Multivariate Nonlinear Time Series Research Articles

Ground air pollutants explanation based on multiple visibility graph of complex network by temporal community division.

In air pollution studies, the correlation analysis of environmental variables has usually been challenged by parametric diversity. Such variable variations are not only from the extrinsic meteorological conditions and industrial activities but also from the interactive influences between the multiple parameters. A promising solution has been motivated by the recent development of visibility graph (VG) on multi-variable data analysis, especially for the characterization of pollutants' correlation in the temporal domain, the multiple visibility graph (MVG) for nonlinear multivariate time series analysis has been verified effectively in different realistic scenarios. To comprehensively study the correlation between pollutant data and season, in this work, we propose a multi-layer complex network with a community division strategy based on the joint analysis of the atmospheric pollutants. Compared to the single-layer-based complex networks, our proposed method can integrate multiple different atmospheric pollutants for analysis, and combine them with multivariate time series data to obtain higher temporary community division for ground air pollutants interpretation. Substantial experiments have shown that this method effectively utilizes air pollution data from multiple representative indicators. By mining community information in the data, it successfully achieves reasonable and strong interpretive analysis of air pollution data.

A novel recursive multivariate nonlinear time-series modeling method by using the coupling identification concept

This paper focuses on the modeling problem of complex time-series based on a type of multivariate nonlinear model with colored noise, i.e., the M-RBF-ARMA model. For the purpose of achieving highly accuracy modeling performance under colored noise interference, a novel recursive parameter identification algorithm for the M-RBF-ARMA model is investigated. In the framework of constructing several univariate system and noise sub-identification models using the mixed parameter characteristic of the model, three recursive sub-algorithms are presented by applying the coupling identification concept. Based on the singular value decomposition, a recursive update approach with numerical stability for covariance matrices is given. Then a three-stage coupled average extended recursive algorithm is proposed for the M-RBF-ARMA model by using the interactive strategy, which can implement the separable and interactive identification of different type of parameters. The effectiveness of the proposed algorithm is verified by an illustrative and a real multivariate nonlinear time-series.

Identifying quasi-periodic variability using multivariate empirical mode decomposition: a case of the tropical Pacific

Abstract. A variety of statistical tools have been used in climate science to gain a better understanding of the climate system's variability on various temporal and spatial scales. However, these tools are mostly linear, stationary, or both. In this study, we use a recently developed nonlinear and nonstationary multivariate time series analysis tool – multivariate empirical mode decomposition (MEMD). MEMD is a powerful tool for objectively identifying (intrinsic) timescales of variability within a given spatio-temporal system without any timescale pre-selection. Additionally, a red noise significance test is developed to robustly extract quasi-periodic modes of variability. We apply these tools to reanalysis and observational data of the tropical Pacific. This reveals a quasi-periodic variability in the tropical Pacific on timescales ∼ 1.5–4.5 years, which is consistent with El Niño–Southern Oscillation (ENSO) – one of the most prominent quasi-periodic modes of variability in the Earth’s climate system. The approach successfully confirms the well-known out-of-phase relationship of the tropical Pacific mean thermocline depth with sea surface temperature in the eastern tropical Pacific (recharge–discharge process). Furthermore, we find a co-variability between zonal wind stress in the western tropical Pacific and the tropical Pacific mean thermocline depth, which only occurs on the quasi-periodic timescale. MEMD coupled with a red noise test can therefore successfully extract (nonstationary) quasi-periodic variability from the spatio-temporal data and could be used in the future for identifying potential (new) relationships between different variables in the climate system.

Forecast accuracy of the linear and nonlinear autoregressive models in macroeconomic modeling

AbstractMost nonlinear vector autoregressive methods in the econometric literature are based on specific functional forms, such as the smooth transition autoregressive model. This study proposes a general form of the nonlinear vector autoregressive model based on global approximators, such as neural networks, Volterra, and Weiner series. The simulation results of 20 linear and nonlinear multivariate time series processes indicate that nonlinear vector autoregressive methods, especially multi‐output neural networks, are more accurate based on the root mean square error and model confidence set criteria. Applying the global approximator approach to a small‐scale macroeconometric model reveals that the new approach can improve forecast accuracy compared to linear and other nonlinear vector error correction models. In addition, forecasting the relevant variables in a typical exchange rate and monetary policy models based on nonlinear specifications gives more successful results than in the linear case.

