Multivariate Time Series Models Research Articles

Dynamic Modeling Data Return by Using BEKK-GARCH (Study: PT. Indofarma Tbk (INAF) and PT. Kimia Farma Tbk (KAEF) from June 2015 to July 2020)

The Vector Autoregressive (VAR) model is a statistical model that can be used for modeling multivariate time series data which is commonly applied in the fields of finance, management, business and economics. However, economic data, especially return values, have quite high data fluctuations, so we need to add the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model in the analysis to obtain efficient results. This study will discuss the formation of the best model for multivariate time series data, namely return data of PT. Indofarma Tbk. (INAF) and PT. Kimia Farma Tbk. (KAEF) from June 2015 to July 2020, where data retuned for the two variables tended to have a high volatility shock at some time and low volatility at other times which characterizes the data as having an ARCH effect so that the GARCH model will be used in this analysis, namely the BEKK-model. GARCH. This model proposes a new parameterization which is easily given a restriction, namely the requirement that H_t must be positive for all values of ε_t and x_t in sample room. Based on the selection of the best model using the AICC, HQC, AIC and SBC criteria, it is found that the VAR (1)-GARCH (1,1) model is the best model for the data used. Then this research will also examine the behavior and relationship between INAF and KAEF based on Granger Causality and Impulse Response. In addition, based on the forecasting results of the VAR (1)-GARCH (1,1) model, it shows that this model is good for short-term forecasting.

DYNAMIC MODELING OF TIME SERIES DATA USING BEKK-GARCH MODEL

The Vector Autoregressive Moving Average (VARMA) model is one of the models that is often used in modeling multivariate time series data. In time-series data of economics, especially data return, they usually have high fluctuations in some periods, so the return volatility is unstable. In modeling data return of share prices ADRO and ITMG, the behavior of high volatility will be considered. This study aims to find the best model that fits the data return of share price of the energy companies of PT Adaro Energy Tbk (ADRO) and PT Indo Tambangraya Megah Tbk (ITMG), to analyze the behavior of impulse response of the variables data return ADRO and ITMG, to analyze the granger causality test, and to forecast the next 12 periods. Based on the selection of the best model using the criteria of AICC, HQC, AIC, and SBC, it was found that the VARMA (2.2) -GARCH (1.1) model is the best one for the data in this study. The model VARMA(2,2)-GARCH (1,1) is then written as a univariate model. For the univariate ADRO model, the test statistics F = 4,73 and P-value = 0,0084, which indicates the model is very significant; and for the univariate ITMG model, the test statistics is F = 5,82 and P-value 0,0001, which indicates the model is significant. Based on the best model selected, the impulse response, Granger causality test, and forecasting for the next 12 periods are discussed.

Comparison of Forecasting Performance with VAR vs. ARIMA Models Using Economic Variables of Bangladesh

The main concept of this research was forecasting a group of variables simultaneously, thus making use of correlations among the variables. This research aims to check forecasting performance among different VAR and ARIMA models applying some economic indicators of Bangladesh. Data sets were collected from secondary sources of Bangladesh such as Bangladesh bank bulletin, Bangladesh economic review, Monthly economic trends of Bangladesh Bank, and Statistical yearbook of Bangladesh. The stationary VAR and ARIMA models were applied for predicting these financial variables and then checked the accuracy by comparing ME, RMSE, MAE, MPE, MAPE, and MASE of respected the variables. This research found that the VAR model presented a better forecast than ARIMA models for the highly correlated variables such as GDP vs. GNP, Export vs. Import, etc. But ARIMA and VAR models performed almost the same for comparatively low correlated variables. That's means the variables were comparatively low correlated couldn't give a better forecast in the multivariate time series model rather than the univariate time series model. Finally, researchers concluded that before forecasting the authority should check correlations among the variables, and for high correlated variables, the VAR model should be used for forecasting, and otherwise, they can consider any models for both of these correlated and uncorrelated variables.

Temporal Aggregation Effects in Spatiotemporal Traffic Modelling.

