Multivariate Autoregressive Model Research Articles

First-order multivariate integer-valued autoregressive model with multivariate mixture distributions

The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time series is barely discussed. In this study, we proposed a first-order multivariate integer-valued autoregressive model to characterize the correlation among multivariate integer-valued time series with higher flexibility. Under the general conditions, we established the stationarity and ergodicity of the proposed model. With the proposed method, we discussed the models with multivariate Poisson-lognormal distribution and multivariate geometric-logitnormal distribution and the corresponding properties. The estimation method based on EM algorithm was developed for the model parameters and extensive simulation studies were performed to evaluate the effectiveness of proposed estimation method. Finally, a real crime dataset was analysed to demonstrate the advantage of the proposed model with comparison to the other models.

Breakdown of effective information flow in disorders of consciousness: Insights from TMS-EEG

BackgroundThe complexity of the neurophysiological mechanisms underlying human consciousness is widely acknowledged, with information processing and flow originating in cortex conceived as a core mechanism of consciousness emergence. Combination of transcranial magnetic stimulation and electroencephalography (TMS-EEG) is considered as a promising technique to understand the effective information flow associated with consciousness. ObjectivesTo investigate information flow with TMS-EEG and its relationship to different consciousness states. MethodsWe applied an effective information flow analysis by combining time-varying multivariate adaptive autoregressive model and adaptive directed transfer function on TMS-EEG data of frontal, motor and parietal cortex in patients with disorder of consciousness (DOC), including 14 vegetative state/unresponsive wakefulness syndrome (VS/UWS) patients, 21 minimally conscious state (MCS) patients, and 22 healthy subjects. ResultsTMS in DOC patients, particularly VS/UWS, induced a significantly weaker effective information flow compared to healthy subjects. The bidirectional directed information flow was lost in DOC patients with TMS of frontal, motor and parietal cortex. The interactive ROI rate of the information flow network induced by TMS of frontal and parietal cortex was significantly lower in VS/UWS than in MCS. The interactive ROI rate correlated with DOC clinical scales. ConclusionsTMS-EEG revealed a physiologically relevant correlation between TMS-induced information flow and levels of consciousness. This suggests that breakdown of effective cortical information flow serves as a viable marker of human consciousness. SignificanceFindings offer a unique perspective on the relevance of information flow in DOC, thus providing a novel way of understanding the physiological basis of human consciousness.

Cross-exchange crypto risk: A high-frequency dynamic network perspective

Cross-exchange crypto trading presents inherent risks, particularly for centralized exchanges. Investors observe exacerbating crypto volatility and counterparty risk and would like to quantify these elements of crypto trades. The multiple exchanges require a multivariate view on the structures of risk spillover across exchanges. Here, a Multivariate Heterogeneous AutoRegression (MHAR) model is designed and analyzed, accommodating the stylized facts of crypto markets, including 24/7 trading and the long-memory effect on return variations. The proposed MHAR approach clearly reveals the intensity of interconnectedness among exchanges during extreme events, e.g., the Bitcoin market. Additionally, one observes extremely volatile eigenvector centralities of Futures Exchange Ltd (FTX), suggesting potential implications for its bankruptcy. Furthermore, portfolios that account for the dynamics of partial correlations or eigenvector centralities offer promising results in terms of risk measures.

Analysis of long-term changes in algal bloom pattern and their association with Ocean, atmosphere, and land-based processes across the northern Indian Ocean

Algal blooms are global phenomena in marine and fresh waters. An understanding of the impacts of climate change and anthropogenic activities on marine algal blooms is essential for protecting marine ecosystems. We have studied the long-term changes in the spatial patterns of algal blooms over the northern Indian Ocean and assessed the influence of the ocean, atmosphere, and land-based processes on them. We have analyzed multi-source satellite data (2003 – 2020) of various parameters such as algal concentration, temperature, salinity, sea level, particulate organic carbon, precipitation, wind speed, and river discharge on an open-source cloud computing platform. The seasonality of variables is assessed using a harmonic model, and their spatial trend is estimated using the non-parametric Mann-Kendall test. The spatial relationship between various geophysical parameters and algal bloom concentration is assessed by the cross-correlation test, and the prediction is done using a multivariate autoregression model. Results suggest that each variable exhibits distinguishable seasonal patterns. Algal bloom duration showed a significant increase over time. However, algal bloom coverage showed a significant decline in the coastal waters in all seasons except post-monsoon. The cross-correlation test unveils that lower temperatures, salinity, and sea level promote algal bloom occurrences in coastal waters rather than open waters. Furthermore, the statistical model with a time lag of 2 months shows better performance for prediction of bloom intensity (r2 = 0.86).

