofing systems for a 23-year period from 1997 to 2019. This data was then used to develop two models for predicting the annual maintenance costs of EPDM roofing systems using VAR and MLR methodologies. The performance of these two models were then compared and analyzed in the validation phase. The findings of this performance analysis indicate that the average accuracy of the stepwise MLR model in predicting the annual maintenance costs of EPDM roofs (85%) was slightly higher than the VAR model (83%). The use of the developed models enables facility managers to improve the accuracy of forecasting future roof annual maintenance costs and to provide a more reliable multi-year plan and budget for their building maintenance programs.

Statistical Causality for Multivariate Nonlinear Time Series via Gaussian Process Models

The ability to test for statistical causality in linear and nonlinear contexts, in stationary or non-stationary settings, and to identify whether statistical causality influences trend of volatility forms a particularly important class of problems to explore in multi-modal and multivariate processes. In this paper, we develop novel testing frameworks for statistical causality in general classes of multivariate nonlinear time series models. Our framework accommodates flexible features where causality may be present in either: trend, volatility or both structural components of the general multivariate Markov processes under study. In addition, we accommodate the added possibilities of flexible structural features such as long memory and persistence in the multivariate processes when applying our semi-parametric approach to causality detection. We design a calibration procedure and formal testing procedure to detect these relationships through classes of Gaussian process models. We provide a generic framework which can be applied to a wide range of problems, including partially observed generalised diffusions or general multivariate linear or nonlinear time series models. We demonstrate several illustrative examples of features that are easily testable under our framework to study the properties of the inference procedure developed including the power of the test, sensitivity and robustness. We then illustrate our method on an interesting real data example from commodity modelling.

Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology

This paper contributes by developing an univariate and multivariate harmonic decomposition methodology to model time series.The models are stated in a state space representation derived from a Fourier series analysis to describe an arbitrary signal. The frequency values of the harmonic content are used to define state variables in order to describe a signal through a time-varying linear state space model, which serves to synthesize an optimal state observer (Kalman-Bucy filter). Once the observer converges and the states (harmonics) become constant, the observer model can be used to predict the signal, i.e., a time series forecasting can be performed.The preocedure can be developed for the univariate or multivariate case of time series modeling, where in the last one, a statistical analysis is used to determine which variables should be taken into account to obtain a more accurate model. The proposed modeling approach is successfully applied for the modeling and forecast of the time series of electrical power demand and a wind/solar profile.

Estimating the effectiveness of permanent price reductions for competing products using multivariate Bayesian structural time series models

The Florence branch of an Italian supermarket chain recently implemented a strategy that permanently lowered the price of numerous store brands in several product categories. To quantify the impact of such a policy change, researchers often use synthetic control methods for estimating causal effects when a subset of units receive a single persistent treatment and the rest are unaffected by the change. In our applications, however, competitor brands not assigned to treatment are likely impacted by the intervention because of substitution effects; more broadly, this type of interference occurs whenever the treatment assignment of one unit affects the outcome of another. This paper extends the synthetic control methods to accommodate partial interference, allowing interference within predefined groups but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention, enabling us to estimate our novel effects. In a simulation study we explore our Bayesian procedures’ empirical properties and show that it achieves good frequentists coverage, even when the model is misspecified. We use our new methodology to make causal statements about the impact on sales of the affected store brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.

The asymmetric relationship between oil price shocks and macroeconomic fluctuation in Tanzania: A multivariate time series model approach

As a developing oil importer, Tanzania relies heavily on crude oil imports for the majority of its industrial and socioeconomic operations. Hence, verifying the link between oil price shocks and macroeconomic variables is critical for effective policy formulation and investment decisions. This paper examines the asymmetric relationship between oil price shocks and macroeconomic fluctuations using the linear and nonlinear autoregressive distributed lag models for Tanzania from 1989 to 2020 data set. Oil price and macroeconomic indicators are not cointegrated according to the results of the asymmetric autoregressive distributed lag model (NARDL), which indicates a specification short-run relationship between oil price shocks and macroeconomic indicators. Meanwhile, the analysis shows that the fitted linear ARDL (1, 0, 0) and nonlinear ARDL (1, 0, 0, 0, 1) time series models are significant, which indicate that there is a linear and assymetric relationship between oil price shocks and macroeconomic variables. The linear model (ARDL) shows that the lag 1 of oil price has a positive significant effect while the asymmetric model (NARDL) shows that the negative change in the inflation rate of Tanzania has a negative significant effect on oil price shock.

Bayesian Computation in Dynamic Latent Factor Models

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled via nonlinear forms involving dynamic latent factors representing cross-series relationships. The resulting methodology offers dramatic speed-up in online Bayesian computations for sequential filtering and forecasting in this broad, flexible class of multivariate models. Two examples in nonlinear models for very heterogeneous time series of nonnegative counts demonstrate massive computational efficiencies relative to existing, simulation-based methods, while defining similar filtering and forecasting outcomes.

Stationary vine copula models for multivariate time series

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.

DeepGate: Global-local decomposition for multivariate time series modeling

In multivariate time series, a substantial amount of variables exhibit common dynamics stemming from a small number of global factors. Recent studies have shown that the shared information from global components can enhance the forecasting performance of time series. However, existing global–local approaches treat the global factors as additional hidden states inside the model without providing global series for downstream analysis. In this study, we propose DeepGate, a novel time series forecasting framework based on the explicit global–local decomposition. To retain the global and local series property, we have built decomposition and prediction modules separately. In this way, DeepGate can produce interpretable global series for further tasks while improving forecasting performance with the aid of global and local series. In addition, to alleviate the discrepancy between the training and testing steps, we employ a denoising training technique for multi-step forecasting problems. In numerous experiments on real-world benchmarks for time series forecasting, DeepGate outperforms the baselines including existing global–local models. In particular, the experimental results on synthetic tasks demonstrate that our model can effectively extract underlying global series.