Multivariate Time Series Models Research Articles

Analysis Multivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia

Many analytical methods can be utilized for multivariate time series modeling. One of the analytical models for modeling time series data with multiple variables is the State Space Model. The data to be analyzed in this study is inflation data from expenditure groups such as processed foods, beverages, cigarettes, and tobacco; and housing inflation for water, electricity, gas, and fuel from January 2001 to December 2021. The aim is to determine the best State Space Model that fits the data for forecasting. In this study, the State Space method will be utilized further with multivariate time series data and represent State Space in Vector Autoregressive (VAR) to determine the relationship between groups of observed variables.

Molecular-Composition Analysis of Glass Chemical Composition Based on Time-Series and Clustering Methods.

The weathering of ancient glass relics has long been a concerned. Therefore, a systematic and more comprehensive mathematical model with which to correctly judge the category of ancient glass products whose chemical composition changes due to weathering should be established. This paper systematically analyzes and studies the changes in the composition of ancient glass products as a result of weathering of. We first analyze the surface weathering of glass relics and its correlation with three properties and establish a multivariable time-series model to predict the chemical-composition content before weathering. Next, we use one-way analysis of variance for subclassification and, finally, we use a principal component analysis of the rationality, and change the significance level to determine its sensitivity, for the reasonable prediction of the chemical-composition content and classification to provide a theoretical basis for improving the model. This allows the model to provide reference values, which can be used in the protection of cultural relics, historical research, and other fields.

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.

Effective short-term forecasts of Saudi stock price trends using technical indicators and large-scale multivariate time series.

Forecasting the stock market trend and movement is a challenging task due to multiple factors, including the stock's natural volatility and nonlinearity. It concerns discovering the market's hidden patterns with respect to time to enable proactive decision-making and better futuristic insights. Recurrent neural network-based methods have been a prime candidate for solving complex and nonlinear sequences, including the task of modeling multivariate time series forecasts. Due to the lack of comprehensive and reference work in short-term forecasts for the Saudi stock price and trends, this article introduces a comprehensive and accurate forecasting methodology tailored to the Saudi stock market. Two steps were configured to render effective short-term forecasts. First, a custom-built feature engineering streamline was constructed to preprocess the raw stock data and enable financial-related technical indicators, followed by a stride-based sliding window to produce multivariate time series data ready for the modeling phase. Second, a well-architected Gated Recurrent Unit (GRU) model was constructed and carefully calibrated to yield accurate multi-step forecasts, which was trained using the recently published historical multivariate time-series data from the primary Saudi stock market index (TASI index), in addition to being benchmarked against a suitable baseline model, namely Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX). The output predictions from the proposed GRU model and the VARMAX model were evaluated using a set of regression-based metrics to assess and interpret the model precision. The empirical results demonstrate that the proposed methodology yields outstanding short-term forecasts of the Saudi stock price trends price compared to existing efforts related to this work.

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. To address this issue, a computationally efficient multivariate Bayesian Circular Lattice Filter is developed, extending the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The proposed estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of the proposed approach, a comprehensive comparison with other competing methods is conducted through simulation studies and finds that, in most cases, the proposed approach performs superior in terms of the average squared error between the estimated and true time-varying spectral density. Finally, the methodology is demonstrated through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.

Efficient Variational Bayes Learning of Graphical Models With Smooth Structural Changes.

Estimating a sequence of dynamic undirected graphical models, in which adjacent graphs share similar structures, is of paramount importance in various social, financial, biological, and engineering systems, since the evolution of such networks can be utilized for example to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. Existing methods for learning dynamic graphical models require the tuning parameters that control the graph sparsity and the temporal smoothness to be selected via brute-force grid search. Furthermore, these methods are computationally burdensome with time complexity O(NP3) for P variables and N time points. As a remedy, we propose a low-complexity tuning-free Bayesian approach, named BASS. Specifically, we impose temporally dependent spike and slab priors on the graphs such that they are sparse and varying smoothly across time. An efficient variational inference algorithm based on natural gradients is then derived to learn the graph structures from the data in an automatic manner. Owing to the pseudo-likelihood and the mean-field approximation, the time complexity of BASS is only O(NP2). To cope with the local maxima problem of variational inference, we resort to simulated annealing and propose a method based on bootstrapping of the observations to generate the annealing noise. We provide numerical evidence that BASS outperforms existing methods on synthetic data in terms of structure estimation, while being more efficient especially when the dimension P becomes high. We further apply the approach to the stock return data of 78 banks from 2005 to 2013 and find that the number of edges in the financial network as a function of time contains three peaks, in coincidence with the 2008 global financial crisis and the two subsequent European debt crisis. On the other hand, by identifying the frequency-domain resemblance to the time-varying graphical models, we show that BASS can be extended to learning frequency-varying inverse spectral density matrices, and further yields graphical models for multivariate stationary time series. As an illustration, we analyze scalp EEG signals of patients at the early stages of Alzheimer's disease (AD) and show that the brain networks extracted by BASS can better distinguish between the patients and the healthy controls.

