Markov Switching Research Articles

The relationship between renewable energy attention and volatility: A HAR model with markov time-varying transition probability

This study investigated whether a renewable energy attention (REA) index, based on natural language processing, Google search volume data, and dimensionality reduction methodology, can predict crude oil volatility. Considering the possible non-linear and time-varying effects, we adopted the time-varying transition probability Markov switching heterogeneous autoregressive-realized volatility (TVTP-MS-HAR-realized volatility (RV)) model. To further represent the impacts of REA, we developed an asymmetric TVTP-MS-HAR-RV model based on this model framework, i.e., the ASTVTP-MS-HAR-RV model. According to the results, the in-sample estimates indicated that West Texas Intermediate (WTI) volatility is more affected by negative REA shocks than by positive ones. Moreover, REA predicted WTI volatility better during low-volatility periods than in high ones. According to the out-of-sample findings, the ASTVTP-MS-HAR-RV-F model outperformed other competing models, indicating that time-varying transition probabilities and REA information can significantly improve volatility forecasting performance.

Fossil fuel prices and economic policy uncertainty– A regime-switching approach

The study investigates the impact of fossil fuel prices on the regime-switching dynamics of economic policy uncertainty for the global economy. The period of investigation spans 25 years; comprising monthly data for the period of 1998:01 to 2023:03 and, due to its propensity to accommodate shocks, swings and shifts in the data, the technique of analysis employed is the Markov Switching Dynamic Regression. The principal component analysis (PCA) method was used in obtaining a composite index for the fossil fuel prices. The results obtained show evidence of regime-switching behaviour with five (5) times persistence of low to high global economic policy uncertainty. In addition, the study finds significant counter-cyclical and pro-cyclical effects of fossil fuel prices on global economic policy uncertainty; especially under the regime of high uncertainty. These results are consistent with the results for the composite index of fossil fuel prices but with alternate persistence effects. These suggest that policymakers should be concerned in stabilizing fluctuating fossil fuel prices in order to contain its spiralling and uncertain effects on the global economic policy. More so, governments should devise series of low carbon-emission means for home and industrial uses to ultimately reduce the excessive demand for fossil fuel so as to crash its prices in the international market.

Switching diffusions for multiscale uncertainty quantification

High-fidelity simulations are increasingly called-upon to resolve the nucleation of instabilities such as crack initiation and propagation and fluid mixing. While multiscale modeling capabilities have progressed rapidly over recent decades, associated simulations still present a computational burden, thus often preempting a systematic statistical analysis of related problems. Given the paucity of data that relate micro-structure to macroscale behavior, and the unavoidable modeling errors at both scales, the lack of a probabilistic characterization significantly limits the value of highly-resolved numerical simulators. The goal of the present research is to develop a probabilistic model that encodes pathwise relationships between micro and macro scales. Specifically, we develop a switching diffusion model to relate damage evolution, characterized at the microscale, to system performance identified with a macroscale property. Microscale behavior is modeled as a Markov switching process with a finite state space while the macroscale counterpart is modeled as a continuous-state diffusion process. The interaction between macro and micro scales is captured by coupling these two processes. Calibrated by data, the switching diffusion model can generate, with minimal computational effort, sample paths with prescribed statistics. The proposed model contributes new capabilities and perspectives at the interface of multiscale simulation, uncertainty quantification, and stochastic modeling.

Neural Network-Based Anti-Disturbance Control of Nonhomogeneous Markov Switching Systems

Neural Network-Based Anti-Disturbance Control of Nonhomogeneous Markov Switching Systems

Markov switching stereotype logit models for longitudinal ordinal data affected by unobserved heterogeneity in responding behavior

AbstractWhen asked to assess their opinion about attitudes or perceptions on Likert-scale, respondents often endorse the midpoint or extremes of the scale and agree or disagree regardless of the content. These responding behaviors are known in the psychometric literature as middle, extremes, aquiescence and disacquiescence response styles that generally introduce bias in the results. One of the key motivations behind our approach is to account for these attitudes and how they evolve over time. The novelty of our proposal, in the context of longitudinal ordered categorical data, is in considering simultaneously the temporal dynamics of the responses (observable ordinal variables) and unobservable answering behaviors, possibly influenced by response styles, through a Markov switching logit model with two latent components. One component accommodates serial dependence and respondent’s unobserved heterogeneity, the other component determines the responding attitude (due to response styles or not). The dependence of the responses on covariates is modelled by a stereotype logit model with parameters varying according to the two latent components. The stereotype logit model is adopted because it is a flexible extension of the proportional odds logit model that retains the advantage of using a single parameter to describe a regressor effect. In the paper, a new interpretation of the parameters of the stereotype model is given by defining the allocation sets as intervals of values of the linear predictor that identify the most probable response. Unobserved heterogeneity, serial dependence and tendency to response style are modelled through our approach on longitudinal data, collected by the Bank of Italy.