A multivariate spatial and spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Uncovering the relationship between incidental emotion toward a disaster and stock market fluctuations: Evidence from the US market

Despite having potentially important implications, there has been little research on the relationship between the public's incidental emotion and the stock market. To that end, we construct a valence-based measure of incidental emotion using BERTweet's sentiment analysis and empirically investigate the association between collective incidental emotion toward the COVID-19 pandemic and the U.S. stock market. We employ multivariate time series autoregressive models to test the relationship between emotion polarity and stock market returns or trading volumes. The results reveal that societal sentiment toward the pandemic has a significant effect on the returns of the Dow Jones Industrial Average and S&P 500. In contrast, the macro-level emotion does not significantly affect the return for NASDAQ 100. The findings also suggest a significant association between incidental emotion and trading volumes. We conduct a battery of sensitivity tests that further support our conjecture. The study underscores the robust role of incidental emotion in investment decision-making, highlighting its significance as a distinctive feature that should be incorporated into financial decision support systems.

Restored off‐channel pond habitats create thermal regime diversity and refuges within a Mediterranean‐climate watershed

Cool‐water habitats provide increasingly vital refuges for cold‐water fish living on the margins of their historical ranges; consequently, efforts to enhance or create cool‐water habitat are becoming a major focus of river restoration practices. However, the effectiveness of restoration projects for providing thermal refuge and creating diverse temperature regimes at the watershed scale remains unclear. In the Klamath River in northern California, the Karuk Tribe Fisheries Program, the Mid‐Klamath Watershed Council, and the U.S. Forest Service constructed a series of off‐channel ponds that recreate floodplain habitat and support juvenile coho salmon (Oncorhynchus kisutch) and steelhead (O. mykiss) along the Klamath River and its tributaries. We instrumented these ponds and applied multivariate autoregressive time series models of fine‐scale temperature data from ponds, tributaries, and the mainstem Klamath River to assess how off‐channel ponds contributed to thermal regime diversity and thermal refuge habitat in the Klamath riverscape. Our analysis demonstrated that ponds provide diverse thermal habitats that are significantly cooler than creek or mainstem river habitats, even during severe drought. Wavelet analysis of long‐term (10 years) temperature data indicated that thermal buffering (i.e. dampening of diel variation) increased over time but was disrupted by drought conditions in 2021. Our analysis demonstrates that in certain situations, human‐made off‐channel ponds can increase thermal diversity in modified riverscapes even during drought conditions, potentially benefiting floodplain‐dependent cold‐water species. Restoration actions that create and maintain thermal regime diversity and thermal refuges will become an essential tool to conserve biodiversity in climate‐sensitive watersheds.

Driving fatigue detection based on brain source activity and ARMA model.

Fatigue among drivers is a significant issue in society, and according to organizational reports, it substantially contributes to accidents. So accurate fatigue detection in drivers plays a crucial role in reducing the number of people fatalities or injured resulting from accidents. Several methods are proposed for fatigue driver recognition among which electroencephalography (EEG) is one. This paper proposed a method for fatigue recognition by EEG signals with extracted features from source and sensor spaces. The proposed method starts with preprocessing by applying filtering and artifact rejection. Then source localization methods are applied to EEG signals for active source extraction. A multivariate autoregressive (MVAR) model is fitted to selected sources, and a dual Kalman filter is applied to estimate the source activity and their relationships. Then multivariate autoregressive moving average (ARMA) is fitted between EEG and source activity signals. Features are extracted from model parameters, source relationship matrix, and wavelet transform of EEG and source activity signals. The novelty of this approach is the use of ARMA model between source activities (as input) and EEG signals (as output) and feature extraction from source relations. Relevant features are selected using a combination of RelifF and neighborhood component analysis (NCA) methods. Three classifiers, namely k-nearest neighbor (KNN), support vector machine (SVM), and naive Bayesian (NB) classifiers, are employed to classify drivers. To improve performance, the final label for fatigue detection is calculated by combining these classifiers using the voting method. The results demonstrate that the proposed method accurately recognizes and classifies fatigued drivers with the ensemble classifiers in comparison with other methods.