On portmanteau-type tests for nonlinear multivariate time series

A general framework to devise portmanteau-type test statistics for a general class of multivariate nonlinear time series models with vector martingale difference errors is formulated. Based on this framework a suite of individual and mixed multivariate test statistics is considered. Two applications are developed: single- and multiple-lag test statistics. In each case, the resulting portmanteau test statistic is based on multivariate residuals and multivariate squared residuals. Moreover, single- and multiple-lag mixed multivariate portmanteau-type tests are introduced. These test statistics are designed to detect different forms of inadequacies in the model residuals jointly. All proposed tests take uncertainty due to model estimation properly into account. The asymptotic null distribution of each test statistic follows from the asymptotic distribution of the general portmanteau-type test statistic in a natural way. Some considerations are given to the empirical size and power of six test statistics via a simulation study. All tests have satisfactory size and power properties in finite samples. To demonstrate their practical use, the proposed test statistics are applied to the residuals of a vector bivariate nonlinear threshold model fitted to U.S. interest rates.

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.

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.

Multilayer Network-Based CNN Model for Emotion Recognition

Human emotions are an important part in daily life. In this paper, a novel multilayer network-based convolutional neural network (CNN) model is proposed for emotion recognition, from multi-channel nonlinear EEG signals. Firstly, in response to the multi-rhythm properties of brain, a multilayer brain network with five rhythm-based layers are derived, where each layer can pertinently describe one specific frequency band. Subsequently, a novel CNN model is carefully designed, which uses the multilayer brain network as input and allows deep learning of the classifiable nonlinear features from the channel and frequency views. Moreover, one DenseNet model is developed as another branch to study time-domain nonlinear features from the EEG signals. All the learned features are eventually concatenated together for emotion recognition. Publicly available SEED dataset is used to test the proposed method, and it shows good results on all 15 subjects, with average accuracy of 91.31%. Our method builds a bridge between the multilayer network and deep learning, suggesting an effective approach for analyzing multivariate nonlinear time series, especially multi-channel EEG signals.

A note on the stability of multivariate non-linear time series with an application to time series of counts

We introduce a simple criterion for studying stationarity and moments properties of some multivariate Markovian autoregressive processes, under a contracting mapping assumption. We apply our results to the Poisson INGARCH model and to one of its multivariate extension recently introduced in the literature. In particular, we obtain optimal stationarity conditions and existence of some exponential moments.

A deep gated recurrent neural network for petroleum production forecasting

Forecasting of oil production plays a vital role in petroleum engineering and contributes to supporting engineers in the management of petroleum reservoirs. However, reliable production forecasting is difficult to achieve, particularly in view of the increase in digital oil big data. Although a significant amount of work has been reported in the literature in relation to the use of machine learning in the oil and gas domain, traditional forecasting approaches have limited potential in terms of representing the complex features of time series data. More specifically, in a high-dimensional nonlinear multivariate time series dataset, a shallow machine is incapable of inferring the dependencies between past and future values. In this context, a novel forecasting model for petroleum production is proposed in this work. The model is a deep-gated recurrent neural network consisting of multiple hidden layers, where each layer has a number of nodes. The proposed model has a low-complexity architecture and the capacity to track long-interval time-series datasets. To evaluate the robustness of our model, the proposed technique was benchmarked with various standard approaches. The extensive empirical results demonstrate that the proposed model outperforms existing approaches.