Inflation Transmission Diagnostics via a Bayesian Graph Vector Autoregressive Model with Markov Switching

Inflation Transmission Diagnostics via a Bayesian Graph Vector Autoregressive Model with Markov Switching

Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

AbstractThe article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.

Well‐posedness and error analysis of wave equations with Markovian switching

Compared to traditional partial differential equation modeling methods, Markov switching models can accurately capture the abrupt changes or jumps that complex systems often experience in the real world. In this paper, we propose a novel wave equation model with Markovian switching to represent complex systems with state‐jumping phenomena better, and the well‐posedness of the model is proved. In addition, a numerical method with non‐uniform grids is also proposed for the proposed model to simulate the data in realistic situations, which is based on the use of finite element discretization in space and central difference discretization in time. Finally, we conduct several experiments to analyze the errors and stability of the proposed model and the traditional model. The results show that the Markov switching model proposed in this paper has a smaller error than the traditional models while ensuring stability and can more accurately simulate the state jump phenomena of real‐world systems.

Zika emergence, persistence, and transmission rate in Colombia: a nationwide application of a space-time Markov switching model.

Zika, a viral disease transmitted to humans by Aedes mosquitoes, emerged in the Americas in 2015, causing large-scale epidemics. Colombia alone reported over 72,000 Zika cases between 2015 and 2016. Using national surveillance data from 1121 municipalities over 70 weeks, we identified sociodemographic and environmental factors associated with Zika's emergence, re-emergence, persistence, and transmission intensity in Colombia. We fitted a zero-state Markov-switching model under the Bayesian framework, assuming Zika switched between periods of presence and absence according to spatially and temporally varying probabilities of emergence/re-emergence (from absence to presence) and persistence (from presence to presence). These probabilities were assumed to follow a series of mixed multiple logistic regressions. When Zika was present, assuming that the cases follow a negative binomial distribution, we estimated the transmission intensity rate. Our results indicate that Zika emerged/re-emerged sooner and that transmission was intensified in municipalities that were more densely populated, at lower altitudes and/or with less vegetation cover. Warmer temperatures and less weekly-accumulated rain were also associated with Zika emergence. Zika cases persisted for longer in more densely populated areas with more cases reported in the previous week. Overall, population density, elevation, and temperature were identified as the main contributors to the first Zika epidemic in Colombia. We also estimated the probability of Zika presence by municipality and week, and the results suggest that the disease circulated undetected by the surveillance system on many occasions. Our results offer insights into priority areas for public health interventions against emerging and re-emerging Aedes-borne diseases.

The functional central limit theorem for Markov-switching GARCH model

In this paper we consider the Markov Switching GARCH model suggested by Haas, Mittnik, and Paolella(2004). We show under proper assumptions that the functional central limit theorems hold for the process, the square of the process, and regime variances. The functional central limit theorem for a linear combination of regime variances is also obtained.

Monetary Policy Spillovers and Inter-Market Dynamics Perspective of Preferred Habitat Model

This study advances the understanding of the Preferred Habitat Model’s capacity to shed light on the inter-market transfer of mean returns and the diffusion of price volatility in Pakistani investment markets. It examines the extent to which returns in one market exert a systematic influence on returns across others under the potential sway of interest rate policy shifts, USD exchange rate volatility, and domestic inflation trends. Employing a methodological arsenal that includes the GARCH process, enhanced by Dynamic Conditional Correlations (DCC), as well as the Markov Switching Model, this research assesses the propagation of mean returns and volatility across markets. The analysis uncovers significant linkages between monetary policy and stock market indices, underscoring the profound impact of monetary policy on cross-market performance transmission. These insights are pivotal for regulators overseeing the nuanced interaction between monetary policy and market performance. They are crucial for local and international investors interested in developing economies, especially in Pakistan’s markets.

Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching

Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching

Bayesian Markov switching model for BRICS currencies' exchange rates

AbstractExchange rate modeling has always fascinated researchers because of its complex macroeconomic dynamics. This study documents the exchange rate dynamics of major emerging economies after accounting for their macroeconomic cycles and explores the Bayesian Vector Error Correction Model (VECM) Markov Regime switching model, which uses time‐varying transition probabilities. The main objective is to study the exchange rate dynamics of Brazil, Russia, India, China, and South Africa (BRICS) vis‐à‐vis the US dollar. The Bayesian setup uses two hierarchal shrinkage priors, the normal‐gamma (NG) prior and the Litterman prior, for parameters' estimation. These shrinkage priors allow for a more comprehensive assessment of the regime‐specific coefficients. The model performed well in differentiating between the two regimes for all currencies. The Russian ruble was identified to be the most depreciated currency, whereas the African Rand was the most appreciated. The evaluation of model features revealed that many regime‐specific coefficients differed significantly from their common mean. A forecasting exercise was then performed for the out‐of‐sample period to assess the model's performance. A significant improvement was observed over the basic random walk (RW) model and the linear Bayesian vector autoregression (BVAR) model.

Identification and forecasting of bull and bear markets using multivariate returns

SummaryBull and bear market identification generally focuses on a broad index of returns through a univariate analysis. This paper proposes a new approach to identify and forecast bull and bear markets through multivariate returns. The model assumes that all assets are directed by a common discrete state variable from a hierarchical Markov switching model. The hierarchical specification allows the cross‐section of state‐specific means and variances to differ over bull and bear markets. We investigate several empirically realistic specifications that permit feasible estimation even with 100 assets. Our results show that the multivariate framework provides competitive bull and bear regime identification and improves portfolio performance and density prediction compared with several benchmark models including univariate Markov switching models.

Partial component consensus in mean‐square for delayed nonlinear multi‐agent systems with uncertain nonhomogeneous Markov switching topologies and aperiodic denial‐of‐service cyber‐attacks

The partial component consensus in mean‐square for delayed nonlinear multi‐agent systems (NMASs) with uncertain nonhomogeneous Markov switching (UNMS) topologies subjected to aperiodic denial‐of‐service (DoS) cyber‐attacks is investigated. Firstly, the partial component ( ‐dimensional) consensus of the system ( ‐dimensional, ) is considered in this paper. When , the partial component consensus degrades into identical consensus. Secondly, the communication topologies governed by uncertain nonhomogeneous Markov chains are random. Thirdly, the communication topologies suffer from aperiodic DoS cyber‐attacks. Then, in view of stochastic analysis technology, distributed control theory and Lyapunov stability theory, the partial component consensus conditions are obtained using permutation matrix and inequality scaling skills. Eventually, the correctness of the results is verified through an example.

149 Dynamical Network State Sequences for Human Language Production

INTRODUCTION: Speech requires the selection of a conceptual representation, the construction of a word form, and the execution of a complex articulatory plan. Investigating this global system requires high-resolution recordings with an analytic approach to resolve discrete cognitive states. We integrated autoregressive hidden Markov models to resolve trial-by-trial state transition sequences in distributed networks derived from a large-scale electrocorticographic dataset with complete coverage of language-dominant cortex. METHODS: Intracranial electrodes (n = 25810, 134 patients), including both surface grids and stereotactic depths, were implanted for the evaluation of epilepsy. Patients performed picture naming of common objects and underwent systematic cortical stimulation mapping of language function. We used cross-validated autoregressive hidden Markov models – combining the interpretability of multivariate autoregressive analysis with the nonlinear embedding of the switching Markov characteristic – to distinguish cognitive states defined by causal interactional motifs of distributed cortical substrates and to simulate in silico lesions of dynamical network structures. RESULTS: We created a detailed spatiotemporal atlas of word production spanning the entire language-dominant cortex. From this map, we resolved network dynamics comprising sequences of state space transitions for each word articulated. This identified five essential states for speech production, each defined by a unique pattern of directed interactions within the language network. We then derived a computational lesion model for state dynamics and compared its predictions with causal perturbation by direct cortical stimulation. We assembled a global dynamical state model for language production and resolved the fine-scale interregional dynamics of conceptualization and lexical access. CONCLUSIONS: The distributed network dynamics detailed within this comprehensive interactional map of speech production advance our understanding of how both local and disconnection injuries yield complex neurological deficits, facilitating the development of novel therapeutic approaches for aphasia.