3D convolutional neural network for schizophrenia detection using as EEG-based functional brain network

Schizophrenia (ScZ) is a chronic mental disorder affecting the function of the brain, which causes emotional, social, and cognitive problems. This paper explored the functional brain network and deep learning methods to detect ScZ using electroencephalogram (EEG) signals. Functional brain network analysis was proposed and implemented using a multivariate autoregressive model and coherence connectivity algorithm. The three machine learning techniques and 3D-convolutional neural network (CNN) models were applied to classify the ScZ patients and health control subjects, and then the public LMSU database was utilized to assess the performance. The proposed 3D-CNN method achieved the performance of a 98.47 ± 1.47 % in accuracy, 99.26 ± 1.07 % in sensitivity, and 97.23 ± 3.76 % in specificity. Moreover, in addition to the default mode network region, the temporal and posterior temporal lobes of both right and left hemispheres were found as the significant difference areas in ScZ brain network analysis.

Factors associated with different types of freight crashes: A macro-level analysis

Introduction: Despite evidence showing higher fatality rates in freight-related crashes, there has been limited exploration of their spatial distribution and factors associated with such distribution. This gap in the literature primarily stems from the focus of existing studies on micro-level factors predicting the frequency or severity of injuries in freight crashes. The present study delves into the factors contributing to freight crashes at the neighborhood level, particularly focusing on different types of freight crashes: collisions involving a freight vehicle and a passenger vehicle, crashes between freight vehicles, and freight vehicle–non-motorized crashes. Method: This study analyzes traffic crash data from the urbanized region of Seoul, collected between 2016 and 2019. To effectively deal with spatial autocorrelation and model different types of crashes in a unified framework, a Bayesian multivariate conditional autoregressive model was employed. Results: Findings show substantial differences in the factors associated with various types of freight crashes. The predictors for crashes between freight vehicles diverge significantly from those for freight vehicle–non-motorized crashes. Crashes between freight vehicles are relatively more influenced by road network structure, while freight crashes involving non-motorized users are relatively more affected by the built environment and freight facilities than the other crash types examined. Freight vehicle–passenger vehicle crashes fall into an intermediate category, sharing most predictors with either of the other two types of freight crashes. Conclusions and Practical Applications: The findings of this study offer valuable lessons for transportation practitioners and policymakers. They can guide the formulation of effective land use policies and infrastructure planning, specifically designed to address the unique characteristics of different types of freight crashes.

The vector error correction index model: representation, estimation and identification

Summary This paper extends the multivariate index autoregressive model to the case of cointegrated time series of order (1,1). In this new modelling, namely the vector error-correction index model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction with reference to the vector error correction model. We show that the VECIM allows one to decompose the reduced-form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.

Are ride-hailing services safer than taxis? A multivariate spatial approach with accommodation of exposure uncertainty