Spatiotemporal models are a popular tool for urban traffic forecasting, and their correct specification is a challenging task. Temporal aggregation of traffic sensor data series is a critical component of model specification, which determines the spatial structure and affects models’ forecasting accuracy. Through extensive experiments with real-world data, we investigated the effects of the selected temporal aggregation level for forecasting performance of different spatiotemporal model specifications. A set of analysed models include travel-time-based and correlation-based spatially restricted vector autoregressive models, compared to classical univariate and multivariate time series models. Research experiments are executed in several dimensions: temporal aggregation levels, forecasting horizons (one-step and multi-step forecasts), spatial complexity (sequential and complex spatial structures), the spatial restriction approach (unrestricted, travel-time-based and correlation-based), and series transformation (original and detrended traffic volumes). The obtained results demonstrate the crucial role of the temporal aggregation level for identification of the spatiotemporal traffic flow structure and selection of the best model specification. We conclude that the common research practice of an arbitrary selection of the temporal aggregation level could lead to incorrect conclusions on optimal model specification. Thus, we recommend extending the traffic forecasting methodology by validation of existing and newly developed model specifications for different temporal aggregation levels. Additionally, we provide empirical results on the selection of the optimal temporal aggregation level for the discussed spatiotemporal models for different forecasting horizons.

Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models

ABSTRACT The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduce the forecasting performances of the existing bootstrap prediction intervals calculated based on non-robust estimators. In the univariate and multivariate autoregressive time series, we propose a robust bootstrap algorithm for constructing prediction intervals and forecast regions. The proposed procedure is based on the weighted likelihood estimates and weighted residuals. Its finite sample properties are examined via a series of Monte Carlo studies and two empirical data examples.

Toward Extremely Precise Radial Velocities. II. A Tool for Using Multivariate Gaussian Processes to Model Stellar Activity

Abstract The radial velocity method is one of the most successful techniques for the discovery and characterization of exoplanets. Modern spectrographs promise measurement precision of 0.2–0.5 m s−1 for an ideal target star. However, the intrinsic variability of stellar spectra can mimic and obscure true planet signals at these levels. Rajpaul et al. and Jones et al. proposed applying a physically motivated, multivariate Gaussian process (GP) to jointly model the apparent Doppler shift and multiple indicators of stellar activity as a function of time, so as to separate the planetary signal from various forms of stellar variability. These methods are promising, but performing the necessary calculations can be computationally intensive and algebraically tedious. In this work, we present a flexible and computationally efficient software package, GPLinearODEMaker.jl, for modeling multivariate time series using a linear combination of univariate GPs and their derivatives. The package allows users to easily and efficiently apply various multivariate GP models and different covariance kernel functions. We demonstrate GPLinearODEMaker.jl by applying the Jones et al. model to fit measurements of the apparent Doppler shift and activity indicators derived from simulated active solar spectra time series affected by many evolving starspots. We show how GPLinearODEMaker.jl makes it easy to explore the effect of different choices for the GP kernel. We find that local kernels could significantly increase the sensitivity and precision of Doppler planet searches relative to the widely used quasiperiodic kernel.

Predicting the Need For Vasopressors in the Intensive Care Unit Using an Attention Based Deep Learning Model.

Previous models on prediction of shock mostly focused on septic shock and often required laboratory results in their models. The purpose of this study was to use deep learning approaches to predict vasopressor requirement for critically ill patients within 24 h of intensive care unit (ICU) admission using only vital signs. We used data from the Medical Information Mart for Intensive Care III database and the eICU Collaborative Research Database to develop a vasopressor prediction model. We performed systematic data preprocessing using matching of cohorts, oversampling, and imputation to control for bias, class imbalance, and missing data. Bidirectional long short-term memory (Bi-LSTM), a multivariate time series model, was used to predict the need for vasopressor therapy using serial physiological data collected 21 h prior to prediction time. Using data from 10,941 critically ill patients from 209 ICUs, our model achieved an initial area under the curve of 0.96 (95% CI 0.96-0.96) to predict the need for vasopressor therapy in 2 h within the first day of ICU admission. After matching to control class imbalance, the Bi-LSTM model had area under the curve of 0.83 (95% CI 0.82-0.83). Heart rate, respiratory rate, and mean arterial pressure contributed most to the model. We used Bi-LSTM to develop a model to predict the need for vasopressor for critically ill patients for the first 24 h of ICU admission. With attention mechanism, respiratory rate, mean arterial pressure, and heart rate were identified as key sequential determinants of vasopressor requirements.