Application of ARIMAX Multivariate Time Series Model in State Revenue Forecasting

Application of ARIMAX Multivariate Time Series Model in State Revenue Forecasting

Deep belief improved bidirectional LSTM for multivariate time series forecasting.

Multivariate time series (MTS) play essential roles in daily life because most real-world time series datasets are multivariate and rich in time-dependent information. Traditional forecasting methods for MTS are time-consuming and filled with complicated limitations. One efficient method being explored within the dynamical systems is the extended short-term memory networks (LSTMs). However, existing MTS models only partially use the hidden spatial relationship as effectively as LSTMs. Shallow LSTMs are inadequate in extracting features from high-dimensional MTS; however, the multilayer bidirectional LSTM (BiLSTM) can learn more MTS features in both directions. This study tries to generate a novel and improved BiLSTM network (DBI-BiLSTM) based on a deep belief network (DBN), bidirectional propagation technique, and a chained structure. The deep structures are constructed by a DBN layer and multiple stacked BiLSTM layers, which increase the feature representation of DBI-BiLSTM and allow for the model to further learn the extended features in two directions. First, the input is processed by DBN to obtain comprehensive features. Then, the known features, divided into clusters based on a global sensitivity analysis method, are used as the inputs of every BiLSTM layer. Meanwhile, the previous outputs of the shallow layer are combined with the clustered features to reconstitute new input signals for the next deep layer. Four experimental real-world time series datasets illustrate our one-step-ahead prediction performance. The simulating results confirm that the DBI-BiLSTM not only outperforms the traditional shallow artificial neural networks (ANNs), deep LSTMs, and some recently improved LSTMs, but also learns more features of the MTS data. As compared with conventional LSTM, the percentage improvement of DBI-BiLSTM on the four MTS datasets is 85.41, 75.47, 61.66 and 30.72%, respectively.

Nowcasting short-term indicators with machine learning methods

The monthly European Union (EU) harmonized Short-term Business Statistics (STS) represents one of the most important sources for the assessment of the European economy. Timeliness of STS is of fundamental importance for policy makers to be able to react adequately to sudden economic changes. In the past time lags between reference periods and release dates have been quite considerable. However, European countries selected various approaches to shorten release times like optimizing the short-term statistics sample or increasing efforts to access and integrate administrative data. In this paper different machine learning algorithms for early estimation of missing survey data are evaluated in order to further improve timeliness of Austrian STS data and to increase granularity of early estimates as well. Currently a multivariate time series model is used for early estimation of economic indexes for the highly aggregated level of Total Industry and Construction. This model could be adapted to the level of NACE-Divisions with the exception of a few Divisions with small populations. The quality of the results could be improved for several NACE-Divisions and variables with machine learning methods. However, for the prediction of a few branches with small populations alternative methods have to be developed.

THE PROMINENCE OF VECTOR AUTOREGRESSIVE MODEL IN MULTIVARIATE TIME SERIES FORECASTING MODELS WITH STATIONARY PROBLEMS

One of the problems in modelling multivariate time series is stationary. Stationary test results do not always produce all stationary variables; mixed stationary and non-stationary variables are possible. When stationary problems are found in multivariate time series modelling, it is necessary to evaluate the model's performance in various stationary conditions to obtain the best forecasting model. This study aims to get a superior multivariate time series forecasting model based on the goodness of the model in various stationary conditions. In this study, the evaluation of the model's performance through simulation data modelling is then applied to the actual data with a stationary problem, namely Bogor City inflation data. The best model in simulation modelling is based on the stability of RMSE and MAD in 100 replications. The results are that the VAR model is the best in various stationary conditions. Meanwhile, the best model on actual data modelling is based on evaluation in 4 folds for model fitting power and model forecasting power. The Bogor City inflation data modelling with the mixed stationary problem resulted in the best model, namely the VAR(1) model. This means the VAR model is good enough to be used as a forecasting model in mixed stationary conditions. Thus, in this study, based on the goodness of the model in two modelling scenarios in various stationary conditions, overall, it was found that the VAR model was superior to the VARD and VECM models.