Despite many research efforts on ride-hailing services and taxis, limited studies have compared the safety performance of the two modes. A major challenge is the need for reliable mode-specific exposure data to model their safety outcomes. Moreover, crash frequencies of the two modes by injury severities tend to be spatially and inherently correlated. To fully address these issues, this study proposes a novel multivariate conditional autoregressive model considering measurement errors in mode-specific exposures (MVCARME). More specially, a classical measurement error structure accommodates the uncertainty of estimated mode-specific exposures, and a multivariate spatial specification is adopted to capture potential spatial and inherent correlations. The model estimation is accelerated by an integrated nest Laplace approximation method. The census tracts in the city of Chicago are set as the spatial analysis unit. The mode-specific exposures (vehicle-mile-traveled) in each census tract are estimated by trip assignments using ride-hailing and taxi trip data in 2019. The modeling results indicate that both ride-hailing crashes and taxi crashes are positively associated with transportation factors (e.g., vehicle-mile-traveled, mode-specific vehicle-mile-traveled, and traffic signal numbers), land use factors (i.e., number of educational and alcohol-related sites), and demographic factors (e.g., median household income, transit ratio, and walk ratio). By comparison, the proposed model outperforms the others (i.e., negative binomial models and multivariate conditional autoregressive model) by yielding the lowest deviance information criterion (DIC), Watanabe-Akaike information criterion (WAIC), mean absolute error (MAE), and root-mean-square error (RMSE). According to the results of t-tests, ride-hailing services are found to be prone to a higher risk of minor injury crashes compared with taxis, despite no significant difference between the risks of severe injury crashes. Methodologically, this study adds a robust safety evaluation approach for comparing crash risks of different modes to the literature. At the same time, practically, it provides researchers, practitioners, and policy-makers insights into the safety management of various mobility alternatives.

Multivariate spatial modelling for predicting missing HIV prevalence rates among key populations

Abstract Ending the HIV/AIDS pandemic is among the sustainable development goals for the next decade. To overcome the problem caused by the imbalances between the need for care and the limited resources, we shall improve our understanding of the local HIV epidemics, especially for key populations at high risk of HIV infection. However, HIV prevalence rates for key populations have been difficult to estimate because their HIV surveillance data are very scarce. This paper develops a multivariate spatial model for predicting unknown HIV prevalence rates among key populations. The proposed multivariate conditional auto-regressive model efficiently pools information from neighbouring locations and correlated populations. As the real data analysis illustrates, it provides more accurate predictions than independently fitting the sub-epidemic for each key population. Furthermore, we investigate how different pieces of surveillance data contribute to the prediction and offer practical suggestions for epidemic data collection.

A novel fusion framework embedded with zero-shot super-resolution and multivariate autoregression for precipitable water vapor across the continental Europe

Precipitable water vapor (PWV), as the most abundant greenhouse gas, significantly impacts the evapotranspiration process and thus the global climate. However, the applicability of mainstream satellite PWV products is limited by the tradeoff between spatial and temporal resolutions, as well as some external factors such as cloud contamination. In this study, we proposed a novel PWV spatio-temporal fusion framework based on the zero-shot super-resolution and the multivariate autoregression models (ZSSR-ARF) to improve the accuracy and continuity of PWV. The framework is implemented in a way that the satellite-derived observations (MOD05) are fused with the reanalysis data (ERA5) to generate accurate and seamless PWV of high spatio-temporal resolution (0.01°, daily) across the European continent from 2001 to 2021. Firstly, the ZSSR approach is used to enhance the spatial resolution of ERA5 PWV based on the internal recurrence of image information. Secondly, the optimal ERA5-MOD05 image pairs are selected based on the image similarity as inputs to improve the fusion accuracy. Thirdly, the framework develops a multivariate autoregressive fusion approach to allocate weights adaptively for the high-resolution image prediction, which primely addresses the non-stationarity and autocorrelation of PWV. The results reveal that the accuracies of fused PWV are consistent with those of the GPS retrievals (r = 0.82–0.95 and RMSE = 2.21–4.01 mm), showing an enhancement in the accuracy and continuity compared to the original MODIS PWV. The ZSSR-ARF fusion framework outperforms the other methods with R2 improved by over 24% and RMSE reduced by over 0.61 mm. Furthermore, the fused PWV exhibits similar temporal consistency (mean difference of 0.40 mm and DSTD of 3.22 mm) to the reliable ERA5 products, and substantial increasing trends (mean of 0.057 mm/year and over 0.1 mm/year near the southern and western coasts) are observed over the European continent. As the accuracy and continuity of PWV are improved, the outcome of this paper has potential for climatic analyses during the land-atmosphere cycle process.

Brain Connectivity Estimation Pitfall in Multiple Trials of Electroencephalography Data.