Study on the dynamic characteristics of shallow groundwater level under the influence of climate change and human activities in Cangzhou, China

Abstract Based on the monitoring data of groundwater level, mining data and meteorological data from 1986 to 2015 in Cangzhou City, the change characteristics of depth of groundwater level were studied. On this basis, the nonparametric statistical test method (Mann–Kendall method) was used to study the trend of depth of groundwater level. Besides In addition, the principal component analysis method and grey correlation method were used to study groundwater influence factors. Finally, the multivariable time series model was used to predict the depth of groundwater level. The results showed that in the past 30 years, influenced by human activities and meteorological changes, the groundwater flow field in 1986–2015 was generally move from southwest to northeast, the depth of groundwater level was increasing from the initial 3.26 to 4.06 m, with an annual increase rate of 0.027 m/a; the contribution rate of exploitation factor, precipitation factor, evaporation factor were 40, 20 and 40%; the fitting figure of the observed values and the predicted values were very good, with an average relative error of 7.73%. According to the prediction schemes, when the evaporation increases by 5%, and the agricultural exploitation decreases by 5%, the depth of groundwater will reach 3.39 m; when the evaporation increases by 10%, and the agricultural exploitation decreases by 10%, the depth of groundwater will reach 3.32 m. This study had important reference significance for regional groundwater treatment and rational utilization.

GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments.

Developing multivariate time series models to examine the interrelations between police enforcement, traffic violations, and traffic crashes

Safer roads and police enforcement are closely associated since the latter directly encourages road users to improve their behavior by complying with basic traffic rules and laws. Understanding the relationships between police enforcement, driving behavior, and traffic safety is a prerequisite for optimizing enforcement strategies. However, there is a dearth of research on the contemporaneous relationships between these three parameters. Using multivariate time series techniques, this study provides an in-depth analysis of contemporaneous relationships and dynamic interactions among police enforcement, traffic violations, and traffic crashes. The amount of police patrol time per day was used as a surrogate measure for police enforcement intensity. A vector autoregressive (VAR) model was first used to examine the influences of exogenous factors including weather conditions and holidays. Based on the findings of the VAR model, a structural vector autoregressive (SVAR) model was developed to determine contemporaneous effects; the Granger causality test was employed to detect any dynamic interactions between the three parameters. The results indicated that traffic crashes and violations had weekly variation and were significantly impacted by holiday and weather conditions, while police patrol time was not impacted. A contemporaneous negative impact of police patrol time was found in traffic crashes: each 1% increase in police patrol time was associated with a 0.15% decrease in contemporaneous crash frequency. The findings from the Granger causality test demonstrated that police patrol time did not Granger-cause traffic crashes, but crashes Granger-caused police patrol time. The significant bidirectional interactions in conditional variances of police enforcement, traffic violations, and traffic crashes further confirm the necessity to analyze the three simultaneously. The findings of this study are expected to assist the relevant traffic authorities in devising policies and strategies such as optimal police patrol scheduling.