Analysis of the Relationship Between COVID-19 Infections and Web-Based Housing Searches

Abstract The study used Google search query data on real estate interest for several countries in the Baltic area. The dynamics of public interest in housing have been compared to the dynamics of the COVID-19 infections in Lithuania, Latvia, Poland, and Sweden. This study uses the Vector autoregressive (VAR) model to forecast such time series. VAR is a multivariate linear time series model in which the endogenous variables in the system are lagged functions of the values of all endogenous variables. The increase in COVID-19 infections negatively affected society’s interest in housing. The study used Google Trends and R software.

PEMODELAN VECTOR AUTOREGRESSIVE EXOGENOUS (VARX) UNTUK MERAMALKAN DATA EKSPOR TOTAL DAN IMPOR TOTAL DI INDONESIA

Vector Autoregressive Exogenous (VARX) is a multivariate time series model which is a development of the Vector Autoregressive (VAR) model. VARX model is a forecasting model that involves endogenous variables and exogenous variables. The endogenous variables in this study are exports and total imports in Indonesia, then the exogenous variable in this study is the composite stock price index in Indonesia. The purpose of this study is to VARX model the export and total import data in Indonesia for the period January 2016 to December 2021 and predict it for the period January 2022 to December 2022. Based on the result of the analysis, the best model for forecasting export and total imports is the VARX(2.2) model with the MAPE value for the total export variable of 5.938% and the total import variable of 8.313%. Furthermore, the results of forecasting total exports have increased in the period January 2022 to December 2022, with forecasting results for January 2022 of US$21,383.06 million and December 2022 of US$23,569.50 million. The results of forecasting total imports have increased in the period January 2022 to December 2022, with forecasting results in January 2022 of US$17,743.17 million and December 2022 of US$20,269.07 million.

Modeling volatility and dependence of European carbon and energy prices

We study the prices of European Emission Allowances (EUA), whereby we analyze their uncertainty and dependencies on related energy prices (natural gas, coal, and oil). We propose a probabilistic multivariate conditional time series model with a VECM-Copula-GARCH structure which exploits key characteristics of the data. Data are normalized with respect to inflation and carbon emissions to allow for proper cross-series evaluation. The forecasting performance is evaluated in an extensive rolling-window forecasting study, covering eight years out-of-sample. We discuss our findings for both levels- and log-transformed data, focusing on time-varying correlations, and in view of the Russian invasion of Ukraine.

A Hidden Markov Model-based fuzzy modeling of multivariate time series

A Hidden Markov Model-based fuzzy modeling of multivariate time series

Models for Integer Data

Over the past few years, interest has increased in models defined on positive and negative integers. Several application areas lead to data that are differences between positive integers. Some important examples are price changes measured discretely in financial applications, pre- and posttreatment measurements of discrete outcomes in clinical trials, the difference in the number of goals in sports events, and differencing of count-valued time series. This review aims at bringing together a wide range of models that have appeared in the literature in recent decades. We provide an extensive review on discrete distributions defined for integer data and then consider univariate and multivariate time-series models, including the class of autoregressive models, stochastic processes, and ARCH-GARCH– (autoregressive conditionally heteroskedastic–generalized autoregressive conditionally heteroskedastic–) type models.

Evolution of global music trends: An exploratory and predictive approach based on Spotify data

Music listening choices are considered to be a factor capable of measuring people’s emotions. Thanks to the explosion of streaming music applications in recent years, it is possible to describe listening trends of the global population based on emotional features. In this paper we have analysed the most popular songs from 52 countries on Spotify through their features of danceability, positivity and intensity. This analysis allows exploring how these song features reflect mood trends along with other contextual factors that may affect the population’s listening behaviour, such as the weather or the influence of the COVID-19 pandemic. Finally, we have proposed a multivariate time series model to predict the preferred type of music in those countries based on their previous music listening patterns and the contextual factors. The results show some relevant behavioural changes in these patterns due to the effect of the pandemic. Furthermore, the resulting prediction model enables forecasting the type of music listened to in three different groups of countries in the next 4 months with an error around 1%. These results may help to better understand streaming music consumption in businesses related to the music and marketing industry.