The electroencephalography signal is well suited to calculate brain connectivity due to its high temporal resolution. When the purpose is to compute connectivity from multi-trial electroencephalography (EEG) data, confusion arises about how these trials involved in calculating the connectivity. The purpose of this paper is to study this confusing issue using simulated and experimental data. To this end, Granger causality-based connectivity measures were considered. Using simulations, two signals were generated with known AR (auto-regressive) coefficients and then simple multivariate autoregressive (MVAR) models based on different numbers of trials were extracted. For accurate estimation of the MVAR model, the data samples should be sufficient. Two Granger causality-based connectivity, granger causality (GC) and Partial directed coherence (PDC) were estimated. Estimating connectivity corresponding to small trial numbers (5 and 10 trials) resulted in an average value of connectivity that is significantly higher and also more variable over different estimates. By increasing the number of trials, the MVAR model has fitted more appropriately to the data and the connectivity values were converged. This procedure was implemented on real EEG data. The obtained results agreed well with the findings of simulated data. The results showed that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. Also, the larger the trial numbers, the MVAR model has fitted more appropriately to the data, and connectivity estimations are more reliable. The average of connectivity values on trials is considered brain connectivity.Connectivity estimations are more reliable for larger trial numbers.Estimations of connectivity for small trial numbers are not valid. Several different techniques can be utilized to evaluate brain connectivity such as functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), electroencephalography (EEG) and etc. Connectivity estimation methods are associated with computing the correspondence of neural signals over time, therefore modalities such as EEG due to their fine temporal resolution are well suited to calculate such connectivity. When the purpose is to compute connectivity from multi-trial data, confusion arises about how these trials and how many trials are involved in calculating the connectivity. During calculating brain connectivity from data with many observation epochs, the question arises whether brain connectivity is calculated for each trial and then average or for the averaged trials. The target of this paper is to study the abovementioned issue using simulated data and realistic EEG data. Our analysis indicated that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. It was also found that estimating connectivity corresponding to small trial numbers resulted in an average value of connectivity that is significantly higher and also more variable over different estimates and is not valid. These findings can help us in the correct estimation of brain connectivity.

High-dimensional multivariate autoregressive model estimation of human electrophysiological data using fMRI priors

Multivariate autoregressive (MVAR) model estimation enables assessment of causal interactions in brain networks. However, accurately estimating MVAR models for high-dimensional electrophysiological recordings is challenging due to the extensive data requirements. Hence, the applicability of MVAR models for study of brain behavior over hundreds of recording sites has been very limited. Prior work has focused on different strategies for selecting a subset of important MVAR coefficients in the model to reduce the data requirements of conventional least-squares estimation algorithms. Here we propose incorporating prior information, such as resting state functional connectivity derived from functional magnetic resonance imaging, into MVAR model estimation using a weighted group least absolute shrinkage and selection operator (LASSO) regularization strategy. The proposed approach is shown to reduce data requirements by a factor of two relative to the recently proposed group LASSO method of Endemann et al (Neuroimage 254:119057, 2022) while resulting in models that are both more parsimonious and more accurate. The effectiveness of the method is demonstrated using simulation studies of physiologically realistic MVAR models derived from intracranial electroencephalography (iEEG) data. The robustness of the approach to deviations between the conditions under which the prior information and iEEG data is obtained is illustrated using models from data collected in different sleep stages. This approach allows accurate effective connectivity analyses over short time scales, facilitating investigations of causal interactions in the brain underlying perception and cognition during rapid transitions in behavioral state.

Robust Bayesian Estimation of EEG-Based Brain Causality Networks.

The multivariate autoregression (MVAR) model is an effective model to construct brain causality networks. However, the accuracy of MVAR parameter estimation is considerably affected by outliers such as head movements and eye blinks contained in EEG signals, especially in short time windows. We proposed a robust MVAR parameter estimation method based on a Bayesian probabilistic framework and Laplace fitting error known as Lap-SBL. With the Bayesian inference framework, we can accurately estimate the MVAR parameters under short time windows. Additionally, to alleviate the influence of outliers, we model the fitting error using the Laplace distribution instead of the typical Gaussian distribution. We employ convex analysis to model the inference task by approximating the Laplace noise prior with a maximum over Gaussian functions with varying scales. The variational inference approach was used to efficiently estimate the MVAR parameters. The numerical results suggest that the proposed method obtains less parameter estimation bias and more consistent linkages than existing benchmark methods, i.e., LS, LASSO, LAPPS and SBL. The motor imagery experimental data analysis shows that Lap-SBL can better describe the lateralization characteristics of brain network. This lateralization is less apparent in a subject with poor MI classification accuracy. Lap-SBL effectively suppresses the influence of outliers and recovers reliable networks in the presence of outliers and short time windows.