A Multivariate Weighted Ordinal Pattern Transition Network for Characterizing Driver Fatigue Behavior from EEG Signals

Driver fatigue has caused numerous vehicle crashes and traffic injuries. Exploring the fatigue mechanism and detecting fatigue state are of great significance for preventing traffic accidents, and further lessening economic and societal loss. Due to the objectivity of EEG signals and the availability of EEG acquisition equipment, EEG-based fatigue detection task has raised great attention in recent years. Although there exist various methods for this task, the study of fatigue mechanism and detection of fatigue state still remain much to be explored. To investigate these problems, a multivariate weighted ordinal pattern transition (MWOPT) network is proposed in this paper. To be specific, a simulated driving experiment was first conducted to obtain the EEG signals of subjects in alert state and fatigue state respectively. Then the MWOPT network is constructed based on a novel Shannon entropy. To probe into the mechanism underlying fatigue behavior, the small-worldness index is extracted from the generated MWOPT network. Furthermore, the nodal degree index is input into a classifier to distinguish the fatigue state from alert state. The obtained high accuracy indicates the effectiveness of the proposed network for EEG-based fatigue detection. Besides, four nodes are found to play an important role in identifying fatigue state. These results suggest that the proposed method enables to analyze nonlinear multivariate time series and investigate the driving fatigue behavior.

Comparing the Prediction Accuracy of LSTM and ARIMA Models for Time-Series with Permanent Fluctuation

In developing countries with an unstable economic system, permanent fluctuation in historical data is always a concern. Recognizing dependency and independency of variables are vague and proceeding a reliable forecast model is more complex than other countries. Although linearization of nonlinear multivariate economic time-series to predict, may give a result, the nature of data which shows irregularities in the economic system, should be ignored. New approaches of artificial neural network (ANN) help to make a prediction model with keeping data attributes. In this paper, we used the Tehran Stock Exchange (TSE) intraday data in 10 years to forecast the next 2 months. Long Short-Term Memory (LSTM) from ANN chooses and outputs compared with the autoregressive integrated moving average (ARIMA) model. The results show, although, in long term prediction, the forecast accuracy of both models reduce, LSTM outperforms ARIMA, in terms of error of accuracy, significantly.

Statistical Causality for Multivariate Non-Linear Time Series via Gaussian Processes

The ability to test for statistical causality in linear and non-linear contexts, in stationary or non-stationary settings and to identify whether statistical causality influences trend of volatility forms a piratically 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 multi-variate non-linear 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 non-linear time series models. We develop several illustrative examples of features that are easily testable under our framework to study the properties of the inference procedure developed including power of the test, sensitivity and robustness. We then illustrate our method on an interesting real data example from commodity modelling.

COMPARING THE PREDICTION ACCURACY OF LSTM AND ARIMA MODELS FOR TIME-SERIES WITH PERMANENT FLUCTUATION

In developing countries with an unstable economic system, permanent fluctuation in historical data is always a concern. Recognizing dependency and independency of variables are vague and proceeding a reliable forecast model is more complex than other countries. Although linearization of nonlinear multivariate economic time-series to predict, may give a result, the nature of data which shows irregularities in the economic system, should be ignored. New approaches of artificial neural network (ANN) help to make a prediction model with keeping data attributes. In this paper, we used the Tehran Stock Exchange (TSE) intraday data in 10 years to forecast the next 2 months. Long Short-Term Memory (LSTM) from ANN chooses and outputs compared with the autoregressive integrated moving average (ARIMA) model. The results show, although, in long term prediction, the forecast accuracy of both models reduce, LSTM outperforms ARIMA, in terms of error of accuracy, significantly.

Bayesian estimation and model selection of a multivariate smooth transition autoregressive model

AbstractThe multivariate smooth transition autoregressive model with order k (M‐STAR)(k) is a nonlinear multivariate time series model able to capture regime changes in the conditional mean. The main aim of this paper is to develop a Bayesian estimation scheme for the M‐STAR(k) model that includes the coefficient parameter matrix, transition function parameters, covariance parameter matrix, and the model order k as parameters to estimate. To achieve this aim, the joint posterior distribution of the parameters for the M‐STAR(k) model is derived. The conditional posterior distributions are then shown, followed by the design of a posterior simulator using a combination of Markov chain Monte Carlo (MCMC) algorithms that includes the Metropolis‐Hastings, Gibbs sampler, and reversible jump MCMC algorithms. Following this, extensive simulation studies, as well as case studies, are detailed at the end.