Forecasting conditional volatility based on hybrid GARCH-type models with long memory, regime switching, leverage effect and heavy-tail: Further evidence from equity market

The properties of clustering, long memory, switching regime, leverage effect and heavy tail in volatility dynamic behavior are induced by important stylized facts in financial markets. There is still a controversy whether incorporating these properties could improve the modelling and forecasting performance of volatility. We construct hybrid volatility models via three perspectives including short memory, long memory and Markov switching GARCH with leverage effect and heavy tail, and empirically compare their performance of in-sample estimation, out-of-sample forecast and risk measurement based on trading data of Chinese equity market index. The out-of-sample forecast results indicate that the FIEGARCH model with innovation distribution of GED outperforms the competing models, and the backtesting results of VaR and ES confirm that this model performs well in the application of risk measurement.

Can green finance be helpful in shifting from resource curse to resource blessing in China? Evidence from Markov switching equilibrium model

AbstractKeeping aside the debate over whether resources are a burden or a blessing, the resource curse theory has been put to the test in the literature using several significant variables. The “resource curse” concept does emphasize the need for green financing, but sadly, this was not taken into account. Recently, due to strong environmental pressure, the need for green financing has been acknowledged. Keeping this in mind, it is crucial to consider how green finance might improve the use of natural resources to stimulate economic growth. Therefore, in this work, we explore the role of green financing, innovation, and economic complexity in the theory of the resource curse. The study used a Markov switching equilibrium correction model with shifts for the data from 2000 to 2019 in a Chinese context. Due to the overuse of natural resources, empirical data support the presence of the resource curse theory in China. The study's findings also support the favorable effects of innovation, the economic complexity index, and green finance on economic performance. In order to turn China's resource curse into a resource blessing, the study directs policymakers, government officials, and scholars toward theoretical and practical implications related to green finance and innovation.

Does private financial development present a trade-off for CO2 emissions reduction in Oman? Evidence from Markov-switching model

ABSTRACT The expansion of the financial sector is often promoted to facilitate economic growth. Nevertheless, the potential implications of financial development on environmental indicators, specifically carbon dioxide (CO2) emissions, have become a subject of concern. This research investigates the impact of financial development on CO2 emissions in Oman, along with other control variables including energy consumption, trade openness, and economic growth, using a Markov switching model. The analysis is conducted for the period from 1989 to 2020 and focuses on two regimes of high and low carbon emissions. The results of the Markov switching model show that energy consumption, gross domestic product (GDP), and private financial development have a significant positive effect on CO2 emissions. Although the study confirms the Kuznets curve, Oman is still in its initial phase. Moreover, our results suggest a higher likelihood of remaining in the high CO2 emissions regime. This underscores the importance for policymakers to carefully weigh the trade-offs associated with fostering financial development, particularly within climate change mitigation endeavors. These findings are highly relevant for policymakers striving to balance economic growth with the reduction of carbon emissions in Oman.

Predicting tail risks by a Markov switching MGARCH model with varying copula regimes

AbstractTo improve the dynamic assessment of risks of speculative assets, we apply a Markov switching MGARCH approach to portfolio risk forecasting. More specifically, we take advantage of the flexible Markov switching copula multivariate GARCH (MS‐C‐MGARCH) model of Fülle and Herwartz (2022). As an empirical illustration, we take the perspective of a risk‐averse agent and employ the suggested model for assessments of future risks of portfolios composed of a high‐yield equity index (S&P 500) and two safe‐haven investment instruments (i.e., Gold and US Treasury Bond Futures). We follow recent suggestions to employ the expected shortfall as a prime assessment of tail risks. To accurately evaluate the merits of the new model, we back‐test the risk forecasting for daily returns over 10 years for heterogeneous market environments including, for example, the COVID‐19 pandemic. We find that the MS‐C‐MGARCH model outperforms benchmark volatility models (MGARCH, C‐MGARCH) in predicting both value‐at‐risk and expected shortfall. The superiority of the MS‐C‐MGARCH model becomes stronger, when the share of comparably risky assets in the portfolio is relatively large.