An approach for evaluating the economic impacts of harmful algal blooms: The effects of blooms of toxic Dinophysis spp. on the productivity of Scottish shellfish farms

Shellfish production is an important activity for the economy of many countries. As well as its direct value, it helps to stabilize communities in rural areas characterized by limited job opportunities. It is also important for consumers who recognize shellfish as a healthy product that gains its nutrition from natural plankton without the need for fertilizers, chemical treatments or other anthropogenic intervention typical of terrestrial agriculture or other marine aquaculture. Nevertheless, global shellfish fisheries are under threat from harmful algal blooms (HABs) and related biotoxins, whose production is potentially exacerbated by global changes. This research provides evidence of economic impacts on Scottish shellfish farms in the last 10 years caused by HABs and their associated biotoxins. In contrast to previous approaches that have focused on variation in production as a function of temporal trends and blooms events, we use a production function approach to show which input factors (labour, capital, climate variables, concentration of biotoxins) have an effect on production. Results show that diarrhoetic shellfish toxins produced by the genera Dinophysis are most significant. A 1% change in the production of these biotoxins reduces shellfish production by 0.66%, with an average yearly negative variation in production of 15% (1,080 ton) and an economic loss (turnover) of £ (GBP) 1.37 m per year (in 2015 currency) over a national annual industry turnover of ~ £ 12 m. The production function approach is coupled with a multivariate time series model (VAR) capturing the statistical relationship between algal concentration, information on climatic variables and biotoxins to forecast the damage to shellfish production from HABs. This provides producers and regulators with the economic information to plan temporal and spatial mitigating measures necessary to limit damages to production by comparing the costs of these measures with the costs of lost production.

Influential nodes and anomalous topic activities in social networks using multivariate time series and topic modeling

It is important to understand the behavior within a social network, particularly excessive communications between nodes. Such excessive activities in a network provide an insight into the pattern of communication between nodes, which, in some cases, could lead to a fraudulent behavior. Scan statistics have been applied before to detect the excessive communications in email networks. However, they alone are not effective in revealing the dynamic relationships and progression of chatter as the scan statistics relate to the maximum of locality statistics. Here a multivariate time series model, vector autoregressive (VAR) model, has been developed and applied to the metadata of organization e-mails as a case study to detect a group of influential nodes and their dynamic relationship. Furthermore, we devise a new methodology, which utilizes the probabilistic topic model obtained from the e-mail content, scan statistics, and time series of maximum information flow. We demonstrate how the influential vertices obtained from the VAR model are connected with the anomalous topic activities. These methodologies would be highly useful in studying the excessive communications and anomalous topic activities in other dynamic networks, such as, twitter networks, telephone calls, scientific collaborations, and other social networks.

Adaptive Variable Selection for Sequential Prediction in Multivariate Dynamic Models

We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant models. Based on formal Bayesian decision-theoretic reasoning, we develop a time-adaptive approach to exploring, weighting, combining and selecting models that differ in terms of predictive variables included. The adaptivity allows for changes in the sets of favored models over time, and is guided by the specific forecasting goals. A synthetic example illustrates how decision-guided variable selection differs from traditional Bayesian model uncertainty analysis and standard model averaging. An applied study in one motivating application of long-term macroeconomic forecasting highlights the utility of the new approach in terms of improving predictions as well as its ability to identify and interpret different sets of relevant models over time with respect to specific, defined forecasting goals.

Multivariate time series analysis from a Bayesian machine learning perspective

In this paper, we perform multivariate time series analysis from a Bayesian machine learning perspective through the proposed multivariate Bayesian time series (MBTS) model. The multivariate structure and the Bayesian framework allow the model to take advantage of the association structure among target series, select important features, and train the data-driven model at the same time. Extensive analyses on both simulated data and empirical data indicate that the MBTS model is able to, cover the true values of regression coefficients in 90% credible intervals, select the most important predictors, and boost the prediction accuracy with higher correlation in absolute value of the target series, and consistently yield superior performance over the univariate Bayesian structural time series (BSTS) model, the autoregressive integrated moving average with regression (ARIMAX) model, and the multivariate ARIMAX (MARIMAX) model, in one-step-ahead forecast and ten-steps-ahead forecast.