The volatility of natural resources implications for sustainable development: Crude oil volatility prediction based on the multivariate structural regime switching

Applying the multivariate heterogeneous autoregressive (MHAR-RV-DCC) model, this article considers the structural mutation characteristics of oil futures and the U.S. stock markets’ information fluctuations, and embeds Markov regime switching (MS) to investigate the prediction performance of the crude oil market volatility prediction model under the transition of high and low states, and explores whether the Markov mechanism conversion multivariate model constructed by nonparametric measurement variables will help the government, scholars and practitioners to judge the future market. We test the in-sample fitting and out-of-sample forecasting. In comparison, our newly proposed multivariate MHAR-RV-DCC model and MS-MHAR-RV-DCC model have stronger predictive capabilities than other high-frequency volatility prediction models, the MS-MHAR-RV-SJV-DCC has the best predictive ability. The above empirical results not only affirm the advantages of the newly constructed multivariate and Markov regime switching models in the application of crude oil futures market forecasting but also broaden the research ideas and specific methods for the characterization and prediction of crude oil market volatility in the future.

Dynamic covariance estimation via predictive Wishart process with an application on brain connectivity estimation

Modeling the complex dependence in multivariate time series data is a fundamental problem in statistics and machine learning. Traditionally, the task has been approached with methods such as multivariate autoregressive models and multivariate generalized autoregressive conditional heteroskedasticity models, and Gaussian process based methods are recently becoming popular by leveraging the flexibility of non-parametric learning. However, few methods exist that directly model the dynamics of the covariance matrices except generalized Wishart process (GWP), and even the generalized Wishart process is limited with applications on small dataset due to the extremely high computational capacity induced by multiple Gaussian processes. In this regard, a novel stochastic process named as Predictive Wishart Process (PWP) is proposed, which provides a collection of positive semi-definite random matrices indexed by input variables. The PWP projects process realizations of GWP to a lower dimensional subspace to efficiently estimate every GWP. The theoretical properties of it are examined, and both Bayesian inference and efficient variational expectation maximization are explored in relation to it. Moreover, the PWP is empirically tested on synthetically generated time-series data to validate competitive reconstructive performance and efficient predictive performance, and applied on a large-scale real functional magnetic resonance imaging (fMRI) dataset from Human Connectome Project (HCP) to demonstrate its practicality. A thorough statistical analysis with visualizations is conducted on the brain connectivity, and also a PWP-based multi-task learning framework is proposed to extract meaningful features from individual fMRIs.

Synchronization in Cycles of China and India During Recent Crises: A Markov Switching Analysis.

We study the impact of recent crisis episodes viz. the Great Recession of 2007-09, the Euro Area crisis of 2010-12 and the COVID-19 pandemic of 2020-21 on the Emerging Market Economies (EMEs) of China and India using data from January, 1986 till June, 2021. A Markov-switching (MS) analysis is applied to discern economy-specific cycles/regimes and common cycles/regimes in the growth rates of the economies. We apply the univariate MS Autoregressive (MS-AR) model to characterize country-specific negative growth, moderate growth and high growth regimes of China and India. We examine the extent of overlap of the identified regimes with the Great Recession, the Eurozone crisis, and the COVID-19 pandemic. Thereafter, we study the regimes depicting common phases in growth rates of China-India and China-India-US by using multivariate MS Vector Autoregressive (MS-VAR) models. The multivariate analysis shows the presence of common negative growth during the turbulent periods during the study period. These results can be explained by the existence of strong trade and financial linkages between the two EMEs and the Advanced economies. The pandemic triggered a recession in the Chinese, Indian and U.S. economies and its impact on growth is much worse than the Great Recession and the Eurozone crises.