A semiparametric approach for modelling multivariate nonlinear time series

AbstractIn this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada

Evaluating Vector Multiplicative Error Models with the Hosking–Ljung–Box Portmanteau Test and Kernel-Based Test Statistics

Multivariate nonlinear time series models have experienced many developments for modeling data coming from financial applications. Several financial time series are realizations from nonnegative processes. An important class of models is composed of vector multiplicative error models (vMEM), which can describe contemporaneous correlations among innovations and the dynamic interdependencies among variables. Modeling and estimation issues have been addressed, but few diagnostic checking procedures are available. Here, new tests are proposed to check vMEM models. The asymptotic distributions of the popular Hosking–Ljung–Box (HLB) test statistics are found to converge in distribution to weighted sums of independent Chi-squared random variables under the null hypothesis of adequacy. A generalized HLB test statistic is motivated by comparing a vector spectral density estimator of the residuals with the spectral density calculated under the null hypothesis. Under general conditions, that kind of approach leads to consistent procedures and to powerful measures of lack of fit. To improve the finite sample properties, the spectral test statistics rely on the power transformation of Chen and Deo (J R Stat Soc Ser B 66:117–130, 2004). Appealing properties of the spectral procedures include the distribution-free property and the fact that they converge in distribution to convenient standard normal distributions under the null hypothesis. Simulation experiments are reported to appreciate the properties of the methods. An application using financial data previously analyzed by Cipollini et al. (J Appl Econom 28:1067–1086, 2013) illustrates the merits of our procedures.

Financial fragmentation and the monetary transmission mechanism in the euro area: a smooth transition VAR approach

Abstract This paper investigates the effect of financial fragmentation on the monetary transmission mechanism in different Euro area economies, categorized into two groups: countries considered as “core” economies and countries characterized as “peripheral” economies. We analyze the effects of financial fragmentation on the monetary transmission mechanism through the traditional interest rate channel. To gauge the impact of changes in policy rates on the behavior of real variables such as aggregate output and employment we use a Smooth Transition VAR (VSTAR) model. Employing a nonlinear multivariate time series approach helps us capture the regime-dependent dynamics of the variables under study. The results obtained show that money market rates targeted by the central bank do not completely pass through to banks’ lending rates to firms, particularly in a financially fragmented environment. This finding supports the hypothesis of an impairment of the monetary transmission mechanism as a result of financial fragmentation. Given this impairment in some sectors and regions an accompanying credit volume policy might have been appropriate.

A novel echo state network for multivariate and nonlinear time series prediction

A robust and adaptive multivariate nonlinear time series prediction model is proposed based on echo state network and variational inference and we call it robust variational echo state network (RVESN). RVESN uses a heavy-tailed and more robust Gaussian mixture distribution as the likelihood function of the model output. The variational inference procedure which has an advantage over the Laplace approximation is utilized to handle the marginal likelihood function of the model output which is analytically intractable for the mixture distribution. RVESN not only has strong capability of nonlinear approximation as echo state network and avoids the cross-validation process of estimating model parameters but also is more robust to outliers compared to the traditional Bayesian learning with a single Gaussian distribution as the likelihood function of the model output. And furthermore, the Gaussian mixture distribution can describe the underlying dynamic characteristics of the multivariate time series more comprehensively and practically than a single Laplace or Gaussian one by an adaptive parameter. The experimental results of artificial and real-world multivariate nonlinear time series with and without outliers demonstrate that RVESN has better prediction performance.

Constructing ordinal partition transition networks from multivariate time series

A growing number of algorithms have been proposed to map a scalar time series into ordinal partition transition networks. However, most observable phenomena in the empirical sciences are of a multivariate nature. We construct ordinal partition transition networks for multivariate time series. This approach yields weighted directed networks representing the pattern transition properties of time series in velocity space, which hence provides dynamic insights of the underling system. Furthermore, we propose a measure of entropy to characterize ordinal partition transition dynamics, which is sensitive to capturing the possible local geometric changes of phase space trajectories. We demonstrate the applicability of pattern transition networks to capture phase coherence to non-coherence transitions, and to characterize paths to phase synchronizations. Therefore, we conclude that the ordinal partition transition network approach provides complementary insight to the traditional symbolic analysis of nonlinear multivariate time series.