Sectoral Employment Dynamics in Australia and the COVID‐19 Pandemic

AbstractWe develop a multivariate time series model of employment in 19 sectors for Australia. We use this model to determine the long‐run effect of a 1% increase in economic activity in any chosen sector on aggregate employment. Our findings point to manufacturing and construction sectors as those that generate the largest positive spillovers for the aggregate economy. Moreover, we provide an interactive web‐based app that produces our model's forecasts based on any user‐specified scenario. As the restrictions associated with the COVID‐19 pandemic evolve, the sectoral employment multipliers together with these interactive tools will provide useful information for policymakers.

Spatiotemporal characteristics and the epidemiology of tuberculosis in China from 2004 to 2017 by the nationwide surveillance system

BackgroundChina has always been one of the countries with the most serious Tuberculosis epidemic in the world. Our study was to observe the Spatial-temporal characteristics and the epidemiology of Tuberculosis in China from 2004 to 2017 with Joinpoint regression analysis, Seasonal Autoregressive integrated moving average (SARIMA) model, geographic cluster, and multivariate time series model.MethodsThe data of TB from January 2004 to December 2017 were obtained from the notifiable infectious disease reporting system supplied by the Chinese Center for Disease Control and Prevention. The incidence trend of TB was observed by the Joinpoint regression analysis. The Seasonal autoregressive integrated moving average (SARIMA) model was used to predict the monthly incidence. Geographic clusters was employed to analyze the spatial autocorrelation. The relative importance component of TB was detected by the multivariate time series model.ResultsWe included 13,991,850 TB cases from January 2004 to December 2017, with a yearly average morbidity of 999,417 cases. The final selected model was the 0 Joinpoint model (P = 0.0001) with an annual average percent change (AAPC) of − 3.3 (95% CI: − 4.3 to − 2.2, P < 0.001). A seasonality was observed across the 14 years, and the seasonal peaks were in January and March every year. The best SARIMA model was (0, 1, 1) X (0, 1, 1)12 which can be written as (1-B) (1-B12) Xt = (1–0.42349B) (1–0.43338B12) εt, with a minimum AIC (880.5) and SBC (886.4). The predicted value and the original incidence data of 2017 were well matched. The MSE, RMSE, MAE, and MAPE of the modelling performance were 201.76, 14.2, 8.4 and 0.06, respectively. The provinces with a high incidence were located in the northwest (Xinjiang, Tibet) and south (Guangxi, Guizhou, Hainan) of China. The hotspot of TB transmission was mainly located at southern region of China from 2004 to 2008, including Hainan, Guangxi, Guizhou, and Chongqing, which disappeared in the later years. The autoregressive component had a leading role in the incidence of TB which accounted for 81.5–84.5% of the patients on average. The endemic component was about twice as large in the western provinces as the average while the spatial-temporal component was less important there. Most of the high incidences (> 70 cases per 100,000) were influenced by the autoregressive component for the past 14 years.ConclusionIn a word, China still has a high TB incidence. However, the incidence rate of TB was significantly decreasing from 2004 to 2017 in China. Seasonal peaks were in January and March every year. Obvious geographical clusters were observed in Tibet and Xinjiang Province. The relative importance component of TB driving transmission was distinguished from the multivariate time series model. For every provinces over the past 14 years, the autoregressive component played a leading role in the incidence of TB which need us to enhance the early protective implementation.

Multivariate Time Series Analysis to Impact Assessment of Nominal Economic Indicators on Federal Government Revenue and Economic Growth in Nigeria