Power transformers fault diagnosis using graph neural networks based on dissolved gas data

The Dissolved Gas Analysis (DGA) is an important way and is now extensively used to detect incipient faults in oil-immersed transformers. Some conventional methods for DGA, such as the Three-Ratio Method, usually misunderstood the gas data and failed to accurately detect multiple fault combinations. Recently, most researchers investigating DGA have utilized machine learning algorithms to improve the accuracy of fault diagnosis. The dissolved gas data are usually treated as tabular data by using machine learning algorithms to achieve better results compared to conventional methods. However, those machine learning methods ignore the internal connection of the dissolved gas data in the time dimension. Therefore, this paper adopted a new DGA method for transformer fault diagnosis based on Graph Neural Network (GNN) and Multivariate Time Series (MTS) model. The results finally showed that the model outperforms the existing machine learning baseline methods and conventional methods on the dataset.

Dynamic Probabilistic Predictable Feature Analysis for Multivariate Temporal Process Monitoring

Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring schemes. However, measurement noise is widespread in real-world industrial processes, and ignoring its effect will lead to suboptimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multistep dynamic predictive monitoring scheme is developed. The model parameters are estimated with an efficient expectation–maximization algorithm, where the genetic algorithm and the Kalman filter are designed and incorporated. Furthermore, a novel dynamic statistical monitoring index, the dynamic index, is proposed as an important supplement of T2 and SPE to detect dynamic anomalies. The effectiveness of the proposed algorithm is demonstrated via its application on the three-phase flow facility and a medium-speed coal mill.

Analysis of Some Variable Energy Companies by Using VAR(p)-GARCH(r,s) Model : Study From Energy Companies of Qatar over the Years 2015–2022

In this study, the nature of the weekly stock price relationships of several Qatar energy companies, namely the weekly stock price of Qatar Fuel Company (QFLS), Qatar Gas Transport Company (QGTS), and Qatar Electricity and Water Company (QEWC), will be discussed. The duration of data weekly stock price is from January 2015 to April 2022. This study aimed to obtain the best model for the weekly stock price relationship of the three companies QFLS, QGTS, and QEWC. The multivariate time series analysis method will be used to evaluate the data. From the analysis using multivariate time series modeling, the best model is VAR(3)-GARCH)(1,1). Based on this best model, further analysis is carried out, namely Granger causality, impulse response function (IRF), and forecasting for the next 12 periods. The Granger causality test found that the QFLS has Granger causality on the QGTS (unidirectional), while the QGTS and QEWC variables have bidirectional Granger causality. The IRF analysis indicated that if there is a shock of 1 standard deviation in QFLS, then QFLS and QEWC will fluctuate for the first six weeks and move toward equilibrium from the seventh week onwards, while the impact on QGTS can be ignored. Suppose there is a shock of 1 standard deviation in the QGTS. In that case, the QFLS and QEWC will respond by fluctuating for the first six weeks, and at the seventh week and move toward equilibrium, while the impact on QGTS can be ignored; and if there is a shock of 1 standard deviation in QEWC, then QFLS and QEWC will respond negatively and fluctuating for the first six weeks, and at the seventh week toward equilibrium, while the impact on QGTS is negligible. Forecasting for the next 12 periods shows that the farther the forecasting period, the larger the standard error. This indicates that the ffarther the period is, the more unstable it is.

Spatial Weighted Robust Clustering of Multivariate Time Series Based on Quantile Dependence With an Application to Mobility During COVID-19 Pandemic

In this article, a fuzzy clustering model for multivariate time series based on the quantile cross-spectral density and principal component analysis is extended by including: 1) a weighting system which assigns a weight to each principal component in accordance with its importance concerning the underlying clustering structure and 2) a penalization term allowing to take into account the spatial information. The iterative solutions of the new model, which employs the exponential distance in order to gain robustness against outlying series, are derived. A simulation study shows that the weighting system substantially enhances the effectiveness of the former approach. The behavior of the extended model in terms of the spatial penalization term is also analyzed. An application involving multivariate time series of mobility indicators concerning COVID-19 pandemic highlights the usefulness of the proposed technique.