Nigeria has all it takes to become Sub-Saharan Africa’s largest economy and a key contributor in the global economy as a result of her agricultural and natural resource endowment. Unfortunately, these resources are not sufficiently and efficiently utilized, resulting to some negative economic implications such as underdeveloped economy in world ranking, high unemployment status, poor standard of living, abject poverty, devaluating currency, lack of technological innovations and unstable economy among others. This paper investigates the impact of the Oil and Non-Oil producing sectors to Federal Government Revenue and Economic Growth in Nigeria, using the concept of multivariate time series vector autoregressive (VAR) model. The basic concepts and techniques of multivariate time series modelling and analysis such as Granger Causality tests; Lag Length Selection based on Information Criteria; Augmented Dickey-Fuller and Phillips-Perron Unit Root tests; Kwiatkowski-Phillips-Schmidt-Shin (kpss) Trend & Level Stationarity tests; Sectoral Contributions to Federal Government Revenue, Economic Growth and Growth Rates using Line & Bar Graphs are discussed in detail. The study applied a model for predicting annual Federal Government Revenue and Economic Growth at any time using their respective historical monetary values together with the historical monetary values of the other economic indicators. The empirical findings in this paper revealed that the Federal Government Revenue and Economic Growth are predictable using their historical values together with the historical values of the other indicators. Furtherance to the statistically significant contribution of both the Oil and Non-Oil producing sectors, it is imperative to diversify the Nigerian economy in order to boost Federal Government Revenue, improve the standard of living, alleviate poverty, create employment opportunities and accelerate a long-run sustainable Economic Growth and stability.

A study of financial cycles and the macroeconomy in Taiwan

This paper studies the characteristics of financial cycles (credit and house prices) and their interactions with business cycles in Taiwan. We employ multivariate structural time series model to estimate trend and cyclical components in real bank credit, real house prices, and real GDP. We find that financial cycles are roughly twice the length of the business cycles, and house price cycles lead both credit and business cycles. Nevertheless, the estimated length of business and financial cycles in Taiwan is much shorter than those in industrialized economies. We then use machine learning to evaluate the importance of a macroeconomic variable that predicts downturns of financial cycles, by conducting both in-sample fitting and out-of-sample forecasting. Those macrovariables selected by machine learning reflects Taiwan’s close linkage in trades and financial interdependence with other countries such as China and spillover effects from the Fed’s monetary policy.

Assessing the effect of containment measures on the spatio-temporal dynamic of COVID-19 in Italy

This paper aims at investigating empirically whether and to what extent the containment measures adopted in Italy had an impact in reducing the diffusion of the COVID-19 disease across provinces. For this purpose, we extend the multivariate time-series model for infection counts proposed in Paul and Held (Stat Med 30(10):118–1136, 2011) by augmenting the model specification with B-spline regressors in order to account for complex nonlinear spatio-temporal dynamics in the propagation of the disease. The results of the model estimated on the time series of the number of infections for the Italian provinces show that the containment measures, despite being globally effective in reducing both the spread of contagion and its self-sustaining dynamics, have had nonlinear impacts across provinces. The impact has been relatively stronger in the northern local areas, where the disease occurred earlier and with a greater incidence. This evidence may be explained by the shared popular belief that the contagion was not a close-to-home problem but rather restricted to a few distant northern areas, which, in turn, might have led individuals to adhere less strictly to containment measures and lockdown rules.

Efficient Bayesian PARCOR approaches for dynamic modeling of multivariate time series

A Bayesian lattice filtering and smoothing approach is proposed for fast and accurate modeling and inference in multivariate non‐stationary time series. This approach offers computational feasibility and interpretable time‐frequency analysis in the multivariate context. The proposed framework allows us to obtain posterior estimates of the time‐varying spectral densities of individual time series components, as well as posterior measurements of the time‐frequency relationships across multiple components, such as time‐varying coherence and partial coherence. The proposed formulation considers multivariate dynamic linear models (MDLMs) on the forward and backward time‐varying partial autocorrelation coefficients (TV‐VPARCOR). Computationally expensive schemes for posterior inference on the multivariate dynamic PARCOR model are avoided using approximations in the MDLM context. Approximate inference on the corresponding time‐varying vector autoregressive (TV‐VAR) coefficients is obtained via Whittle's algorithm. A key aspect of the proposed TV‐VPARCOR representations is that they are of lower dimension, and therefore more efficient, than TV‐VAR representations. The performance of the TV‐VPARCOR models is illustrated in simulation studies and in the analysis of multivariate non‐stationary temporal data arising in neuroscience and environmental applications. Model performance is evaluated using goodness‐of‐fit measurements in the time‐frequency domain and also by assessing the quality of short‐term forecasting.